Research ArticleOptimization of Microwave Vacuum Drying and PretreatmentMethods for Polygonum cuspidatum

Wanxiu Xu 1 Guanyu Zhu1 Chunfang Song12 Shaogang Hu1 and Zhenfeng Li 12

1 Jiangnan University Wuxi Jiangsu China2Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology Wuxi Jiangsu China

Correspondence should be addressed to Zhenfeng Li 1010525570qqcom

Received 20 September 2017 Revised 25 January 2018 Accepted 6 February 2018 Published 8 March 2018

Academic Editor Anna Vila

Copyright copy 2018 Wanxiu Xu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study was conducted to optimize the drying process of Polygonum cuspidatum slices using an orthogonal experimental designThe combined effects of pretreatment methods vacuum pressure and temperature of inner material drying kinetics color valueand retention of the indicator compounds were investigated Seven mathematical models on thin-layer drying were used to studyand analyze the drying kinetics Pretreatment method with blanching for 30 s at 100∘C increased the intensity of the red color ofP cuspidatum slices compared with other pretreatment methods and fresh P cuspidatum slices P cuspidatum slices dried at 60∘Cretainedmore indicator compounds Furthermoremicrowave pretreatmentmethods followed bymicrowave vacuum for 200mbarat 50∘C resulted in high concentration of indicator compounds with short drying time and less energy This optimized conditionfor microwave vacuum drying and pretreatment methods would be useful for processing P cuspidatum The Newton Page andWang and Singh models slightly fitted the microwave vacuum drying system The logarithmic Henderson and Pabis two-termand Midilli et al models can be used to scale up the microwave vacuum drying system to a commercial scale The two-term andMidilli et al models were the best fitting mathematical models for the no-pretreatment case at 600mbar and 60∘C

1 Introduction

Polygonum cuspidatum is a well-known Chinese herb andis officially listed in the Chinese Pharmacopoeia This herbhas been traditionally used for the treatment of variousinflammatory diseases including hepatitis tumors and diar-rhea in Eastern Asian countries such as China Korea andJapan [1] The phytochemistry of the root of this plant hasbeen well studied Currently over 67 compounds from thisplant have been isolated and identified [2] The four kindsof indicator compounds are polydatin emodin physcionand resveratrol [3] To retain indicator compounds theroots must be dried Furthermore the degree of retentionof the indicator compounds was determined by dryingconditions

P cuspidatum are usually sun-dried However this pro-cess takes a long time because it is dependent on the weatherMoreover the plant can easily become moldy because reach-ing a low safe moisture content to prevent the growth ofmolds is difficult and the retention of indicator compoundsis low Microwave vacuum drying is a promising rapid

and efficient dehydration method which yields improvedproduct appearance and quality compared to conventionallydried products [4ndash12] In the literaturemicrowave power andvacuum levels are key factors As moisture decreases withdrying an increasing number of burnt spots can be found inthe last stage of drying process [13] Li et al used temperaturecontrol to avoid burning [14] Pretreatment of material byblanching and microwaving can influence product qualityThe efficiency of the blanching process is usually based onthe inactivation of heat-resistant enzymes such as peroxidaseand polyphenol oxidaseMicrowave irradiation has been suc-cessfully used in the pretreatment of various types of biomassincluding agricultural residues woody biomass grass energyplants and industrial residuals [15] Pretreatment methodsvacuum pressure and temperature of inner materials wereshown to be factors influencing the indicator compounds anddrying time

The aims of this paper are as follows

(1) Design and build amicrowave vacuum drying systemand test the system

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 4967356 11 pageshttpsdoiorg10115520184967356

2 Mathematical Problems in Engineering

Controller Vacuum pump

PC withLabview DAQ

Microwave oven

A fiber optic sensor

Moisturecondenser

A vacuummanometer

Tefloncontainer

Fiber opticapparatus

NI6800

Figure 1 Schematic diagram of the microwave vacuum drying system

(2) Analyze the effect of pretreatment methods vacuumpressure and temperature of inner material on indi-cator compounds and drying kinetics

(3) Optimize conditions for pretreatment andmicrowavevacuum drying of P cuspidatum

(4) Develop mathematical models for the microwavevacuum drying of carrot slices to help in the scalingup of this drying technology

2 Materials and Methods

21 Sample Preparation Raw and sun-dried P cuspidatumwere purchased from farmers (Liu Jianhui Liu Jiandong) inJiangxi Province Raw P cuspidatum was washed vacuum-packed and sent to Jiangnan University The samples werekept in the fridge at 4∘C for 3 days Before they wereprocessed each group was washed with tap water for 5minand sliced to 5mm thickness with a radius of 2185ndash2415mmThe initial moisture content was determined by drying thesamples for 24 h in a hot air oven at 80∘C Samples weredried to a final moisture content of less than 011 (dry basiskg waterkg dry solid) Sample (25 g) was used for eachdrying experiment Nine groups were tested and dried Allexperiments were performed in triplicate

22 Microwave Vacuum Drying System A microwave vac-uum drying system for drying P cuspidatum was designedby our team and built in our laboratory (Figure 1) Thesystem consisted of a microwave drying unit a power andtemperature control unit a moisture condenser a vacuumpump a vacuum manometer and a PC-based data acqui-sition unit The microwave unit consisted of a reequippedmicrowave oven The power and temperature control unitconsisted of a fiber optic apparatus a fiber optic sensor andthe power supply for the microwave ovenThe PC-based dataacquisition unit was anNI6800with analog and digital inputsand outputs to record the temperature of inner materialand to control the microwave oven power A 2450MHzmicrowave oven (media MM720KG1-PW) and a hot airgenerator (Kada 850) were modified for the experiments asthe microwave dryer The schematic diagram of the system isshown in Figure 1

Samples were placed in a closed Teflon container whichwas a cylinderwith 110mm in height and 120mm in diameterA porous basket was also fixed at 30mm over the bottom ofthe containerThe container was supportedwith an electronic

Figure 2 LabVIEW program

balance (Lightever LBA5200) to measure the weight of thesamples

One fiber optic sensor (Optsensor ThermAigle-RD HQ-28) was inserted in the center of one of the samples fortemperature measurement The temperature of the center ofsample and power control of magnetron was integrated inthe DAQ board with a self-developed LabVIEW programwhich used Proportion Integral Derivative (PID) controlmethod (Figure 2) The recorded temperature is shown inFigure 3 Temperature was successfully maintained with theappropriate power levels The maximum deviation in surfacetemperaturewasplusmn3∘C and standard deviationswere less than2∘C All the data were recorded at a time interval of 1 s

23 Orthogonal Experiment Design Three factors were stud-ied pretreatment method temperature of the inner materialand vacuum (Table 1) Each pretreatment method changedthe structure of the P cuspidatum in a distinct way By consid-ering the cost of processing samples were pretreated in threeways as follows blanching for 30 s at 100∘C microwaving at700W for 10 s and no pretreatment The temperature of theinner material had a significant influence on the indicatorcomponentsWhen the temperature of the innermaterial washigher than 90∘C less indicator compounds were retainedand toxic chemicals were produced Below 40∘C the dryingtimewas too long and the energy consumptionwasmore thanthat of other drying methods Therefore the temperatureof the inner material should be controlled in the range of50∘Cndash80∘C The use of a high vacuum lowered the dryingtemperature of the inner material More thermosensitivecompounds were retained under a high-temperature vac-uumThree pressures were used 200 400 and 600mbar

Mathematical Problems in Engineering 3

Table 1 Orthogonal experiment design

Expt number Pretreatment methods Vacuum pressure (mbar) Temperature of inner materials (∘C)(1) 1 (blanching for 30 s at 100∘C) 1 (200) 1 (50)(2) 1 2 (400) 2 (60)(3) 1 3 (600) 3 (70)(4) 2 (microwave 700w for 10 s) 1 2(5) 2 2 3(6) 2 3 1(7) 3 (no pretreatment) 1 3(8) 3 2 1(9) 3 3 2

MD60 degree CMD70 degree CMD80 degree C

0

20

40

60

80

100

Tem

pera

ture

(deg

ree)

1000 2000 3000 4000 50000Time (s)

Figure 3 Recorded temperature of the microwave vacuum dryingsystem

24 Mathematical Models The data on the drying of Pcuspidatum slices in microwave vacuum dryer were used tostudy the drying kinetics and to analyze the fit of mathemat-ical models on thin-layer drying including Newton Pagelogarithmic Wang and Singh Henderson and Pabis two-term and Midilli et al models (Table 2) In Table 2 the MRin (i)ndash(vii) is the moisture ratio which is defined in

MR = 119872119905 minus119872119890119872119900 minus119872119890 (1)

where119872119905119872119900 and119872119890 are the moisture content (db) at timet initial moisture content (db) and equilibrium moisturecontent (db) respectively k is the drying rate constant(minminus1) n a b and 119888 are the drying coefficients (unitless)that have different values depending on the equation and thedrying curve and 119905 is time (min)

When the difference between themoisture content at time119905 and the equilibrium moisture content is negligible (1) isreduced to

MR = 119872119905119872119900 (2)

25 Color Measurement Color change is one of the qualitycriteria for dried products Color parameters (119871lowast 119886lowast 119887lowast)were measured directly on the surface of fresh dried andrehydrated P cuspidatum slices by using a chromameter withd0 diffuse illumination0∘ viewing system (Model CR-300XMinolta Co Ltd Japan) The CIE 1976 (119871lowast 119886lowast 119887lowast) colorspace was used to estimate the color values of P cuspidatumslice samples Color values expressed as 119871lowast (whiteness orbrightnessdarkness) 119886lowast (rednessgreenness) and 119887lowast (yel-lownessblueness) were determined for a sample in all dryingconditions The total color difference (Δ119864) was calculatedbased on color values of fresh (119871119891lowast 119886119891lowast and 119887119891lowast) and driedP cuspidatum slices (119871119889lowast 119886119889lowast and 119887119889lowast) based on

Δ119864 = radic(119871119891lowast minus 119871119889lowast)2 + (119886119891lowast minus 119886119889lowast)2 + (119887119891lowast minus 119887119889lowast)2 (3)

26 Chemicals Polydatin (3410158405-trihydro-hydroxystil-bene-3-b-mono-D-glucoside) emodin (6-ethyl-138-trihydrox-yanthraquinone) physcion(18-dihydroxy-3-methoxy-6-meth-ylanthraquinone emodin 3-methyl ether) and resveratrol(3410158405-trihydrohydroxystilbene) were provided by theNational Institute for the Control of Pharmaceuticaland Biological Products (China) For standard solutionspolydatin emodin physcion and resveratrol were dissolvedin 50 ethanol and used to prepare standard solutionscontaining 2397 8368 1078 and 6296120583gmL respectivelywhich were diluted with the same solvent to obtain solutionswith different concentrations

27 High Performance Liquid Chromatography (HPLC) Anal-ysis Samples (200mg) were ground to powders and wererefluxed with 25ml ethanol (50 50 vv) for 30 minutesThe weight loss was made up with ethanol (50 50 vv) Thesolution obtained was filtered through a 045 120583m microporemembrane Ten 120583l solution was injected into the HPLCinstrument for analysis (Palo Alto CA USA) Samples wereseparated on an Agilent ZORBAX SB-C18 column (250mmtimes 46mm 5120583m particles) (Agilent USA) together witha C18 guard column The mobile phase was a gradientprepared from acetonitrile (component A) and 01 formic

4 Mathematical Problems in Engineering

Table 2 Mathematical models of the kinetics of fluidized bed drying

Model name Model equation Reference Equation numberNewton MR = 119890minus119896119905 [16] (i)Page MR = 119890minus119896119905119899 [17] (ii)Logarithmic MR = 119886119890minus119896119905 + 119888 [18] (iii)Wang and Singh MR = 1 + 119886119905 + 1198871199052 [19] (iv)Henderson and Pabis MR = 119886119890minus119896119905 [20] (v)Two-term MR = 1198861198901198960119905 + 1198871198901198961119905 [21] (vi)Midilli et al MR = 119886119890minus119896119905119899 + 119887119905 [22] (vii)

Table 3 Color values of P cuspidatum slices in all drying conditions

Samples Color values119871lowast 119886lowast 119887lowast Δ119864Fresh 6278 825 3663 -(1) 5178 934 3412 1133(2) 4859 997 3390 1455(3) 493 857 3419 1370(4) 5157 705 3435 1150(5) 5682 723 4105 749(6) 5194 798 3649 1084(7) 5548 704 3885 773(8) 5479 777 3748 805(9) 5625 769 4124 801

acid (component B) prepared in water The elution programwas 0ndash15min 15 (A) to 20 (A) and 15ndash60min 20(A) to 80 (A) and the total acquisition time was 65minThe mobile phase flow rate was 10mLmin and the columntemperature was set at 25∘C [23]

28 Correlation Coefficients and Error Analysis Statisticalparameters such as rootmean square error (RMSE) (see (4))chi-square (1205942) (see (5)) and correlation coefficient (1198772) (see(6)) were used to estimate the quality of fit of drying modelsto the observed values

RMSE = [ 1119873119873sum119894=1

(MRpre119894 minusMRexp119894)2]12

(4)

where MRexp119894 is the experimental moisture ratio at time 119905MRpre119894 is the predicted moisture ratio at time t and119873 is theobservation number

1205942 = sum119873119894=1 (MRexp119894 minusMRpre119894)2119873 minus 119899 (5)

where 119899 is the constant number in drying models

1198772 = 1 minus sum119873119894=1 (MRpre119894 minusMRexp119894)2sum119873119894=1 (MRexp119894 minusMRexp)2 (6)

where MRexp is the mean experimentally measured value ofMR

In addition to the parameters mentioned above thereduced sum square error (SSE) (see (7)) was also used as acriterion to analyze the closeness of fit

SSE = 1119873119873sum119894=1

(MRpre119894 minusMRexp119894)2 (7)

29 Statistical Analysis The statistical analysis of variance ofthe experiment resultswas conducted using the SPSS170 (SASInstitute Inc Cary NC USA) with a confidence level (119901 le005) of 95Themathematicalmodels of the drying of carrotslices in microwave vacuum drying were fitted and analyzedby using SPSS

3 Results and Discussion

31 Color Values The results of color parameters of driedP cuspidatum slices in microwave vacuum drying systemare presented in Table 3 The 119871lowast values of all the dried Pcuspidatum slices decreased in comparison with the freshP cuspidatum slices However 119887lowast values almost stayed thesame in all drying conditions which shows the yellownessof P cuspidatum slices and ranged from 3390 to 4124The 119886lowast values varied with different pretreatment methodsPretreatment method with blanching for 30 s at 100∘C madeP cuspidatum slices redder than other pretreatment methodsand fresh P cuspidatum slices The total color difference(Δ119864) of the dried P cuspidatum slices from all the dryingconditions was between 749 and 1455

Mathematical Problems in Engineering 5

(1)(2)(3)

40 80 120 1600Time (min)

0

1

2

3

4

Moi

sture

cont

ent (

dry

basis

)

Figure 4 Drying curves of P cuspidatum slices at (1) blanching for30 s at 100∘C vacuum pressure at 200mbar and 50∘C (2) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 60∘C and (3)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 70∘C

32 Drying Curves The pretreatment methods of the ninegroups were various hence the initial moisture content (drybasis) of each sample was different The lowest moisturecontent was found in the pretreated material microwavedat 700w for 10 s before the drying process (186 dry basis)whereas the dried material blanched for 30 s at 100∘C had thehighest moisture content (306 dry basis) Figure 4 showsthe change of moisture content for groups (1) to (3) Thedrying curve for group (2) was similar to that for group(3) The moisture content of group (1) slowly decreased overtime Thus a low temperature of the inner material and lowvacuumpressure requiredmore time for drying to occurThisphenomenon was due to the fact that at a low temperaturethe pressure of water vapor inside the material was low thusthe water was not easily transferred Similar observationswere reported by Li et al [14]

Figure 5 shows the drying curves for groups (4) to (6)which were pretreated with microwave at 700w for 10 s Asthe initialmoisturewas the least the drying time for group (5)(22 minutes) was the shortest The use of a high temperatureand a high vacuum pressure to the inner material resultedin fast drying The drying time for group (6) (600mbar and50∘C) was 16 times longer than that for group (4) (600mbarand 60∘C) Thus the influence of temperature of the innermaterial on the drying time was more significant than that ofvacuum pressure

Figure 6 shows the drying curves of groups withoutpretreatments The initial moisture was 233 (dry basis)Vacuum pressure had little influence on drying time hencethe drying time of group (8) at 50∘C was almost 2 timesmore than that for group (7) at 70∘C without consideringthe vacuum pressure Furthermore atmospheric pressure for

00

05

10

15

20

Moi

sture

cont

ent (

dry

basis

)

(4)(5)(6)

40 80 1200Time (min)

Figure 5 Drying curves of P cuspidatum slices at (4) blanching for30 s at 100∘C vacuum pressure at 200mbar and 60∘C (5) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 70∘C and (6)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 50∘C

(7)(8)(9)

40 80 120 160 2000Time (min)

00

05

10

15

20

25

Moi

sture

cont

ent (

dry

basis

)

Figure 6 Drying curves of P cuspidatum slices at (7) vacuumpressure at 200mbar and 70∘C (8) vacuumpressure at 400mbar and50∘C and (9) vacuum pressure at 600mbar and 60∘C

group (7) was 200mbar lower than that for group (8) Thetemperature of the root hadmore significant influence on thedrying time for microwave vacuum drying

To compare the influence of pretreatment on the dryingtime the groups with the same temperature should beconsidered The lengths of drying times of groups with atemperature of 50∘C were in the following order the lengthof drying time of group (8)was greater than that of groups (1)and (6) In addition the initial moisture of group (8) with a

6 Mathematical Problems in Engineering

(1)

(2)

(3)(4)

0 20 30 40 5010

Time (min)

0

100

200

300

400

500

600

(mAU

)

Figure 7 HPLC chromatograms of compound retained in sample(1) (peak (1) polydatin peak (2) resveratrol peak (3) emodin andpeak (4) physcion)

higher vacuum pressure was less than that of group (1) withlower vacuum pressure Thus pretreatment methods withblanching for 30 s at 100∘C made dry process faster than nopretreatment The lengths of drying times of groups with atemperature of 70∘C were in the following order the lengthof drying time of group (7) was greater than that of groups(3) and (5) In addition the vacuum pressure of group (3)was lower than that for group (5) Thus pretreatment withmicrowave for 10 s made dry process faster than blanchingfor 30 s

33MathematicalModels and Statistical Analysis Thedryingcurves of P cuspidatum slices were fitted into the math-ematical models (see (i)ndash(vii)) The statistical values werecalculated to estimate the accuracy of closeness of fit and areshown in Tables 4ndash6 The best fitting model was determinedaccording to the lowest 1205942 RMSE and SSE and the highest1198772values The 1198772 values ranged from 02090 to 10000 and theSSE values ranged from 00065 to 00997 respectively (Tables4ndash6)The1198772 in Tables 4 and 6 is lowThus Newton Page andWang and Singhmodel were not suitable under all the dryingconditions

The two-term and Midilli et al models were the bestfitting mathematical models for the no-pretreatment case at600mbar and 60∘C Moreover the lowest 1205942 values were00001 and 00002 The logarithmic Henderson and Pabistwo-term and Midilli et al models can be used to scale upthe microwave vacuum drying system to a commercial scale

34 Effect of Microwave Vacuum Drying and PretreatmentMethods on Concentrations of Indicator Compounds Theconcentrations of indicator compounds in sample 1 wereanalyzed by HPLC (Figure 7) The results of nine groups ofexperiments are listed in Table 7 The highest concentrationsof polydatin were found in samples pretreated by blanchingfor 30 s andmicrowave vacuumdrying at 400mbar and 60∘CEmodin and physcion were the highest when samples were

pretreated with blanching for 30 s and microwave vacuumdrying at 200mbar and 50∘C Furthermore resveratrol con-centrations were the highest when samples were pretreatedwith microwave at 700W for 10 s and dried with microwavevacuum at 600mbar and 50∘C

341 Factors Affecting the Retention of Polydatin The vari-ance of the concentrations of polydatin for each of thefactors was analyzed in Table 7 Pretreatment had a significantinfluence on the retention of polydatin at a confidencelevel of 005 whereas vacuum pressure and temperature ofroot material had a significant influence on retention at aconfidence level of 001The concentrations of polydatin werethe highest in groups (1) (2) and (3) (Table 2) which werepretreated with blanching for 30 s This effect was probablydue to the inhibition of the hydrolysis of the polydatin As thetemperature of the root increased retention decreased whichmay be due to the decomposition of polydatin Moreover asthe temperature of the inner material increased the moisturecontent decreased and less polydatin was retained becausepolydatin is soluble in water When the vacuum pressure washigher the temperature of inner material should be lower[24] Thus with a low temperature of inner material lesspolydatin was retained

342 Factors Affecting the Retention of Emodin and PhyscionThe effect of the factors on the retention of emodin isin the following order The effect of temperature of innermaterial was greater than that in pretreatment methodsand use of vacuum pressure (Table 8) Vacuum pressureand pretreatment had no significant influence whereas thetemperature of inner material had a significant influence at aconfidence level of 01 A high temperature of the root maydecrease the retention of emodin In addition a high thermalprocess may affect the stability of bioactive compounds infood including vitamins and trace elements as proposed byHirun et al [25]

The effect of the different factors on the retention ofphyscion is discussed in Table 8 Pretreatment and vac-uum pressure had no significant influence whereas thetemperature of inner material had a significant influenceat a confidence level of 01 This finding was the same asthat obtained for emodin thus suggesting the use of lowtemperature

343 Factors Affecting the Retention of Resveratrol The effecton the factors on the retention of resveratrol is in thefollowing order the temperature of the root was greater thanthat in pretreatment and vacuum pressure use (Table 8) Thethree factors had no significant influence at a confidencelevel of 01 Table 2 shows the least retention of resveratrolin the no-pretreatment case followed by microwave vacuumdryingwith a vacuumpressure of 002Mpa and a temperatureof 70∘C A high temperature led to chemical changes inthe resveratrol The highest retention was 0397mgg whichwas 13 times more than the highest retention (0029mgg)obtained by Zhang et al [23] Drying at 50∘C caused mostof the retention in the groups but drying time with lowtemperature of the inner material was long

Mathematical Problems in Engineering 7

Table4Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(1)(2)and

(3)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(1)

11987720209

0319

0993

0334

0992

0992

0998

SSE

000

653125

000

9969

0031031

0010438

0031

0031

0031188

RMSE

0080816149

0099844

0176157

0102164

01760

6801760

6801766

1205942064

8780935

0577014

000

6232

0564585

000

6624

0007097

0002238

(2)

11987720211

0302

0983

0295

0982

0984

0997

SSE

0015071

0021571

0070214

0021071

0070143

0070286

0071214

RMSE

0122766

0146872

026498

014516

0264845

0265115

026686

12059420821399

0786975

0021068

0795255

0020394

0021737

000

4037

(3)

1198772023

0343

0997

0337

0993

0998

0998

SSE

0017692

0026385

0076692

0025923

0076385

0076769

0076769

RMSE

0133012

0162433

0276934

0161006

0276378

0277073

0277073

12059420755287

070324

0003333

070912

000756

000291

0002067

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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AnalysisInternational Journal of

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 3

Table 1 Orthogonal experiment design

Expt number Pretreatment methods Vacuum pressure (mbar) Temperature of inner materials (∘C)(1) 1 (blanching for 30 s at 100∘C) 1 (200) 1 (50)(2) 1 2 (400) 2 (60)(3) 1 3 (600) 3 (70)(4) 2 (microwave 700w for 10 s) 1 2(5) 2 2 3(6) 2 3 1(7) 3 (no pretreatment) 1 3(8) 3 2 1(9) 3 3 2

MD60 degree CMD70 degree CMD80 degree C

0

20

40

60

80

100

Tem

pera

ture

(deg

ree)

1000 2000 3000 4000 50000Time (s)

Figure 3 Recorded temperature of the microwave vacuum dryingsystem

24 Mathematical Models The data on the drying of Pcuspidatum slices in microwave vacuum dryer were used tostudy the drying kinetics and to analyze the fit of mathemat-ical models on thin-layer drying including Newton Pagelogarithmic Wang and Singh Henderson and Pabis two-term and Midilli et al models (Table 2) In Table 2 the MRin (i)ndash(vii) is the moisture ratio which is defined in

MR = 119872119905 minus119872119890119872119900 minus119872119890 (1)

where119872119905119872119900 and119872119890 are the moisture content (db) at timet initial moisture content (db) and equilibrium moisturecontent (db) respectively k is the drying rate constant(minminus1) n a b and 119888 are the drying coefficients (unitless)that have different values depending on the equation and thedrying curve and 119905 is time (min)

When the difference between themoisture content at time119905 and the equilibrium moisture content is negligible (1) isreduced to

MR = 119872119905119872119900 (2)

25 Color Measurement Color change is one of the qualitycriteria for dried products Color parameters (119871lowast 119886lowast 119887lowast)were measured directly on the surface of fresh dried andrehydrated P cuspidatum slices by using a chromameter withd0 diffuse illumination0∘ viewing system (Model CR-300XMinolta Co Ltd Japan) The CIE 1976 (119871lowast 119886lowast 119887lowast) colorspace was used to estimate the color values of P cuspidatumslice samples Color values expressed as 119871lowast (whiteness orbrightnessdarkness) 119886lowast (rednessgreenness) and 119887lowast (yel-lownessblueness) were determined for a sample in all dryingconditions The total color difference (Δ119864) was calculatedbased on color values of fresh (119871119891lowast 119886119891lowast and 119887119891lowast) and driedP cuspidatum slices (119871119889lowast 119886119889lowast and 119887119889lowast) based on

Δ119864 = radic(119871119891lowast minus 119871119889lowast)2 + (119886119891lowast minus 119886119889lowast)2 + (119887119891lowast minus 119887119889lowast)2 (3)

26 Chemicals Polydatin (3410158405-trihydro-hydroxystil-bene-3-b-mono-D-glucoside) emodin (6-ethyl-138-trihydrox-yanthraquinone) physcion(18-dihydroxy-3-methoxy-6-meth-ylanthraquinone emodin 3-methyl ether) and resveratrol(3410158405-trihydrohydroxystilbene) were provided by theNational Institute for the Control of Pharmaceuticaland Biological Products (China) For standard solutionspolydatin emodin physcion and resveratrol were dissolvedin 50 ethanol and used to prepare standard solutionscontaining 2397 8368 1078 and 6296120583gmL respectivelywhich were diluted with the same solvent to obtain solutionswith different concentrations

27 High Performance Liquid Chromatography (HPLC) Anal-ysis Samples (200mg) were ground to powders and wererefluxed with 25ml ethanol (50 50 vv) for 30 minutesThe weight loss was made up with ethanol (50 50 vv) Thesolution obtained was filtered through a 045 120583m microporemembrane Ten 120583l solution was injected into the HPLCinstrument for analysis (Palo Alto CA USA) Samples wereseparated on an Agilent ZORBAX SB-C18 column (250mmtimes 46mm 5120583m particles) (Agilent USA) together witha C18 guard column The mobile phase was a gradientprepared from acetonitrile (component A) and 01 formic

4 Mathematical Problems in Engineering

Table 2 Mathematical models of the kinetics of fluidized bed drying

Model name Model equation Reference Equation numberNewton MR = 119890minus119896119905 [16] (i)Page MR = 119890minus119896119905119899 [17] (ii)Logarithmic MR = 119886119890minus119896119905 + 119888 [18] (iii)Wang and Singh MR = 1 + 119886119905 + 1198871199052 [19] (iv)Henderson and Pabis MR = 119886119890minus119896119905 [20] (v)Two-term MR = 1198861198901198960119905 + 1198871198901198961119905 [21] (vi)Midilli et al MR = 119886119890minus119896119905119899 + 119887119905 [22] (vii)

Table 3 Color values of P cuspidatum slices in all drying conditions

Samples Color values119871lowast 119886lowast 119887lowast Δ119864Fresh 6278 825 3663 -(1) 5178 934 3412 1133(2) 4859 997 3390 1455(3) 493 857 3419 1370(4) 5157 705 3435 1150(5) 5682 723 4105 749(6) 5194 798 3649 1084(7) 5548 704 3885 773(8) 5479 777 3748 805(9) 5625 769 4124 801

acid (component B) prepared in water The elution programwas 0ndash15min 15 (A) to 20 (A) and 15ndash60min 20(A) to 80 (A) and the total acquisition time was 65minThe mobile phase flow rate was 10mLmin and the columntemperature was set at 25∘C [23]

28 Correlation Coefficients and Error Analysis Statisticalparameters such as rootmean square error (RMSE) (see (4))chi-square (1205942) (see (5)) and correlation coefficient (1198772) (see(6)) were used to estimate the quality of fit of drying modelsto the observed values

RMSE = [ 1119873119873sum119894=1

(MRpre119894 minusMRexp119894)2]12

(4)

where MRexp119894 is the experimental moisture ratio at time 119905MRpre119894 is the predicted moisture ratio at time t and119873 is theobservation number

1205942 = sum119873119894=1 (MRexp119894 minusMRpre119894)2119873 minus 119899 (5)

where 119899 is the constant number in drying models

1198772 = 1 minus sum119873119894=1 (MRpre119894 minusMRexp119894)2sum119873119894=1 (MRexp119894 minusMRexp)2 (6)

where MRexp is the mean experimentally measured value ofMR

In addition to the parameters mentioned above thereduced sum square error (SSE) (see (7)) was also used as acriterion to analyze the closeness of fit

SSE = 1119873119873sum119894=1

(MRpre119894 minusMRexp119894)2 (7)

29 Statistical Analysis The statistical analysis of variance ofthe experiment resultswas conducted using the SPSS170 (SASInstitute Inc Cary NC USA) with a confidence level (119901 le005) of 95Themathematicalmodels of the drying of carrotslices in microwave vacuum drying were fitted and analyzedby using SPSS

3 Results and Discussion

31 Color Values The results of color parameters of driedP cuspidatum slices in microwave vacuum drying systemare presented in Table 3 The 119871lowast values of all the dried Pcuspidatum slices decreased in comparison with the freshP cuspidatum slices However 119887lowast values almost stayed thesame in all drying conditions which shows the yellownessof P cuspidatum slices and ranged from 3390 to 4124The 119886lowast values varied with different pretreatment methodsPretreatment method with blanching for 30 s at 100∘C madeP cuspidatum slices redder than other pretreatment methodsand fresh P cuspidatum slices The total color difference(Δ119864) of the dried P cuspidatum slices from all the dryingconditions was between 749 and 1455

Mathematical Problems in Engineering 5

(1)(2)(3)

40 80 120 1600Time (min)

0

1

2

3

4

Moi

sture

cont

ent (

dry

basis

)

Figure 4 Drying curves of P cuspidatum slices at (1) blanching for30 s at 100∘C vacuum pressure at 200mbar and 50∘C (2) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 60∘C and (3)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 70∘C

32 Drying Curves The pretreatment methods of the ninegroups were various hence the initial moisture content (drybasis) of each sample was different The lowest moisturecontent was found in the pretreated material microwavedat 700w for 10 s before the drying process (186 dry basis)whereas the dried material blanched for 30 s at 100∘C had thehighest moisture content (306 dry basis) Figure 4 showsthe change of moisture content for groups (1) to (3) Thedrying curve for group (2) was similar to that for group(3) The moisture content of group (1) slowly decreased overtime Thus a low temperature of the inner material and lowvacuumpressure requiredmore time for drying to occurThisphenomenon was due to the fact that at a low temperaturethe pressure of water vapor inside the material was low thusthe water was not easily transferred Similar observationswere reported by Li et al [14]

Figure 5 shows the drying curves for groups (4) to (6)which were pretreated with microwave at 700w for 10 s Asthe initialmoisturewas the least the drying time for group (5)(22 minutes) was the shortest The use of a high temperatureand a high vacuum pressure to the inner material resultedin fast drying The drying time for group (6) (600mbar and50∘C) was 16 times longer than that for group (4) (600mbarand 60∘C) Thus the influence of temperature of the innermaterial on the drying time was more significant than that ofvacuum pressure

Figure 6 shows the drying curves of groups withoutpretreatments The initial moisture was 233 (dry basis)Vacuum pressure had little influence on drying time hencethe drying time of group (8) at 50∘C was almost 2 timesmore than that for group (7) at 70∘C without consideringthe vacuum pressure Furthermore atmospheric pressure for

00

05

10

15

20

Moi

sture

cont

ent (

dry

basis

)

(4)(5)(6)

40 80 1200Time (min)

Figure 5 Drying curves of P cuspidatum slices at (4) blanching for30 s at 100∘C vacuum pressure at 200mbar and 60∘C (5) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 70∘C and (6)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 50∘C

(7)(8)(9)

40 80 120 160 2000Time (min)

00

05

10

15

20

25

Moi

sture

cont

ent (

dry

basis

)

Figure 6 Drying curves of P cuspidatum slices at (7) vacuumpressure at 200mbar and 70∘C (8) vacuumpressure at 400mbar and50∘C and (9) vacuum pressure at 600mbar and 60∘C

group (7) was 200mbar lower than that for group (8) Thetemperature of the root hadmore significant influence on thedrying time for microwave vacuum drying

To compare the influence of pretreatment on the dryingtime the groups with the same temperature should beconsidered The lengths of drying times of groups with atemperature of 50∘C were in the following order the lengthof drying time of group (8)was greater than that of groups (1)and (6) In addition the initial moisture of group (8) with a

6 Mathematical Problems in Engineering

(1)

(2)

(3)(4)

0 20 30 40 5010

Time (min)

0

100

200

300

400

500

600

(mAU

)

Figure 7 HPLC chromatograms of compound retained in sample(1) (peak (1) polydatin peak (2) resveratrol peak (3) emodin andpeak (4) physcion)

higher vacuum pressure was less than that of group (1) withlower vacuum pressure Thus pretreatment methods withblanching for 30 s at 100∘C made dry process faster than nopretreatment The lengths of drying times of groups with atemperature of 70∘C were in the following order the lengthof drying time of group (7) was greater than that of groups(3) and (5) In addition the vacuum pressure of group (3)was lower than that for group (5) Thus pretreatment withmicrowave for 10 s made dry process faster than blanchingfor 30 s

33MathematicalModels and Statistical Analysis Thedryingcurves of P cuspidatum slices were fitted into the math-ematical models (see (i)ndash(vii)) The statistical values werecalculated to estimate the accuracy of closeness of fit and areshown in Tables 4ndash6 The best fitting model was determinedaccording to the lowest 1205942 RMSE and SSE and the highest1198772values The 1198772 values ranged from 02090 to 10000 and theSSE values ranged from 00065 to 00997 respectively (Tables4ndash6)The1198772 in Tables 4 and 6 is lowThus Newton Page andWang and Singhmodel were not suitable under all the dryingconditions

The two-term and Midilli et al models were the bestfitting mathematical models for the no-pretreatment case at600mbar and 60∘C Moreover the lowest 1205942 values were00001 and 00002 The logarithmic Henderson and Pabistwo-term and Midilli et al models can be used to scale upthe microwave vacuum drying system to a commercial scale

34 Effect of Microwave Vacuum Drying and PretreatmentMethods on Concentrations of Indicator Compounds Theconcentrations of indicator compounds in sample 1 wereanalyzed by HPLC (Figure 7) The results of nine groups ofexperiments are listed in Table 7 The highest concentrationsof polydatin were found in samples pretreated by blanchingfor 30 s andmicrowave vacuumdrying at 400mbar and 60∘CEmodin and physcion were the highest when samples were

pretreated with blanching for 30 s and microwave vacuumdrying at 200mbar and 50∘C Furthermore resveratrol con-centrations were the highest when samples were pretreatedwith microwave at 700W for 10 s and dried with microwavevacuum at 600mbar and 50∘C

341 Factors Affecting the Retention of Polydatin The vari-ance of the concentrations of polydatin for each of thefactors was analyzed in Table 7 Pretreatment had a significantinfluence on the retention of polydatin at a confidencelevel of 005 whereas vacuum pressure and temperature ofroot material had a significant influence on retention at aconfidence level of 001The concentrations of polydatin werethe highest in groups (1) (2) and (3) (Table 2) which werepretreated with blanching for 30 s This effect was probablydue to the inhibition of the hydrolysis of the polydatin As thetemperature of the root increased retention decreased whichmay be due to the decomposition of polydatin Moreover asthe temperature of the inner material increased the moisturecontent decreased and less polydatin was retained becausepolydatin is soluble in water When the vacuum pressure washigher the temperature of inner material should be lower[24] Thus with a low temperature of inner material lesspolydatin was retained

342 Factors Affecting the Retention of Emodin and PhyscionThe effect of the factors on the retention of emodin isin the following order The effect of temperature of innermaterial was greater than that in pretreatment methodsand use of vacuum pressure (Table 8) Vacuum pressureand pretreatment had no significant influence whereas thetemperature of inner material had a significant influence at aconfidence level of 01 A high temperature of the root maydecrease the retention of emodin In addition a high thermalprocess may affect the stability of bioactive compounds infood including vitamins and trace elements as proposed byHirun et al [25]

The effect of the different factors on the retention ofphyscion is discussed in Table 8 Pretreatment and vac-uum pressure had no significant influence whereas thetemperature of inner material had a significant influenceat a confidence level of 01 This finding was the same asthat obtained for emodin thus suggesting the use of lowtemperature

343 Factors Affecting the Retention of Resveratrol The effecton the factors on the retention of resveratrol is in thefollowing order the temperature of the root was greater thanthat in pretreatment and vacuum pressure use (Table 8) Thethree factors had no significant influence at a confidencelevel of 01 Table 2 shows the least retention of resveratrolin the no-pretreatment case followed by microwave vacuumdryingwith a vacuumpressure of 002Mpa and a temperatureof 70∘C A high temperature led to chemical changes inthe resveratrol The highest retention was 0397mgg whichwas 13 times more than the highest retention (0029mgg)obtained by Zhang et al [23] Drying at 50∘C caused mostof the retention in the groups but drying time with lowtemperature of the inner material was long

Mathematical Problems in Engineering 7

Table4Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(1)(2)and

(3)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(1)

11987720209

0319

0993

0334

0992

0992

0998

SSE

000

653125

000

9969

0031031

0010438

0031

0031

0031188

RMSE

0080816149

0099844

0176157

0102164

01760

6801760

6801766

1205942064

8780935

0577014

000

6232

0564585

000

6624

0007097

0002238

(2)

11987720211

0302

0983

0295

0982

0984

0997

SSE

0015071

0021571

0070214

0021071

0070143

0070286

0071214

RMSE

0122766

0146872

026498

014516

0264845

0265115

026686

12059420821399

0786975

0021068

0795255

0020394

0021737

000

4037

(3)

1198772023

0343

0997

0337

0993

0998

0998

SSE

0017692

0026385

0076692

0025923

0076385

0076769

0076769

RMSE

0133012

0162433

0276934

0161006

0276378

0277073

0277073

12059420755287

070324

0003333

070912

000756

000291

0002067

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

4 Mathematical Problems in Engineering

Table 2 Mathematical models of the kinetics of fluidized bed drying

Model name Model equation Reference Equation numberNewton MR = 119890minus119896119905 [16] (i)Page MR = 119890minus119896119905119899 [17] (ii)Logarithmic MR = 119886119890minus119896119905 + 119888 [18] (iii)Wang and Singh MR = 1 + 119886119905 + 1198871199052 [19] (iv)Henderson and Pabis MR = 119886119890minus119896119905 [20] (v)Two-term MR = 1198861198901198960119905 + 1198871198901198961119905 [21] (vi)Midilli et al MR = 119886119890minus119896119905119899 + 119887119905 [22] (vii)

Table 3 Color values of P cuspidatum slices in all drying conditions

Samples Color values119871lowast 119886lowast 119887lowast Δ119864Fresh 6278 825 3663 -(1) 5178 934 3412 1133(2) 4859 997 3390 1455(3) 493 857 3419 1370(4) 5157 705 3435 1150(5) 5682 723 4105 749(6) 5194 798 3649 1084(7) 5548 704 3885 773(8) 5479 777 3748 805(9) 5625 769 4124 801

acid (component B) prepared in water The elution programwas 0ndash15min 15 (A) to 20 (A) and 15ndash60min 20(A) to 80 (A) and the total acquisition time was 65minThe mobile phase flow rate was 10mLmin and the columntemperature was set at 25∘C [23]

28 Correlation Coefficients and Error Analysis Statisticalparameters such as rootmean square error (RMSE) (see (4))chi-square (1205942) (see (5)) and correlation coefficient (1198772) (see(6)) were used to estimate the quality of fit of drying modelsto the observed values

RMSE = [ 1119873119873sum119894=1

(MRpre119894 minusMRexp119894)2]12

(4)

where MRexp119894 is the experimental moisture ratio at time 119905MRpre119894 is the predicted moisture ratio at time t and119873 is theobservation number

1205942 = sum119873119894=1 (MRexp119894 minusMRpre119894)2119873 minus 119899 (5)

where 119899 is the constant number in drying models

1198772 = 1 minus sum119873119894=1 (MRpre119894 minusMRexp119894)2sum119873119894=1 (MRexp119894 minusMRexp)2 (6)

where MRexp is the mean experimentally measured value ofMR

In addition to the parameters mentioned above thereduced sum square error (SSE) (see (7)) was also used as acriterion to analyze the closeness of fit

SSE = 1119873119873sum119894=1

(MRpre119894 minusMRexp119894)2 (7)

29 Statistical Analysis The statistical analysis of variance ofthe experiment resultswas conducted using the SPSS170 (SASInstitute Inc Cary NC USA) with a confidence level (119901 le005) of 95Themathematicalmodels of the drying of carrotslices in microwave vacuum drying were fitted and analyzedby using SPSS

3 Results and Discussion

31 Color Values The results of color parameters of driedP cuspidatum slices in microwave vacuum drying systemare presented in Table 3 The 119871lowast values of all the dried Pcuspidatum slices decreased in comparison with the freshP cuspidatum slices However 119887lowast values almost stayed thesame in all drying conditions which shows the yellownessof P cuspidatum slices and ranged from 3390 to 4124The 119886lowast values varied with different pretreatment methodsPretreatment method with blanching for 30 s at 100∘C madeP cuspidatum slices redder than other pretreatment methodsand fresh P cuspidatum slices The total color difference(Δ119864) of the dried P cuspidatum slices from all the dryingconditions was between 749 and 1455

Mathematical Problems in Engineering 5

(1)(2)(3)

40 80 120 1600Time (min)

0

1

2

3

4

Moi

sture

cont

ent (

dry

basis

)

Figure 4 Drying curves of P cuspidatum slices at (1) blanching for30 s at 100∘C vacuum pressure at 200mbar and 50∘C (2) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 60∘C and (3)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 70∘C

32 Drying Curves The pretreatment methods of the ninegroups were various hence the initial moisture content (drybasis) of each sample was different The lowest moisturecontent was found in the pretreated material microwavedat 700w for 10 s before the drying process (186 dry basis)whereas the dried material blanched for 30 s at 100∘C had thehighest moisture content (306 dry basis) Figure 4 showsthe change of moisture content for groups (1) to (3) Thedrying curve for group (2) was similar to that for group(3) The moisture content of group (1) slowly decreased overtime Thus a low temperature of the inner material and lowvacuumpressure requiredmore time for drying to occurThisphenomenon was due to the fact that at a low temperaturethe pressure of water vapor inside the material was low thusthe water was not easily transferred Similar observationswere reported by Li et al [14]

Figure 5 shows the drying curves for groups (4) to (6)which were pretreated with microwave at 700w for 10 s Asthe initialmoisturewas the least the drying time for group (5)(22 minutes) was the shortest The use of a high temperatureand a high vacuum pressure to the inner material resultedin fast drying The drying time for group (6) (600mbar and50∘C) was 16 times longer than that for group (4) (600mbarand 60∘C) Thus the influence of temperature of the innermaterial on the drying time was more significant than that ofvacuum pressure

Figure 6 shows the drying curves of groups withoutpretreatments The initial moisture was 233 (dry basis)Vacuum pressure had little influence on drying time hencethe drying time of group (8) at 50∘C was almost 2 timesmore than that for group (7) at 70∘C without consideringthe vacuum pressure Furthermore atmospheric pressure for

00

05

10

15

20

Moi

sture

cont

ent (

dry

basis

)

(4)(5)(6)

40 80 1200Time (min)

Figure 5 Drying curves of P cuspidatum slices at (4) blanching for30 s at 100∘C vacuum pressure at 200mbar and 60∘C (5) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 70∘C and (6)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 50∘C

(7)(8)(9)

40 80 120 160 2000Time (min)

00

05

10

15

20

25

Moi

sture

cont

ent (

dry

basis

)

Figure 6 Drying curves of P cuspidatum slices at (7) vacuumpressure at 200mbar and 70∘C (8) vacuumpressure at 400mbar and50∘C and (9) vacuum pressure at 600mbar and 60∘C

group (7) was 200mbar lower than that for group (8) Thetemperature of the root hadmore significant influence on thedrying time for microwave vacuum drying

To compare the influence of pretreatment on the dryingtime the groups with the same temperature should beconsidered The lengths of drying times of groups with atemperature of 50∘C were in the following order the lengthof drying time of group (8)was greater than that of groups (1)and (6) In addition the initial moisture of group (8) with a

6 Mathematical Problems in Engineering

(1)

(2)

(3)(4)

0 20 30 40 5010

Time (min)

0

100

200

300

400

500

600

(mAU

)

Figure 7 HPLC chromatograms of compound retained in sample(1) (peak (1) polydatin peak (2) resveratrol peak (3) emodin andpeak (4) physcion)

higher vacuum pressure was less than that of group (1) withlower vacuum pressure Thus pretreatment methods withblanching for 30 s at 100∘C made dry process faster than nopretreatment The lengths of drying times of groups with atemperature of 70∘C were in the following order the lengthof drying time of group (7) was greater than that of groups(3) and (5) In addition the vacuum pressure of group (3)was lower than that for group (5) Thus pretreatment withmicrowave for 10 s made dry process faster than blanchingfor 30 s

33MathematicalModels and Statistical Analysis Thedryingcurves of P cuspidatum slices were fitted into the math-ematical models (see (i)ndash(vii)) The statistical values werecalculated to estimate the accuracy of closeness of fit and areshown in Tables 4ndash6 The best fitting model was determinedaccording to the lowest 1205942 RMSE and SSE and the highest1198772values The 1198772 values ranged from 02090 to 10000 and theSSE values ranged from 00065 to 00997 respectively (Tables4ndash6)The1198772 in Tables 4 and 6 is lowThus Newton Page andWang and Singhmodel were not suitable under all the dryingconditions

The two-term and Midilli et al models were the bestfitting mathematical models for the no-pretreatment case at600mbar and 60∘C Moreover the lowest 1205942 values were00001 and 00002 The logarithmic Henderson and Pabistwo-term and Midilli et al models can be used to scale upthe microwave vacuum drying system to a commercial scale

34 Effect of Microwave Vacuum Drying and PretreatmentMethods on Concentrations of Indicator Compounds Theconcentrations of indicator compounds in sample 1 wereanalyzed by HPLC (Figure 7) The results of nine groups ofexperiments are listed in Table 7 The highest concentrationsof polydatin were found in samples pretreated by blanchingfor 30 s andmicrowave vacuumdrying at 400mbar and 60∘CEmodin and physcion were the highest when samples were

pretreated with blanching for 30 s and microwave vacuumdrying at 200mbar and 50∘C Furthermore resveratrol con-centrations were the highest when samples were pretreatedwith microwave at 700W for 10 s and dried with microwavevacuum at 600mbar and 50∘C

341 Factors Affecting the Retention of Polydatin The vari-ance of the concentrations of polydatin for each of thefactors was analyzed in Table 7 Pretreatment had a significantinfluence on the retention of polydatin at a confidencelevel of 005 whereas vacuum pressure and temperature ofroot material had a significant influence on retention at aconfidence level of 001The concentrations of polydatin werethe highest in groups (1) (2) and (3) (Table 2) which werepretreated with blanching for 30 s This effect was probablydue to the inhibition of the hydrolysis of the polydatin As thetemperature of the root increased retention decreased whichmay be due to the decomposition of polydatin Moreover asthe temperature of the inner material increased the moisturecontent decreased and less polydatin was retained becausepolydatin is soluble in water When the vacuum pressure washigher the temperature of inner material should be lower[24] Thus with a low temperature of inner material lesspolydatin was retained

342 Factors Affecting the Retention of Emodin and PhyscionThe effect of the factors on the retention of emodin isin the following order The effect of temperature of innermaterial was greater than that in pretreatment methodsand use of vacuum pressure (Table 8) Vacuum pressureand pretreatment had no significant influence whereas thetemperature of inner material had a significant influence at aconfidence level of 01 A high temperature of the root maydecrease the retention of emodin In addition a high thermalprocess may affect the stability of bioactive compounds infood including vitamins and trace elements as proposed byHirun et al [25]

The effect of the different factors on the retention ofphyscion is discussed in Table 8 Pretreatment and vac-uum pressure had no significant influence whereas thetemperature of inner material had a significant influenceat a confidence level of 01 This finding was the same asthat obtained for emodin thus suggesting the use of lowtemperature

343 Factors Affecting the Retention of Resveratrol The effecton the factors on the retention of resveratrol is in thefollowing order the temperature of the root was greater thanthat in pretreatment and vacuum pressure use (Table 8) Thethree factors had no significant influence at a confidencelevel of 01 Table 2 shows the least retention of resveratrolin the no-pretreatment case followed by microwave vacuumdryingwith a vacuumpressure of 002Mpa and a temperatureof 70∘C A high temperature led to chemical changes inthe resveratrol The highest retention was 0397mgg whichwas 13 times more than the highest retention (0029mgg)obtained by Zhang et al [23] Drying at 50∘C caused mostof the retention in the groups but drying time with lowtemperature of the inner material was long

Mathematical Problems in Engineering 7

Table4Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(1)(2)and

(3)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(1)

11987720209

0319

0993

0334

0992

0992

0998

SSE

000

653125

000

9969

0031031

0010438

0031

0031

0031188

RMSE

0080816149

0099844

0176157

0102164

01760

6801760

6801766

1205942064

8780935

0577014

000

6232

0564585

000

6624

0007097

0002238

(2)

11987720211

0302

0983

0295

0982

0984

0997

SSE

0015071

0021571

0070214

0021071

0070143

0070286

0071214

RMSE

0122766

0146872

026498

014516

0264845

0265115

026686

12059420821399

0786975

0021068

0795255

0020394

0021737

000

4037

(3)

1198772023

0343

0997

0337

0993

0998

0998

SSE

0017692

0026385

0076692

0025923

0076385

0076769

0076769

RMSE

0133012

0162433

0276934

0161006

0276378

0277073

0277073

12059420755287

070324

0003333

070912

000756

000291

0002067

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

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Dierential EquationsInternational Journal of

Volume 2018

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Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 5

(1)(2)(3)

40 80 120 1600Time (min)

0

1

2

3

4

Moi

sture

cont

ent (

dry

basis

)

Figure 4 Drying curves of P cuspidatum slices at (1) blanching for30 s at 100∘C vacuum pressure at 200mbar and 50∘C (2) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 60∘C and (3)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 70∘C

32 Drying Curves The pretreatment methods of the ninegroups were various hence the initial moisture content (drybasis) of each sample was different The lowest moisturecontent was found in the pretreated material microwavedat 700w for 10 s before the drying process (186 dry basis)whereas the dried material blanched for 30 s at 100∘C had thehighest moisture content (306 dry basis) Figure 4 showsthe change of moisture content for groups (1) to (3) Thedrying curve for group (2) was similar to that for group(3) The moisture content of group (1) slowly decreased overtime Thus a low temperature of the inner material and lowvacuumpressure requiredmore time for drying to occurThisphenomenon was due to the fact that at a low temperaturethe pressure of water vapor inside the material was low thusthe water was not easily transferred Similar observationswere reported by Li et al [14]

Figure 5 shows the drying curves for groups (4) to (6)which were pretreated with microwave at 700w for 10 s Asthe initialmoisturewas the least the drying time for group (5)(22 minutes) was the shortest The use of a high temperatureand a high vacuum pressure to the inner material resultedin fast drying The drying time for group (6) (600mbar and50∘C) was 16 times longer than that for group (4) (600mbarand 60∘C) Thus the influence of temperature of the innermaterial on the drying time was more significant than that ofvacuum pressure

Figure 6 shows the drying curves of groups withoutpretreatments The initial moisture was 233 (dry basis)Vacuum pressure had little influence on drying time hencethe drying time of group (8) at 50∘C was almost 2 timesmore than that for group (7) at 70∘C without consideringthe vacuum pressure Furthermore atmospheric pressure for

00

05

10

15

20

Moi

sture

cont

ent (

dry

basis

)

(4)(5)(6)

40 80 1200Time (min)

Figure 5 Drying curves of P cuspidatum slices at (4) blanching for30 s at 100∘C vacuum pressure at 200mbar and 60∘C (5) blanchingfor 30 s at 100∘C vacuum pressure at 400mbar and 70∘C and (6)blanching for 30 s at 100∘C vacuum pressure at 600mbar and 50∘C

(7)(8)(9)

40 80 120 160 2000Time (min)

00

05

10

15

20

25

Moi

sture

cont

ent (

dry

basis

)

Figure 6 Drying curves of P cuspidatum slices at (7) vacuumpressure at 200mbar and 70∘C (8) vacuumpressure at 400mbar and50∘C and (9) vacuum pressure at 600mbar and 60∘C

group (7) was 200mbar lower than that for group (8) Thetemperature of the root hadmore significant influence on thedrying time for microwave vacuum drying

To compare the influence of pretreatment on the dryingtime the groups with the same temperature should beconsidered The lengths of drying times of groups with atemperature of 50∘C were in the following order the lengthof drying time of group (8)was greater than that of groups (1)and (6) In addition the initial moisture of group (8) with a

6 Mathematical Problems in Engineering

(1)

(2)

(3)(4)

0 20 30 40 5010

Time (min)

0

100

200

300

400

500

600

(mAU

)

Figure 7 HPLC chromatograms of compound retained in sample(1) (peak (1) polydatin peak (2) resveratrol peak (3) emodin andpeak (4) physcion)

higher vacuum pressure was less than that of group (1) withlower vacuum pressure Thus pretreatment methods withblanching for 30 s at 100∘C made dry process faster than nopretreatment The lengths of drying times of groups with atemperature of 70∘C were in the following order the lengthof drying time of group (7) was greater than that of groups(3) and (5) In addition the vacuum pressure of group (3)was lower than that for group (5) Thus pretreatment withmicrowave for 10 s made dry process faster than blanchingfor 30 s

33MathematicalModels and Statistical Analysis Thedryingcurves of P cuspidatum slices were fitted into the math-ematical models (see (i)ndash(vii)) The statistical values werecalculated to estimate the accuracy of closeness of fit and areshown in Tables 4ndash6 The best fitting model was determinedaccording to the lowest 1205942 RMSE and SSE and the highest1198772values The 1198772 values ranged from 02090 to 10000 and theSSE values ranged from 00065 to 00997 respectively (Tables4ndash6)The1198772 in Tables 4 and 6 is lowThus Newton Page andWang and Singhmodel were not suitable under all the dryingconditions

The two-term and Midilli et al models were the bestfitting mathematical models for the no-pretreatment case at600mbar and 60∘C Moreover the lowest 1205942 values were00001 and 00002 The logarithmic Henderson and Pabistwo-term and Midilli et al models can be used to scale upthe microwave vacuum drying system to a commercial scale

34 Effect of Microwave Vacuum Drying and PretreatmentMethods on Concentrations of Indicator Compounds Theconcentrations of indicator compounds in sample 1 wereanalyzed by HPLC (Figure 7) The results of nine groups ofexperiments are listed in Table 7 The highest concentrationsof polydatin were found in samples pretreated by blanchingfor 30 s andmicrowave vacuumdrying at 400mbar and 60∘CEmodin and physcion were the highest when samples were

pretreated with blanching for 30 s and microwave vacuumdrying at 200mbar and 50∘C Furthermore resveratrol con-centrations were the highest when samples were pretreatedwith microwave at 700W for 10 s and dried with microwavevacuum at 600mbar and 50∘C

341 Factors Affecting the Retention of Polydatin The vari-ance of the concentrations of polydatin for each of thefactors was analyzed in Table 7 Pretreatment had a significantinfluence on the retention of polydatin at a confidencelevel of 005 whereas vacuum pressure and temperature ofroot material had a significant influence on retention at aconfidence level of 001The concentrations of polydatin werethe highest in groups (1) (2) and (3) (Table 2) which werepretreated with blanching for 30 s This effect was probablydue to the inhibition of the hydrolysis of the polydatin As thetemperature of the root increased retention decreased whichmay be due to the decomposition of polydatin Moreover asthe temperature of the inner material increased the moisturecontent decreased and less polydatin was retained becausepolydatin is soluble in water When the vacuum pressure washigher the temperature of inner material should be lower[24] Thus with a low temperature of inner material lesspolydatin was retained

342 Factors Affecting the Retention of Emodin and PhyscionThe effect of the factors on the retention of emodin isin the following order The effect of temperature of innermaterial was greater than that in pretreatment methodsand use of vacuum pressure (Table 8) Vacuum pressureand pretreatment had no significant influence whereas thetemperature of inner material had a significant influence at aconfidence level of 01 A high temperature of the root maydecrease the retention of emodin In addition a high thermalprocess may affect the stability of bioactive compounds infood including vitamins and trace elements as proposed byHirun et al [25]

The effect of the different factors on the retention ofphyscion is discussed in Table 8 Pretreatment and vac-uum pressure had no significant influence whereas thetemperature of inner material had a significant influenceat a confidence level of 01 This finding was the same asthat obtained for emodin thus suggesting the use of lowtemperature

343 Factors Affecting the Retention of Resveratrol The effecton the factors on the retention of resveratrol is in thefollowing order the temperature of the root was greater thanthat in pretreatment and vacuum pressure use (Table 8) Thethree factors had no significant influence at a confidencelevel of 01 Table 2 shows the least retention of resveratrolin the no-pretreatment case followed by microwave vacuumdryingwith a vacuumpressure of 002Mpa and a temperatureof 70∘C A high temperature led to chemical changes inthe resveratrol The highest retention was 0397mgg whichwas 13 times more than the highest retention (0029mgg)obtained by Zhang et al [23] Drying at 50∘C caused mostof the retention in the groups but drying time with lowtemperature of the inner material was long

Mathematical Problems in Engineering 7

Table4Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(1)(2)and

(3)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(1)

11987720209

0319

0993

0334

0992

0992

0998

SSE

000

653125

000

9969

0031031

0010438

0031

0031

0031188

RMSE

0080816149

0099844

0176157

0102164

01760

6801760

6801766

1205942064

8780935

0577014

000

6232

0564585

000

6624

0007097

0002238

(2)

11987720211

0302

0983

0295

0982

0984

0997

SSE

0015071

0021571

0070214

0021071

0070143

0070286

0071214

RMSE

0122766

0146872

026498

014516

0264845

0265115

026686

12059420821399

0786975

0021068

0795255

0020394

0021737

000

4037

(3)

1198772023

0343

0997

0337

0993

0998

0998

SSE

0017692

0026385

0076692

0025923

0076385

0076769

0076769

RMSE

0133012

0162433

0276934

0161006

0276378

0277073

0277073

12059420755287

070324

0003333

070912

000756

000291

0002067

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

(1)

(2)

(3)(4)

0 20 30 40 5010

Time (min)

0

100

200

300

400

500

600

(mAU

)

Figure 7 HPLC chromatograms of compound retained in sample(1) (peak (1) polydatin peak (2) resveratrol peak (3) emodin andpeak (4) physcion)

higher vacuum pressure was less than that of group (1) withlower vacuum pressure Thus pretreatment methods withblanching for 30 s at 100∘C made dry process faster than nopretreatment The lengths of drying times of groups with atemperature of 70∘C were in the following order the lengthof drying time of group (7) was greater than that of groups(3) and (5) In addition the vacuum pressure of group (3)was lower than that for group (5) Thus pretreatment withmicrowave for 10 s made dry process faster than blanchingfor 30 s

33MathematicalModels and Statistical Analysis Thedryingcurves of P cuspidatum slices were fitted into the math-ematical models (see (i)ndash(vii)) The statistical values werecalculated to estimate the accuracy of closeness of fit and areshown in Tables 4ndash6 The best fitting model was determinedaccording to the lowest 1205942 RMSE and SSE and the highest1198772values The 1198772 values ranged from 02090 to 10000 and theSSE values ranged from 00065 to 00997 respectively (Tables4ndash6)The1198772 in Tables 4 and 6 is lowThus Newton Page andWang and Singhmodel were not suitable under all the dryingconditions

The two-term and Midilli et al models were the bestfitting mathematical models for the no-pretreatment case at600mbar and 60∘C Moreover the lowest 1205942 values were00001 and 00002 The logarithmic Henderson and Pabistwo-term and Midilli et al models can be used to scale upthe microwave vacuum drying system to a commercial scale

34 Effect of Microwave Vacuum Drying and PretreatmentMethods on Concentrations of Indicator Compounds Theconcentrations of indicator compounds in sample 1 wereanalyzed by HPLC (Figure 7) The results of nine groups ofexperiments are listed in Table 7 The highest concentrationsof polydatin were found in samples pretreated by blanchingfor 30 s andmicrowave vacuumdrying at 400mbar and 60∘CEmodin and physcion were the highest when samples were

pretreated with blanching for 30 s and microwave vacuumdrying at 200mbar and 50∘C Furthermore resveratrol con-centrations were the highest when samples were pretreatedwith microwave at 700W for 10 s and dried with microwavevacuum at 600mbar and 50∘C

341 Factors Affecting the Retention of Polydatin The vari-ance of the concentrations of polydatin for each of thefactors was analyzed in Table 7 Pretreatment had a significantinfluence on the retention of polydatin at a confidencelevel of 005 whereas vacuum pressure and temperature ofroot material had a significant influence on retention at aconfidence level of 001The concentrations of polydatin werethe highest in groups (1) (2) and (3) (Table 2) which werepretreated with blanching for 30 s This effect was probablydue to the inhibition of the hydrolysis of the polydatin As thetemperature of the root increased retention decreased whichmay be due to the decomposition of polydatin Moreover asthe temperature of the inner material increased the moisturecontent decreased and less polydatin was retained becausepolydatin is soluble in water When the vacuum pressure washigher the temperature of inner material should be lower[24] Thus with a low temperature of inner material lesspolydatin was retained

342 Factors Affecting the Retention of Emodin and PhyscionThe effect of the factors on the retention of emodin isin the following order The effect of temperature of innermaterial was greater than that in pretreatment methodsand use of vacuum pressure (Table 8) Vacuum pressureand pretreatment had no significant influence whereas thetemperature of inner material had a significant influence at aconfidence level of 01 A high temperature of the root maydecrease the retention of emodin In addition a high thermalprocess may affect the stability of bioactive compounds infood including vitamins and trace elements as proposed byHirun et al [25]

The effect of the different factors on the retention ofphyscion is discussed in Table 8 Pretreatment and vac-uum pressure had no significant influence whereas thetemperature of inner material had a significant influenceat a confidence level of 01 This finding was the same asthat obtained for emodin thus suggesting the use of lowtemperature

343 Factors Affecting the Retention of Resveratrol The effecton the factors on the retention of resveratrol is in thefollowing order the temperature of the root was greater thanthat in pretreatment and vacuum pressure use (Table 8) Thethree factors had no significant influence at a confidencelevel of 01 Table 2 shows the least retention of resveratrolin the no-pretreatment case followed by microwave vacuumdryingwith a vacuumpressure of 002Mpa and a temperatureof 70∘C A high temperature led to chemical changes inthe resveratrol The highest retention was 0397mgg whichwas 13 times more than the highest retention (0029mgg)obtained by Zhang et al [23] Drying at 50∘C caused mostof the retention in the groups but drying time with lowtemperature of the inner material was long

Mathematical Problems in Engineering 7

Table4Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(1)(2)and

(3)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(1)

11987720209

0319

0993

0334

0992

0992

0998

SSE

000

653125

000

9969

0031031

0010438

0031

0031

0031188

RMSE

0080816149

0099844

0176157

0102164

01760

6801760

6801766

1205942064

8780935

0577014

000

6232

0564585

000

6624

0007097

0002238

(2)

11987720211

0302

0983

0295

0982

0984

0997

SSE

0015071

0021571

0070214

0021071

0070143

0070286

0071214

RMSE

0122766

0146872

026498

014516

0264845

0265115

026686

12059420821399

0786975

0021068

0795255

0020394

0021737

000

4037

(3)

1198772023

0343

0997

0337

0993

0998

0998

SSE

0017692

0026385

0076692

0025923

0076385

0076769

0076769

RMSE

0133012

0162433

0276934

0161006

0276378

0277073

0277073

12059420755287

070324

0003333

070912

000756

000291

0002067

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

Table4Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(1)(2)and

(3)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(1)

11987720209

0319

0993

0334

0992

0992

0998

SSE

000

653125

000

9969

0031031

0010438

0031

0031

0031188

RMSE

0080816149

0099844

0176157

0102164

01760

6801760

6801766

1205942064

8780935

0577014

000

6232

0564585

000

6624

0007097

0002238

(2)

11987720211

0302

0983

0295

0982

0984

0997

SSE

0015071

0021571

0070214

0021071

0070143

0070286

0071214

RMSE

0122766

0146872

026498

014516

0264845

0265115

026686

12059420821399

0786975

0021068

0795255

0020394

0021737

000

4037

(3)

1198772023

0343

0997

0337

0993

0998

0998

SSE

0017692

0026385

0076692

0025923

0076385

0076769

0076769

RMSE

0133012

0162433

0276934

0161006

0276378

0277073

0277073

12059420755287

070324

0003333

070912

000756

000291

0002067

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

Table5Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(4)(5)and

(6)

Exptnum

ber

Statisticscoeffi

cient

Mod

elsNew

ton

Page

Logarithm

icWangandSing

Henderson

andPabis

Two-term

Midillietal

(4)

11987720653

0771

0983

069

0979

0985

0996

SSE

00653

0036714

004

681

0032857

004

6619

004

6905

0047429

RMSE

0255539

019161

0216355

0181265

0215914

0216575

0217781

12059420120337

0087957

000

6901

0118

796

0008169

000

6536

0001526

(5)

11987720588

0751

0989

0678

0989

099

0997

SSE

0025565

00751

00989

00678

00989

0099

00997

RMSE

0159891

02740

4403144

840260384

03144

8403146

430315753

12059420241822

0129542

000

6555

0167694

0005932

000

6765

0002055

(6)

1198772041

0727

0995

0699

0991

0995

0997

SSE

0018636

0031609

0043261

0030391

0043087

0043261

0043348

RMSE

0136515

0177788

0207992

0174331

0207574

0207992

0208201

120594203664

0091569

0001927

011117

40003075

0001801

0001044

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 9

Table6Statisticalresults

ofmathematicalmod

elforP

cuspidatum

forg

roup

s(7)(8)

and(9)

Exptnum

ber

Statisticscoeffi

cient

Mod

els

New

ton

Page

Logarithm

icWangandSing

Henderson

and

Pabis

Two-term

Midillietal

(7)

11987720491

0513

0988

0507

0983

0994

0993

SSE

0018885

0023318

004

4909

0023045

004

4682

0045182

0045136

RMSE

0137421

0152703

0211918

0151807

0211381

021256

0212453

12059420344994

0181661

000

4813

0183733

000

6275

0002431

0002721

(8)1198772

0521

0573

0989

0551

098

0994

0909

SSE

0013711

0022038

0038038

002119

20037692

0038231

0034962

RMSE

0117

092

0148454

0195035

0145576

0194145

0195527

018698

120594205440

950144854

0003781

0152392

000

6815

0002187

0033678

(9)1198772

0657

0617

0999

0573

0997

11

SSE

0031286

0016237

0026289

0015079

0026237

0026316

0026316

RMSE

0176878

0127424

016214

0122796

0161978

0162221

0162221

12059420214399

0145253

000

0242

0161685

0001093

000

0129

000

0178

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

10 Mathematical Problems in Engineering

Table 7 Indicator compounds retained in samples with drying condition

Number Polydatin (mgg) Emodin (mgg) Physcion (mgg) Resveratrol (mgg)(1) 18828 18589 0128 0379(2) 20656 13664 0011 0228(3) 17806 10186 0004 0285(4) 12619 14154 0027 0272(5) 12037 6397 0004 0068(6) 13931 17397 0055 0397(7) 11795 549 0026 0112(8) 15013 14714 0111 0377(9) 12405 7513 0008 0188

Table 8 Variance analysis of the retention of polydatin

Indicator compounds 1198772 Source of variation Sum of squares Degree of freedom Mean square F value Sig

Polydatin 0991Pretreatment 88853 2 44427 89450 0011

Vacuum pressure 9291 2 4646 9354 0097Temperature of inner material 15266 2 7633 15369 0061

Emodin 0939Pretreatment 27766 2 13883 2273 0306

Vacuum pressure 1646 2 0823 0135 0881Temperature of inner material 157277 2 78639 12873 0072

Physcion 0944Pretreatment 0001 2 0000 0535 0652

Vacuum pressure 0002 2 0001 1421 0413Temperature of inner material 0016 2 0008 14791 0063

Resveratrol 0865Pretreatment 0008 2 0004 0543 0648Air pressure 0006 2 0003 0428 0700

Temperature of inner material 0082 2 0041 5418 0156

4 Conclusion

Pretreatment method with blanching for 30 s at 100∘C inten-sified the red color of P cuspidatum slices compared withother pretreatment methods and fresh P cuspidatum slicesThe logarithmic Henderson and Pabis two-term andMidilliet al models can be used to scale up the microwave vacuumdrying system to a commercial scale The temperature of theroot had a significant influence on the retention of polydatinemodin and physcion at a confidence level of 01 Thetemperature of the root pretreatment and vacuum pressurehad no significant influence on the retention of resveratrolIn addition low temperature of inner material retained allthe indicator compounds of P cuspidatum However low roottemperature required a long drying timeThe order of dryingtime with pretreatment was as follows The drying time ofno-pretreatment case was greater than that of blanching for30 s andmicrowaving at 700w for 10 s Furthermore the tem-perature of the root had more significant influence on dryingtime than vacuum pressure In conclusion pretreatment withmicrowave at 700w for 10 s with a low temperature and lowvacuum pressure would retain more indicator compoundsand require less drying time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the Cooperative Innovation Fundof Jiangsu Province (BY2016022-10) and the Colleges andUniversities in Jiangsu Province for graduate research andinnovation (KYLX 1158)

References

[1] H Chen T Tuck X Ji et al ldquoQuality assessment of Japaneseknotweed (Fallopia japonica) grown on Prince Edward Islandas a source of resveratrolrdquo Journal of Agricultural and FoodChemistry vol 61 no 26 pp 6383ndash6392 2013

[2] W Peng R Qin X Li and H Zhou ldquoBotany phytochemistrypharmacology and potential application of Polygonum cuspida-tum Siebet Zucc a reviewrdquo Journal of Ethnopharmacology vol148 no 3 pp 729ndash745 2013

[3] P Ma K Luo Y Peng et al ldquoQuality control of polygonumcuspidatum by uplc-pda and related statistical analysisrdquo Journalof Liquid Chromatography amp Related Technologies vol 36 no20 pp 2844ndash2854 2013

[4] A Figiel ldquoDrying kinetics and quality of vacuum-microwavedehydrated garlic cloves and slicesrdquo Journal of Food Engineeringvol 94 no 1 pp 98ndash104 2009

[5] A Calın-Sanchez A Figiel A Wojdyło M Szarycz and AA Carbonell-Barrachina ldquoDrying of Garlic Slices Using Con-vective Pre-drying and Vacuum-Microwave Finishing Drying

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 11

Kinetics Energy Consumption and Quality Studiesrdquo Food andBioprocess Technology vol 7 no 2 pp 398ndash408 2014

[6] S Ferenczi B Czukor and Z Cserhalmi ldquoEvaluation ofmicrowave vacuum drying combined with hot-air drying andcompared with freeze- and hot-air drying by the qualityof the dried apple productrdquo Periodica Polytechnica ChemicalEngineering vol 58 no 2 pp 111ndash116 2014

[7] A Figiel and A Michalska ldquoOverall quality of fruits andvegetables products affected by the drying processes with theassistance of vacuum-microwavesrdquo International Journal ofMolecular Sciences vol 18 no 1 article no 71 2017

[8] S Ambros S AW Bauer L Shylkina P Foerst andU KulozikldquoMicrowave-Vacuum Drying of Lactic Acid Bacteria Influenceof Process Parameters on Survival and Acidification ActivityrdquoFood and Bioprocess Technology vol 9 no 11 pp 1901ndash1911 2016

[9] J de Bruijn F Rivas Y Rodriguez et al ldquoEffect of VacuumMicrowave Drying on the Quality and Storage Stability ofStrawberriesrdquo Journal of Food Processing and Preservation vol40 no 5 pp 1104ndash1115 2016

[10] M Zielinska P Sadowski andW Błaszczak ldquoCombined hot airconvective drying and microwave-vacuum drying of blueber-ries (Vaccinium corymbosum L) Drying kinetics and qualitycharacteristicsrdquo Drying Technology vol 34 no 6 pp 665ndash6842016

[11] Y Tian SWu Y ZhaoQ Zhang J Huang andB Zheng ldquoDry-ing Characteristics and Processing Parameters for Microwave-Vacuum Drying of Kiwifruit (Actinidia deliciosa) Slicesrdquo Jour-nal of Food Processing and Preservation vol 39 no 6 pp 2620ndash2629 2015

[12] D Wray and H S Ramaswamy ldquoQuality Attributes ofMicrowave Vacuum Finish-Dried Fresh and Microwave-Osmotic PretreatedCranberriesrdquo Journal of Food Processing andPreservation vol 39 no 6 pp 3067ndash3079 2015

[13] N Therdthai and W Zhou ldquoCharacterization of microwavevacuum drying and hot air drying of mint leaves (Menthacordifolia Opiz ex Fresen)rdquo Journal of Food Engineering vol 91no 3 pp 482ndash489 2009

[14] Z Li G S V Raghavan and V Orsat ldquoTemperature and powercontrol in microwave dryingrdquo Journal of Food Engineering vol97 no 4 pp 478ndash483 2010

[15] J Xu Chapter 9 - Microwave Pretreatment A P N B LarrocheEd Pretreatment of Biomass Elsevier Amsterdam p 157-1722015

[16] P C Correa F M Botelho G H H Oliveira A L DGoneli O Resende and S de Carvalho Campos ldquoMathe-matical modeling of the drying process of corn earsrdquo ActaScientiarummdashAgronomy vol 33 no 4 pp 575ndash581 2011

[17] Q Shi Y Zheng and Y Zhao ldquoMathematical modeling onthin-layer heat pumpdrying of yacon (Smallanthus sonchifolius)slicesrdquoEnergyConversion andManagement vol 71 pp 208ndash2162013

[18] M Ozdemir and Y Onur Devres ldquoThe thin layer dryingcharacteristics of hazelnuts during roastingrdquo Journal of FoodProcess Engineering vol 42 no 4 pp 225ndash233 1999

[19] C Chen and P-C Wu ldquoThin-layer drying model for rough ricewith highmoisture contentrdquo Journal of Agricultural EngineeringResearch vol 80 no 1 pp 45ndash52 2001

[20] A Midilli H Kucuk and Z Yapar ldquoA new model for single-layer dryingrdquo Drying Technology vol 20 no 7 pp 1503ndash15132002

[21] S M Henderson ldquoProgress in developing the thin layer dryingequationrdquo Transactions of the ASAE vol 17 no 6 pp 1167ndash11721974

[22] H O Menges and C Ertekin ldquoMathematical modeling of thinlayer drying of Golden applesrdquo Journal of Food Engineering vol77 no 1 pp 119ndash125 2006

[23] W Zhang Y Jia Q Huang Q Li and K Bi ldquoSimultaneousdetermination of fivemajor compounds in Polygonum cuspida-tum byHPLCrdquoChromatographia vol 66 no 9-10 pp 685ndash6892007

[24] N Hamidi and T Tsuruta ldquoImprovement of freezing qualityof food by pre-dehydration with microwave-vacuum dryingrdquoJournal of Thermal Science and Technology vol 3 no 1 pp 86ndash93 2008

[25] S Hirun N Utama-ang and P D Roach ldquoTurmeric (Curcumalonga L) drying an optimization approach using microwave-vacuum dryingrdquo Journal of Food Science and Technology vol51 no 9 pp 2127ndash2133 2014

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom