Dispersion coefficient of coffee berries in vibrated bed dryer

J.R.D. Finzer a,b,*, M.A. Sfredo a, G.D.B. Sousa a, J.R. Limaverde a

a Faculty of Chemical Engineering, Federal University of Uberlandia, P.O. Box 593, 38400-902 Uberlandia, MG, Brazilb School of Food Engineering, Uberaba Associated Faculty, Av. Tutunas, 720, 38061-500 Uberaba, MG, BrazilAbstract

This paper interprets the experimentally measured residence time distribution of coffee berries on a vibrated tray dryer with recycle bymeans of the dispersion coefficients and the Peclet number. Drying was carried out on a vibrated tray dryer operating with recycle con-sisting of four parts: a vertical drying tunnel, vibration system, warm air supply to the drying tunnel and recycle system of coffee berries.Using the stimulusresponse method the flow behavior of the coffee berries was examined. The dispersion coefficients were calculated bythe Taylor Dispersion Model and Free Dispersion Model. The differences in prediction of the dispersion coefficient between the twomodels were appreciable, but the more reliable values for the dispersion coefficients Ez were those obtained by the Free DispersionModel. The dispersion coefficient (Free Dispersion) ranged from 2.32 104 to 76.81 104 m2/s. The average Peclet number, Pewas approximately equal to 6.5, despite greatest variation of the Ez. Therefore, flow velocity variation of coffee berries was the samemagnitude of the dispersion coefficient variation.

Keywords: Coffee drying; Drying with recycle; Dispersion coefficient; Peclet number1. Introduction

Knowledge of residence time distribution (RTD) of par-ticles flowing in equipment is fundamental for determiningthe dynamics of the process and the expected characteris-tics of the finished product. According to Sharp (1982)the purpose of a dryer is to reduce the material moistureto a safe level required for storage without the occurrenceof any significant deterioration. Hence it becomes neces-sary to know the material behavior on the bed in orderto avoid an unfavorable moisture distribution in the prod-uct. In practice it is not possible to reach a uniform mois-ture content for the material.

Some variability in the moisture content is inevitable. Inparticular, a distribution in the initial moisture content,variability in material properties due to its biological originand to random variations in geometry and drying condi-* Corresponding author. Tel.: +55 34 3239 4189; fax: +55 34 3239 4249.E-mail address: jrdfinzer@ufu.br (J.R.D. Finzer).tions contribute to the uncertainty in the output (Cronin,1998).

In coffee drying on moving bed dryer, particles with lessresidence time will have higher moisture content; thosewith higher residence time will dry excessively and presentcracks. In both cases microorganism growth can occur,which can impair the organoleptic properties of coffeedrink.

The purpose of this work is to study the residence timedistribution of coffee berries on a vibrated tray dryer withrecycle and determine the dispersion coefficients and thePeclet number.

Dispersion is a form of mixing and it involves diffusionof molecules at microscopic level. Hence, dispersion anddiffusion are described with very similar mathematics,despite having very different physical origins and occur ata time scale, speed and space that is absolutely different(Cussler, 1997; Sahoo & Roetzel, 2002).

Dispersion coefficients are characterized by residencetime distribution of the material that is flowing (Roetzel

mailto:jrdfinzer@ufu.brAliHighlight

Nomenclature

a coefficient of Eqs. (6) and (8), b coefficient of Eqs. (6) and (8), c coefficient of Eq. (6), C local concentration, kg/kgCi tracer particles concentration, kg/kge margin of error, kg H2O/kg dry coffeeExp. experiment, Ez dispersion coefficient, m

2/sG coffee berries mass rate, g/minKL constant of Eq. (2), KT constant of Eq. (1)L length of bed, mmp average mass of one coffee berry, gM coffee cherries mass, kg wet coffeen number of the experiments (1, 2 or 3), np number of particles, Pe Peclet number, PVC polyvinyl chloride, Q air mass rate, kg air/min

R2 correlation coefficient, RTD residence time distribution, t time, sti average time of sampling, mintm average residence time, minto t distribution, Tcoffee coffee berries temperature, Cv particle flow velocity, m/svmf velocity of minimum fluidization, m/sV volume of void spaces, m3

VT material total volume, m3

X moisture content of coffee berries, kg H2O/kgdry coffee

Greek symbols

Dt time interval, mine porosity, r standard deviation

Outer skin

PulpSilverskin

MucilageParchment

Bean

Fig. 1. Section of coffee cherry (adapted from Smith, 1985).& Balzereit, 1997), which frequently is a Gaussian distribu-tion. Eq. (1) consists of the Taylor Dispersion Model orig-inally applied to the fluid flow in tube for laminar regime.Eq. (2) consists of the Free Dispersion Model originallyapplied for gas dispersion from stacks (Cussler, 1997).Finzer, Limaverde, and Sfredo (2004) used the mentionedmodels on parchment coffee flow in vibrated system

C KTffiffiffiffiffiffiffiffiffiffiEz t

p expLvt24Ez t

1

C KLffiffiffiffiffiffiffiffiffiffiffiffiEz t3

p expLvt24Ez t

2

where KT and KL are constants; L is the length of the tubeor bed (m); v is the particle flow velocity (m/s); t is the time(s); C is the local concentration (g/g) and Ez is the disper-sion coefficient (m2/s).

The axial dispersed plug flow model, or simply the dis-persion model is probably the most applied approach fortube flow. This model considers that axial diffusion issuperimposed to plug flow, and the resulting axial disper-sion, Ez, is included into the Peclet number, Pe, as indi-cated in the following equation (Torres & Oliveira, 1998):

Pe v LEz

3

The Peclet number is useful for to predict the dispersionin porous media. When the Peclet number is on the magni-tude order of porosity (e), the molecular diffusion is pre-dominant; when Pe is on the order of one, diffusion stillpredominates in a small scale; when Peclet is on the orderof e1, convection tends to predominate; and convection ispredominant when Pe is on the order of e2 (Auriault &Adler, 1995).

According to Strumillo and Kudra (1986) porosity of awet material is given by the ratio between the volume ofvoid spaces and the material total volume, expressed inthe following equation:

e VV T

. 42. Coffee cherries drying

2.1. Harvest

Coffee cherries (see Fig. 1) were harvested at theFazenda Estancia Paraso in the Municipality of Araguari,Minas Gerais State, and were processed in the Research

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and Development Laboratory of the Faculty of ChemicalEngineering of UFU.

Dry processing (without pulping) is the simplestmethod, which is used in Brazil for the majority of coffeescherries. It consists of drying the whole fruits immediatelyafter harvesting (Vincent, 1987).

The first stage of processing is washing with runningwater followed by selection of coffee cherries where allimpurities found on the sample are removed as well as onberries in other stages of the maturation (green and dried).

2.2. Drying

Following the selection of coffee cherries, from the coffeemass initially fed into dryer (M) 10 coffee cherries wereremoved at random in order to determine the initial mois-ture content in a drying oven at 105 C until a constantmass was obtained. Coffee cherries were slowly fed intothe dryer until the formation of an even bed in the fourvibrated trays of equipment.

2.2.1. Description and operation of vibrated tray dryerDrying was carried out on a vibrated tray dryer operat-

ing with recycle, sketched in Fig. 2, basically consisting offour parts: drying vertical tunnel, vibration system, systemof warm air supply to the drying tunnel and recycle systemof coffee berries. The enlargement of the drying chambershows the dynamic of coffee berries and to air flow.

The drying tunnel (2) contains: four perforated trays(through which the coffee berries and air flow out, incrossed flow) with dimensions of 0.179 m 0.265 m 1

2

3

4

5

67

8

9

10

wet air

air

coffee

Fig. 2. Scheme of vibrated tray dryer with recycle. 1, vibratory feeder; 2,drying tunnel; 3, conveyor belt; 4, electromagnetic vibrators; 5, dischargedevice; 6, air piping; 7, motor and speed reducer; 8, flexible rubber device;9, inspection windows; 10, PVC piping.0.06 m; three inner electric resistances connected to theelectric network (220 V) and in series with two voltage var-iators for control of air reheating temperature, regenerat-ing its drying potential prior to feeding of the upper tray;eight thermocouples for measuring the air temperature atthe inlet and outlet of each tray, which were connected toa data acquisition system composed of a repeater (LR-7018), a converter (LR-7520) and a microcomputer; fourdowncomers that made it possible for the coffee berriesto flow from the upper tray to the lower one; five curtainscomposed of aluminum and rubber (0.216 m long and0.179 m wide), which prevent the drying air from flowingthrough downcomer; and a discharge device (5) that directsthe coffee berries flowing to a conveyor belt (to effect therecycle). The discharge device was built with a higher slopethan the rest angle of coffee berries.

The vibration system, consisting of four electromagneticvibrators (4) connected to the four trays of the drying tun-nel and an electromagnetic vibrator connected to a vibra-tory feeder (1) enabled the control of coffee berries flowat the drying tunnel. The four vibrators (CE NormaEquipamentos Ltd., model CV.3), coupled to trays, possesscontrol dial that enables the modification of the vibrationamplitude. A carbonsteel shaft connects the tray to thevibrator. On the dryer wall, a flexible rubber device (8)was installed in order to prevent the air from flowing outthrough the hole where the shaft was introduced into thedryer.

The inspection windows (9) possess acrylic sights withdimensions of 0.063 m 0.182 m in order to visualize thecoffee bed flowing inside the dryer. This device is veryimportant because it enables that the flow control be car-ried out by changing the vibration amplitude of the excita-tion coffee bed.

The air injection system in the dryer was composed of a3.1 hp blower operating at 3500 rpm, a piping (6), 4.50 mlong and 0.20 m in diameter, which carries the drying airup to the dryer tunnel and an electric heating system com-posed of four electric resistances, one of them being con-nected to a voltage variator that enables the fine controlof air temperature.

The recycle system of coffee berries was composed of abelt (3) that conveys berries leaving the dryer on dischargeup to a PVC piping (10), 0.2 m in diameter and 2.23 mlong, where berries flowed to the vibratory feeder at thetop of the drying tunnel. The belt, 0.2 m wide and approx-imately 4 m long, contains flights, 0.017 m high, arrangedat a distance of approximately 0.202 m among them, madeof white rubber, standard for foodstuffs.

The slope of the conveyor belt with regard to the hori-zontal line is approximately 42. The belt speed is con-trolled by changing revolution of the WEG 0.5 hp and1720 rpm motor (induction-cage), responsible for itsmotion, coupled to a speed reducer (7), with reduction of1:60. The set is connected to a WEG frequency inverter(Series CFW-08), which enables to change the speed ofthe conveyor belt whose lowest revolution if 3 rpm.

Table 1Drying conditions of coffee berries

Parameters Exp. 1 Exp. 2 Exp. 3

Variety Acaia Catua Mundo NovoM (kg wet coffee) 12.5 12.5 12.5Q (kg air/min) 7.0 8.0 9.0Tcoffee (C) 50.0 45.0 40.0

0 10 15 20 25 30 35 400.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

X (

kg H

2O/k

g dr

y co

ffee

)

Drying time (h)5

Fig. 4. Drying curve of Experiment 2.

0 10 20 30 40 50 600.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

X (

kg H

2O/k

g dr

y co

ffee

)

Drying time (h)

Fig. 5. Drying curve of Experiment 3.The coffee drying was carried out with three varieties ofthe Coffea Arabica species: Acaia do Cerrado, Catua andMundo Novo. Operational conditions selected in the coffeeberries drying are presented in Table 1.

2.3. Drying curves

Moisture content was measured by randomly selectingfour coffee berries every hour from the conveyor belt ondischarge of the dryer (at the beginning of drying, every1 h, and in the end, every 2 h). The coffee berries wereplaced in a drying oven at 105 C until a constant masswas obtained. This obviously introduces a random sam-pling error into the estimation of mean moisture content.The margin of error (estimated for the confidence intervalof 95%) was calculated by Eq. (5), according to Box,Hunter, and Hunter (1978):

X torffiffiffin

p 5

where to is the tail area probability of the t distribution(3.182); r is the standard deviation and n is the numberof samples.

Figs. 35 present drying curves indicating the margin oferror. Despite the error having been bigger in the beginningof the drying, due to heterogeneity of the coffee cherries, atthe end it was inferior to 10%.

The drying curves indicate the greatest time of dryingwas of the variety Mundo Novo, the shortest time of dryingwas obtained by the variety Catua. All experimentsshowed two periods with decreasing drying rate.0 10 15 20 25 30 35 400.0

0.5

1.0

1.5

2.0

2.5

X (

kg H

2O/k

g dr

y co

ffee

)

Drying time (h)5

Fig. 3. Drying curve of Experiment 1.Eq. (6) represents the drying curves fitted to experimen-tal data. Coefficients a, b, and c, for each test andfor the two drying periods, are presented in Table 2:

X n a b exptc 6

where X[n] is the moisture content of coffee berries in kgH2O/kg dry coffee; n corresponds to drying experiments(1, 2, and 3) and t is time of drying in hours.

Using standard drying theory and taking the limit astime goes to zero implies that the sum of constants a andb is equal to initial moisture content; when the time goesto infinity implies that the constant a is equal to theequilibrium moisture content; the derivate of Eq. (6) is aTable 2Coefficients from Eq. (6) for the drying tests

Exp. Drying period () Coefficients R2

a b c

1 1 0.1963 2.1707 4.8136 0.981 2 0.0891 0.7582 26.2478 0.952 1 0.1445 1.6993 6.8097 0.962 2 0.0049 0.9702 18.6363 0.943 1 0.2669 1.4246 8.9635 0.963 2 0.1923 2.5169 9.7343 0.85

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constant for beginning of drying hence, c is the reciprocalof a drying rate constant.

3. Determination of residence time of coffee berries

During the coffee berries drying, the conveyor belt speedand the tray vibration intensity and vibratory feeder werechanged in accordance with the coffee bed behavior in traysand conveyor belt. Generally the tray and feeder vibrationintensity was decreased along the drying whereas the speedof the conveyor belt had to be increased. Change was nec-essary in order to maintain the uniform flow inside andoutside the dryer since the system dynamics changed withthe course of drying due to change in the berries moisturecontent, decreasing thus their mass, volume and resistanceto flow.

The stimulusresponse method was performed to studycoffee berries behavior on flow. At a time t = 0, a pulseof one hundred coffee berries marked were added into thevibratory feeder of the vibrated tray dryer (Fig. 2), whichconsisted of tracers for the study of time residence distribu-tion of coffee berries. Simultaneously, a chronometer wasactivated for quantifying the time in which each particlewould spend to cover the distance from the feeder to theobservation point, which was located at the conveyor belt.The tracer particles flowing out through the point of obser-vation were collected and registered according to time.

The curves of residence time distribution (RTD) wereplotted using the data obtained of particle number for timeinterval and the tracer particles concentration (C[n]) thatwas determined by using the following equation:

Cn np mpnG Dt 7

where np is the particles number in time interval; G (g/min)is the coffee berries mass rate in the dryer, quantified bydetermination of coffee mass discharged into the dryervibratory feeder; Dt is the time interval (min); mp[n] is theaverage mass (g) of one particle, which is estimated as afunction of X as indicated in Eq. (8). Coefficients aand b of coffee berry mass equation are presented inTable 3:

mpn a b X n 8The average residence time tm, in minutes, of coffee ber-

ries in the dryer was calculated by using the followingequation:

tm P

CitiDtPCiDt

; 9Table 3Coefficients of Eq. (8) for the drying tests

Exp. Coefficients R2

a b

1 0.5938 0.6641 0.952 0.4834 0.4250 0.823 0.5206 0.4853 0.90where Ci is the tracer particles concentration at the dryeroutlet (g/g); ti is the average time of sampling (min); Dt isthe time interval of sampling (Gautam & Choudhury,1999; Iwe, Van Zuilichem, Ngoddy, & Ariahu, 2001;Levenspiel, 1972; Ramaswamy, Abdelrahim, Simpson, &Smith, 1995; Renaud, Thibault, & Alvarez, 2001; Singh &Rizvi, 1998).

Table 4 presents results obtained during the drying andcarried out the RTD for Experiments 1, 2, and 3, where v isobtained by dividing the trajectory effected by coffee berriesinside the dryer (L = 3.04 m) by the average residence time(tm).

By using Eqs. (1) and (2), Ez was determined by theTaylor Dispersion Model and Free Dispersion. Resultsare presented in Table 4.

The average residence time during the drying tends todecrease as moisture content decreases, the same phenom-enon being observed by Renaud et al. (2001) in sand dryingin a rotary dryer. However, that behavior was not observedfor the Experiment 3, at the end of drying.

In the initial stage of drying, coffee berries showedsticky, very moist, and plastic, in terms of vibration trans-mission, with close behavior to the plug flow. At the dryingend when particles acquired an elastic behavior, with theabsence of stickiness and a lesser diameter, the dispersioncoefficient increased considerably, what was reflected in ahigher degree of mixture.

The Ez differences of the two models are appreciable,but correlation coefficients (see Table 4) for the FreeDispersion Equation were higher. Hence, the more reliablevalues for Ez, statistically, are those obtained by the FreeDispersion Model.

The dispersion coefficient (Free Dispersion) ranged from2.32 104 to 76.81 104 m2/s (see Table 4). Typicalresults of Ez reported in the literature are on the order of1 104 to 20 104 m2/s, for much smaller particles(Fyhr, Kemp, & Wimmerstedt, 1999).

For the apatite ([Ca5(OHF)(PO4)3] is a mineral used as araw material for the fertilizer industry) drying in fluidizedbed dryer and by using the tracer technique, Fyhr et al.(1999) obtained Ez values of 8 104 and 14 104 m2/sfor solids flow speeds of 0.008 and 0.012 m/s, respectively.In parchment coffee drying, in multiple vibrated trays,Menezes, Finzer, and Oliveira (1998) obtained Ez valuesfrom 6 104 to 15 104 m2/s by using the Taylor Dis-persion Model.

Pydisetty, Krishnaiah, and Varma (1989) indicated acorrelation for the dispersion coefficient of copper particlesprocessing in fluidized bed by using nickel as a tracer,where Ez was in the range of 0.35 104 to 2.36 104

m2/s, with particle diameter of 4 104 m, operating withv/vmf in the range of 1.22.1.

Figs. 611 present RTD curves for tests carried out. Theupper horizontal axis in Figs. 8 and 9 is valid only forcurves and experimental points of RTD 1.

All curves of residence time distribution (Figs. 611)presented displacement to the right with the existence of

Table 4Experimental results obtained during the residence time distribution in the dryer

Exp. RTD X (kg H2O/kg dry coffee) G (g/min) tm (min) v 104 (m/s) Ez 104 R2

Taylor Free Taylor Free

1 1 1.6540 70.00 66.79 7.58 31.82 4.25 0.70 0.851 2 0.6377 87.50 22.57 22.42 12.09 13.10 0.83 0.981 3 0.3593 192.33 12.88 39.30 31.71 22.36 0.81 0.981 4 0.3392 117.00 22.23 22.77 4.95 4.54 0.87 0.961 5 0.2699 125.20 22.58 22.42 19.33 10.92 0.71 0.851 6 0.1092 383.73 11.34 44.62 24.32 21.73 0.79 0.96

2 1 1.3216 124.47 50.71 9.98 1.99 2.32 0.79 0.922 2 0.4501 703.11 5.52 91.74 49.57 38.46 0.87 0.992 3 0.4095 753.00 5.22 97.00 68.46 76.81 0.80 0.982 4 0.3080 883.00 5.51 91.72 94.21 51.79 0.88 0.972 5 0.2506 907.47 5.38 94.10 99.09 61.03 0.86 0.992 6 0.2345 589.50 5.03 100.65 72.36 42.56 0.73 0.922 7 0.1891 471.21 6.80 74.46 102.99 40.19 0.75 0.94

3 1 0.7707 186.00 11.94 42.38 40.57 20.59 0.68 0.863 2 0.5585 116.77 10.59 47.78 16.48 12.41 0.82 0.913 3 0.3969 128.50 13.49 37.52 35.81 25.39 0.78 0.973 4 0.3642 381.68 10.24 49.41 13.25 22.64 0.88 0.993 5 0.2758 122.33 17.40 29.10 8.12 6.95 0.90 0.993 6 0.2411 190.55 15.09 33.53 24.98 18.72 0.84 0.993 7 0.2171 235.54 12.90 39.24 23.14 16.91 0.85 0.993 8 0.2067 179.10 20.15 25.12 15.72 11.01 0.83 0.98

0 2000 4000 6000 80000.00

0.01

0.02

0.03

0.04

0.05

0.06 RTD 1 RTD 2 RTD 3 RTD 6

Con

cent

ratio

n (g

/g)

Time (s)tail indicating, according to Alhamdan and Sastry (1998),the presence of dead space in dryer.

Tail from RTD curves generally is observed and severalmodels have been presented for explaining that anomaly.The tail assumes an important role in the accurate estima-tion of the model parameters (Torres & Oliveira, 1998).

4. Determination of the Peclet number

The Peclet number was calculated by using Eq. (3).Results are presented in Fig. 12, for Taylor Dispersion,and in Fig. 13, for Free Dispersion.

Despite Ez varying appreciably for the variety Catua(Experiment 2) with respect to the other varieties, the0 2000 4000 6000 80000.00

0.01

0.02

0.03

0.04

0.05

0.06RTD 1

RTD 2

RTD 3

RTD 6

Con

cent

ratio

n (g

/g)

Time (s)

Fig. 6. RTD for Experiment 1 Taylor Dispersion Model. d, RTD 1; s,RTD 2; m, RTD 3; e, RTD 6.

Fig. 7. RTD for Experiment 1 Free Dispersion Model. d, RTD 1; s,RTD 2; m, RTD 3; e, RTD 6.Peclet number for the Dispersion Models of Taylor andFree remained around 6.5 for all experiments as shown inTable 5.

Dispersion coefficients for the coffee variety Catua werelarger than other varieties. Particles from this variety aresmaller and more spherical. In addition, these particlesare less viscous than the other two varieties. This explainsthe differentiated behavior with a higher trend to dispersiondue to easy of flowing.

The Pe number, which is an important dimensionlessnumber, can be used for the forecast of dispersion coeffi-cient (Ez). This study showed that for experimental condi-tion studied, with Pe 6.5, Ez values can be estimated.

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0 600 1200 1800 2400 3000 36000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 RTD 1 RTD 2 RTD 4 RTD 6

Con

cent

ratio

n (g

/g)

Time (s)

Fig. 10. RTD for Experiment 3 Taylor Dispersion Model.d, RTD 1;s,RTD 2; D, RTD 4; e, RTD 6.

0 600 1200 1800 2400 3000 36000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 RTD 1 RTD 2 RTD 4 RTD 6

Con

cent

ratio

n (g

/g)

Time (s)

Fig. 11. RTD for Experiment 3 Free Dispersion Model. d, RTD 1; s,RTD 2; D, RTD 4; e, RTD 6.

0.00 0.25 0.50 0.75 1.00 1.25 1.500

2

4

6

8

10

12

14

16

PeT

aylo

r ()

X (kg H2O/kg dry coffee)

Exp. 1 Exp. 2 Exp. 3

Fig. 12. Peclet number for Taylor Dispersion.

0 200 400 600 800 1000 1200 14000.000

0.005

0.010

0.015

0.020

0.025

0.0300 1500 3000 4500 6000 7500 9000

RTD 2 RTD 5 RTD 7

Con

cent

ratio

n (g

/g)

Time (s)

RTD 1

Time (s)

Fig. 8. RTD for Experiment 2 Taylor Dispersion Model. d, RTD 1; s,RTD 2; , RTD 5; j, RTD 7.

0 200 400 600 800 1000 1200 14000.000

0.005

0.010

0.015

0.020

0.025

0.0300 1500 3000 4500 6000 7500 9000

RTD 2 RTD 5 RTD 7

Con

cent

ratio

n (g

/g)

Time (s)

RTD 1

Time (s)

Fig. 9. RTD for Experiment 2 Free Dispersion Model. d, RTD 1; s,RTD 2; , RTD 5; j, RTD 7.

0.00 0.25 0.50 0.75 1.00 1.25 1.500

2

4

6

8

10

12

14

16

Pe

[

]

X (kg H2O/kg dry coffee)

Exp. 1 Exp. 2 Exp. 3

Free

Fig. 13. Peclet number for Free Dispersion.Thus, only the coffee berries flow velocity influenced indispersion.Porosity values of coffee cherry before the drying oper-ation to be initiated were: 0.41 (Exp. 1 Acaia), 0.41(Exp. 2 Catua), and 0.40 (Exp. 3 Mundo Novo). For

Table 5Average values of Ez and Pe

Exp. Ez 104 (m2/s) Pe ()

Taylor Free Taylor Free

1 20.70 12.82 5.53 7.282 69.81 44.74 5.35 6.723 22.26 16.83 6.43 7.65

Average 37.59 24.80 5.77 7.22the relationship between Pe and e presented by Auriaultand Adler (1995), we have that Pe (estimated from the FreeDispersion Model) is approximately on the order of e2.Values for the porosity exponent were: 2.23 (Exp. 1), 2.08(Exp. 2), and 2.28 (Exp. 3), indicating that the convectionpredominates on flow of coffee berries in the dryer studied.For the extreme values of Pe, maximum and minimum,found in drying tests Pe on the order of e3.05 and e1.47,respectively.

Ez and Pe results are useful for forecasting dispersion ofcoffee berries in dryers with continuous flow, especially inaccomplishment of modeling for forecast of product homo-geneity, obtained after drying.

5. Conclusions

The best estimative of Ez values was obtained by FreeDispersion Equation (higher correlation coefficients). Thecoffee variety that presented the highest Ez was the Catua(Experiment 2) due to be composed of smaller particles,greater sphericity and to be less stickiness. The Peclet num-ber remained practically constant (6.5) for all experiments,in spite of the great Ez variation. Therefore, flow velocityvariation of coffee berries was the same magnitude of thedispersion coefficient variation. Convection is the domi-nant effect on coffee berries flow in the vibrated tray dryer.

Acknowledgements

This work counted on the financial support from Capesand CNPq, Processes 472200/2001-1 and 470915/200309.

The producer Sr. Serafin Peres, of Amanhece District,Araguari municipality, Minas Gerais State, Brazil, sup-plied coffee cherries.

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Dispersion coefficient of coffee berries in vibrated bed dryerIntroductionCoffee cherries dryingHarvestDryingDescription and operation of vibrated tray dryer

Drying curves

Determination of residence time of coffee berriesDetermination of the Peclet numberConclusionsAcknowledgementsReferences