how to deal with visco-elastic properties of cellular tissues during osmotic dehydration

Journal of Food Engineering 110 (2012) 278–288

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Journal of Food Engineering

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How to deal with visco-elastic properties of cellular tissues duringosmotic dehydration

Laura Oliver a,b,⇑, Noelia Betoret a, Pedro Fito a, Marcel B.J. Meinders b,c,⇑a Instituto Universitario de Ingeniería de Alimentos para el Desarrollo, Universidad Politécnica de Valencia, Valencia, Spainb TI Food and Nutrition, Wageningen, The Netherlandsc Wageningen University and Research Centre, Wageningen, The Netherlands

a r t i c l e i n f o

Article history:Available online 4 May 2011

Keywords:Osmotic dehydrationVisco-elastic behaviourMass transportRelaxation

0260-8774/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2011.04.028

⇑ Corresponding authors. Addresses: TI Food and NuWageningen, The Netherlands. Tel.: +31 317 485University and Research Centre, P.O. Box 17, 6700 AA WTel.: +31 317 480 165 (M.B.J. Meinders).

E-mail addresses: [email protected] (L. Oliv(M.B.J. Meinders).

a b s t r a c t

In this work, vacuum impregnated apple discs with different isotonic solutions (sucrose and trehalose)were equilibrated during osmotic dehydration (55�Brix glucose at 40 �C). Changes in sample composition(water and soluble solid contents), weight and volume are analysed. A mathematical model is proposedto describe and quantify the outflow of water from the protoplast as well as the visco-elastic behaviour ofthe cell. Good correspondence between simulated and measured data of non impregnated samples andsamples impregnated with isotonic solutions of sucrose or trehalose during long term osmotic dehydra-tion is obtained. Fitted values of the cell permeability correspond well with tabulated values. Further-more, also the obtained values of the parameters describing the mechanical properties of the cell walland Hectian strands seem to reflect the observed structural development of these structures for the dif-ferent treated samples well.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Dehydration of agriculture products leads to prolong their shelflife, reduce shipping and packaging cost as a result of decreasedweight and volume, and increase market diversification. Amongthe dehydration treatments, osmotic dehydration has attractedthe attention of many food product developers due to its goodquality preservation results. Osmotic dehydration can be carriedout to obtain several types of products, such as minimally pro-cessed or intermediate moisture products, or as a pre-treatmentbefore drying or freezing.

In osmotic dehydration a cellular tissue is introduced in ahypertonic solution to reduce its water activity. Due to the micro-structure of the plant tissue, the osmotic dehydration cannot sim-ply be explained as a pure osmotic process in which cellmembranes act as a semipermeable barrier, but it should be ex-plained as a process where many other mechanisms are responsi-ble for mass transport (Chiralt and Fito, 2003; Tyerman et al.,1999).

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trition, P.O. Box 557, 6700 AN383 (L. Oliver), Wageningen

ageningen, The Netherlands.

er), [email protected]

In fact, when a cellular tissue is immersed in a hipertonic solu-tion it is exposed to a gradient of chemical potential between thehipertonic solution and the intracellular liquid phase of the cellscontacting the hipertonic solution. This gradient causes an out-flow of water from these cells. As a result, the volume of the pro-toplast decreases and the cells begin to shrink. The water lossfrom the cells in the first layer generates a gradient of waterchemical potential with the subsequent layer of cells, which actsas driving force for water transfer from inner to outer cells.Therefore, the phenomena of mass transfer and tissue shrinkagespread simultaneously from the surface to the center of the tissuewith operation time. Finally, the cells in the tissue center losewater and mass transfer process tends to equilibration with time(Shi and LeMaguer, 2002).

Furthermore, due to the open structure of the tissue and thesemipermeability of cell membranes, there is diffusion of solutesfrom the osmotic solution to the extracellular liquid phase andgain of osmotic solution by capillary forces (Chiralt and Talens,2005). Therefore, the extracellular phase concentrates with timegenerating a chemical potential gradient between the intercellu-lar liquid phase and the intracellular liquid phase; as a resultwater is transferred from cells into the intercellular space throughmembranes. Cells in different layers experience different condi-tions of water loss, solid gain, and tissue shrinkage (Salvatoriet al., 1998).

In addition to mass fluxes in the tissue, structural changes andcell alteration also occur. In fact the microstructure of the plant

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Nomenclature

Ai,t projected area side i at time t [m2]Ap area of the protplast [m2]aw water activity [dimensionless]F force [N]J water flux through the membrane per unit area [kg/

m2 s]K Norrish characteristic constant [dimensionless]k spring constant [N/m3]k/ rate constant porosity change [1/s]L water permeability of the membrane [kg/Pa m2 s]lt thickness at time t [m]m mass [g]m0 initial mass [g]Ms molecular weights of sugar [g/mol]ms mass of soluble solutes [g]ms,i mass of sucrose in the intercellular space [g]ms,l mass of sucrose in the region between the cell wall and

the protoplast [g]ms,p mass of the sucrose in the protoplast [g]mt mass at time t [g]Mw molecular weights of water [g/mol]mw total water mass [g]mw,i mass of water in the intercellular space [g]mw,l mass of water in the region between the cell wall and

the protoplast [g]mw,p mass of the water in the protoplast [g]mx mass of the cell wall and other compounds in the sam-

ple [g]ns number of solute molecules [mol]nw number of water molecules [mol]

R universal gas constant [J/mol K]T absolute temperature [K]t time [s]V volume [m3]V0 initial volume of the sample [m3]Va volume of the air pores [m3]Vc volume of the cell [m3]Vc0 initial volume of the cell [m3]Vi volume between the protoplast and the cell wall [m3]Vl volume of the intercellular liquid [m3]Vp volume of the protoplast [m3]Vp0 initial volume of the protoplast [m3]Vt volume at time t [m3]x solute molar fractionx0 initial solute molar fraction in the protoplastxO environmental solute molar fractionXss mass fraction of soluble solutes of the samples [g/g]Xw moisture content of the sample [g/g]xw water molar fractionZss soluble solutes content of the fruit liquid phase [g/g]DP difference in osmotic pressure [Pa]DP turgor pressure [Pa]/ porosity/0 initial porosity/1 porosity at time t =1g dashpot constant [N/m3]qs density of the sugar solution [g/m3]r membrane reflection coefficient [dimensionless]srel relaxation time [1/s]Vw partial molar volume of water [m3/mol]

L. Oliver et al. / Journal of Food Engineering 110 (2012) 278–288 279

tissue affects the mass transport kinetics (Barat et al., 2001;Marcotte et al., 1991) at the same time as the mass transportprovokes microscopic and macroscopic structure alterations thatin turn affect kinetics development and equilibrium status (Baratet al., 1999; Chiralt and Fito, 2003; Fito and Chiralt, 2003; Lazá-rides et al., 1999). Most of the models for osmotic dehydrationprocess focus on the effect of process conditions on the kineticsof water loss and solids gains. So far, little attention has beenpaid to the influence of structure on mass transfer, even thoughsome authors have demonstrated that structure affects globalmass transfer (Ferrando and Spiess, 2003; King, 1968; Rotsteinand Cornish, 1978; Seguí et al., 2006, 2010) The modelling ofthe osmotic treatments requires a thorough description of thetransport phenomena, the structural changes and their interac-tion since this interaction is directly related to process kineticsand final product quality. Moreover, to develop theoretical mod-els, data is also required on the equilibrium status of the productto define the acting driving force along the process (Fito, 1994).Previous studies (Barat et al., 1999, 2007; Cháfer et al., 2001) inosmotic equilibration or long term osmotic treatments in planttissues have reported the existence of two periods throughoutthermodynamic equilibrium. In the first period, mass and volumedecreased until the compositional equilibrium (pseudoequilibrium) was reached. In this period, the sample shrinkageand deformation was associated with stress accumulation inthe solid matrix (Barat et al., 1998). In the second period, massand volume increased until asymptotic values. Structurerelaxation was reported to promote a bulk flux of osmotic solu-tion into the fruit tissue (Barat et al., 1999). Finally, differencesin pressure disappeared, and the solid cellular matrix becamefully relaxed.

Evaluation of the long term osmotic treatments provides a bet-ter understanding of the phenomena that control the mass trans-fer processes in osmotic dehydration. Moreover, vacuumimpregnation allows the introduction of a solution with somespecific components into products (Fito and Pastor, 1994; Fito,1994) adapting their composition to certain quality or stabilityrequirements (Martínez-Monzo et al., 1998). The products modifytheir mass transfer behaviour, not only because of its porosityreduction (Barat et al., 2001; Fito and Chiralt, 1997), but alsodue to the protective action that some components may haveon the cellular structures. Disaccharides, as glucose and trehalose,have a significant role in preserving the membrane functionalityin dry state (Ferrando and Spiess, 2001). Combination of vacuumimpregnation pre-treatment with long term osmotic treatmentmakes it possible, to some extent, to promote and controlchanges on the structural elements. This gives us the opportunityto characterise the response of the structural elements and theireffect in mass transport.

The aim of this paper is to progress in the knowledge of theimportance of cellular structure in dehydration of plant tissue atthe macroscopic level; and to develop dehydration models suitableto evaluate and quantify the mechanical characteristics of thematerials and the relationship between the structural elementsin the mass transfer process. Therefore, vacuum impregnated applediscs with different isotonic solutions (sucrose and trehalose) aswell as non-impregnated apple discs were equilibrated during os-motic dehydration (55�Brix glucose solution at 40 �C). Their prop-erties like mass, volume, moisture content, and soluble solidconcentration were followed in time. A mathematical model wasdeveloped and the simulation results compared with the experi-mental results.

280 L. Oliver et al. / Journal of Food Engineering 110 (2012) 278–288

2. Materials and methods

2.1. Raw material

Granny Smith apples of appropriate ripeness (moisture content0.857 ± 0.012 H2O g/g w.b., aw = 0.984 ± 0.004 and 11.9 ± 1.2 �Brix)were purchased from the local market and stored at 4 �C until fur-ther use. The apples were sliced perpendicular to the axe directionin slices of 5 mm thickness and having 20.70 and 64.40 mm innerand outer diameter, respectively.

2.2. Solutions

2.2.1. Impregnating solutionsVacuum impregnation experiments were carried out with aque-

ous solutions of sucrose and trehalose. The impregnation solutionswere isotonic regarding to the content of apple native soluble sol-ids to avoid mass transfer other than the bulk flux in the openpores, which is caused by pressure gradients (hydrodynamicmechanism). As reported by Barat et al. (1999), the water activityof fresh Granny Smith apple was considered 0.986 (which is inthe deviation range of the used samples). Consequently, it was pos-sible to analyze the effect of the different sugars.

2.2.2. Osmotic solutionIn all the osmotic treatments, a 55�Brix sucrose solution was

employed as the osmotic solution. Potassium sorbate (Sigma,Poole, UK, 5000 ppm) was added to the osmotic solution to preventmicrobial growth.

2.3. Experimental methodology

The apple slices were dipped in a plastic vessel containing theimpregnating solution. Vacuum impregnation (VI) was carriedout in vacuum desiccators at room temperature. A pressure of50 mbar was applied to the system for 10 min, followed by atmo-spheric pressure restoration. Samples were kept immersed for10 min more. After VI, the samples were transferred to the osmoticsolution. In order to assure the internal control of mass transfer, anappropriate agitation level (280 rpm) was applied to the system.The solution-fruit ratio was 20:1 to avoid significant changes inthe solution concentration during the process. The processing tem-perature was maintained at 40 �C by placing the flask in a thermo-static bath. The effect of vacuum impregnation on the behaviour ofthe samples during the osmotic treatment was analysed by pro-cessing fresh samples using the same operation conditions. At dif-ferent times after immersion samples were taken out of theosmotic solution, gently drained with tissue paper and character-ised in terms of weight, volume, moisture content and soluble sol-ids content. Samples were controlled until the samples massreached a constant value.

Vacuum impregnation pre-treatment and all the experimentalseries were carried out in triplicates and mean values are reportedfor measured variables.

2.4. Analytical determinations

All the analytical determinations were carried out in triplicate.The samples were homogenised before the analysis.

2.4.1. Moisture contentThe moisture content Xw of fresh and treated samples was

determined gravimetrically by drying the samples in a vacuumoven (�410 mbar) at 60 �C until constant weight was reached(AOAC, 1997).

2.4.2. Soluble solutes contentThe soluble solutes content of the fruit liquid phase Zss was

measured with a portable refractometer Refracto 30GS (Mettler-Toledo, Germany). The measured value was used to calculate thesoluble solutes content of the fruit samples Xss (Eq. (1)).

Xss ¼ Zss � Xw

ð1� ZssÞ ð1Þ

where Xw is the moisture content of the sample [g/g], Xss is the massfraction of soluble solutes of the samples [g/g], and Zss is the solublesolutes content of the fruit liquid phase [g/g].

2.4.3. Determination of volume changesThe sample volume at time t was determined by Eq. (2):

Vt ¼ ðA1;t þ A2;t

2Þ � lt ð2Þ

where Vt [m3] is the volume at time t, Ai,t [m2] is the projected areaside i at time t, and lt [m] is the thickness at time t.

The projected area Ai,t was measured from a digital picture ofthe sample taken at different times. Therefore the apple slices wereplaced between two glasses and a perpendicular image was ac-quired for each side. Acquired images were analysed using AdobePhotoshop CS (v 8.0.1). The thickness lt was measured using a dig-ital calliper.

2.4.4. Statistical analysisStatistical analyses were carried out using STATGRAPHICS� Plus

5.1 software. Data were subjected to a multiple analysis of variance(ANOVA) at the 95% confidence level.

2.5. Mathematical modelling

In order to study in detail the osmotic dehydration operationand to be able to describe the different mechanisms involved inthe process. A mathematical model is proposed that describesthe flux of water through the cell membrane as well as the relaxa-tion of the structural elements. For the modelling, the apple isviewed as an ensemble of identical cells. In between the cells thereare pores partly filled with air and partly with intercellular liquid.For simplicity we assume that all cells and pores are exposed to thesame environment. In that case the apple can be modeled as a sin-gle cell so that the total volume of the apple V can be written as

V ¼ V c þ Va þ V l ð3Þ

with Vc is the volume of the cell [m3], Va is the volume of the airwithin the pores [m3], Vl is the volume of the intercellular liquid[m3] .

2.5.1. Single cellFig. 1 shows a schematic diagram of the evolution of one cell

during the osmotic dehydration process (for a more detail descrip-tion, see e.g. Seguí et al., 2010). In a fresh plant tissue, the intracel-lular solutes exert high osmotic pressure in the protoplast pressingtightly the protoplast to the cell wall. Due to the elasticity of thecell walls, hydrostatic pressures can be built up inside plant cells.This pressure is defined as the turgor pressure (Fig. 1a). When planttissue is placed in a hypertonic solution, water flows from the pro-toplasm to the solution due to the gradient in chemical potential.Upon removal of some water the protoplast shrinks (1b). Conse-quently the protoplasm may retract from the peripheral layers ofthe cell towards the middle either pulling away from the cell wall(Hurst and Stubbs, 1969) and/or detaching from the latest(plasmolysis, Fig. 1c). During the plasmolysis, the cell walls are stillable to withstand the tension from the Hechtian strands(membrane-to-wall linkers), and deform (Seguí et al., 2010). Due

Jos

a c edb

x0

x

Jw

x0< x x0< x

x0

x

Jw

x0< xVc=Vp+Vi

x0

x

Jw

Jos

x0≈ x

Vp

Vix0

x Jos

x0≈ x

x0

x

t

k11k12

η12

k21 Vc

Vp

f

x0 x0

w

x0 Vp

Vix0 x0

t

k11k12

η12

k21 Vc

Vp

Fig. 1. Schematic diagram of the evolution of one cell during the osmotic dehydration process (a–e) and springs-dashpot model describing the visco-elastic behaviour of thecell (f). x is the solute fraction inside the protoplast, xO is the solute fraction of the environment, Jw is the transmembrane water outflow, Jos is the bulk osmotic solution flux, Vc

is the volume of the cell, Vp is the volume of the protoplast and Vi is the volume between the cell wall and the protoplast.


to the visco-elastic properties of the cell it may relax towards itsundeformed state. This structural relaxation causes that the out-side osmotic solution flows into the space between the protoplastand cell wall. When the chemical equilibrium between the proto-plast and surroundings is achieved (1d), the loss of cellular waterand shrinkage of the protoplast and cell stops. After that the struc-tural relaxation becomes more apparent and provokes volumerecovery (Fig. 1e).

The cell is considered to consist of the protoplast and the regionbetween the protoplast and the cell wall. The volume of the cell Vc

is than given by

V c ¼ Vp þ Vi ð4Þ

with Vp is the volume of the protoplast [m3], and Vi is the volumebetween the protoplast and the cell wall [m3].

2.5.1.1. Change of protoplast volume due to water flux across themembrane. According to Kedem and Katchalsky (1958) the waterflux crossing a plant membrane may be written as:

J ¼ LðDP � rDPÞ ð5Þ

where J is the water flux through the membrane per unit area [kg/m2 s], L is the water permeability of the membrane [kg/Pa m2 s], DPis the turgor pressure [Pa], D

Qis the difference in osmotic pressure

across the semipermeable membrane [Pa], is r is the membranereflection coefficient [dimensionless]. The cell membrane is consid-ered to be a semipermeable barrier. An ideal semipermeable mem-brane would have r = 1. The cell wall is considered to be permeable.

The osmotic pressure across a semipermeable membrane (DP)can be approximated using the van’t Hoff equation:

DP ¼ � RTVw

D ln aw ð6Þ

where R is the universal gas constant [J/mol K], T is the absolutetemperature [K], Vw is the partial molar volume of water [m3/mol], and aw is the water activity.

According to Norrish (1966):

aw ¼ xw expð�K � x2Þ ð7Þ

where K is the characteristic constant for each solute [dimension-less], xw is the water molar fraction, and x is the solute molarfraction.

The solute molar mass fraction may be defined as:

x ¼ ns

ns þ nwð8Þ

xw ¼ 1� x ð9Þ

where ns is the number of solute molecules [mol], and nw is thenumber of water molecules [mol].

Substituting the Norris equation (Eq. (7)) into the van’t Hoffequation (Eq.(6)) gives after some straightforward algebra:

DP ¼ RT

Vw

11� x

þ 2kx� �

Dx ð10Þ

For small x this reduces to:

DP ¼ aDx ð11Þ

where a ¼ RT=Vw is a constant and Dx = x � xO is the difference be-tween the solute molar mass fraction in the protoplast (x) and thatof the environment (xO).

The turgor pressure is positive at the beginning of the dryingprocess. However, a small water flow outside of the protoplast im-plies the loss of the turgor pressure. Therefore, we assume that DPcan be neglected. Otherwise the effect of P can also be covered bythe variable a. We find that:

J ¼ a0Dx ð12Þ

with

a0 ¼ Lar ¼ RTVw

Lr ð13Þ

When there is a difference in solute concentration, there will be awater flux across the membrane that will result in a change inthe amount of water in the protoplast and consequently a volume


change of the protoplast. Assuming that the protoplast is spherical,the time derivative of the water mass in the protoplasm can beapproximated by,

_mw;p ¼ ApJ ¼ kV23pDx ð14Þ

where the dot indicates the time derivative, mwp is the mass of thewater in the protoplast [g] and Ap and Vp are the area [m2] and vol-ume of the protoplast [m3], respectively, and

k ¼ ð36pÞ13a0 ¼ ð36pÞ

13

RT

Vw

� �Lr ð15Þ

is a constant. The volume of the protoplast may be approximatedby:

Vp ¼mw;p þms;p

qs¼ nwMw þ nsMs

qsð16Þ

where ms,p is the sugar mass in the protoplast [g], Mw and Ms are themolecular weights of water and sugar [g/mol], respectively, and qs

is the density of the sugar solution [g/m3]. The latter is a function ofthe sugar concentration. For the calculation we used the approxi-mation by Bubnik et al. (1995).

The molar solute fraction (x) can directly be calculated frommw,p and ms,p, the latter being constant in the protoplast, usingEqs. (8) and (16) The same formulas can be used to calculatems,p, from protoplast volume and solute fraction, assumed to beknown at the beginning of the experiment. The change of the vol-ume of the protoplast with time can be calculated by differentiat-ing Eq. (16) with time. This yields:

_Vp ¼1qsþ Vp

qs

dqs

dms;p

� �_mw;p ð17Þ

2.5.1.2. Change of cell volume due to shrinkage protoplast and visco-elastic behaviour. It is assumed that the cell wall and the Hech-tian strands behave visco-elastically with respect to a change inshape. It is also assumed that the turgor pressure due to the elas-ticity of the cell wall does not change the water flux and that thelatter is thus determined solely by the solute concentration dif-ference between protoplasm and environment. The visco-elasticbehaviour of the cell may be approximated by the springs-dash-pot model depicted in Fig. 1f. The volume of the protoplast (Vp) iscontrolled by the water flux (J) due to a difference in solute con-centration between the in and outside of the protoplast. Due to achange in Vp a force (F11) due to the spring (k11), a force (F12) dueto the spring (k12)-dashpot (g12) system, and a force due tot thespring (k21) will be exerted on the cell wall. It is found that:

F11 ¼ �k11ðV c � Vp � ðV c0 � Vp0ÞÞ ð18Þ

F21 ¼ k21ðVc0 � V cÞ ð19Þ

_F12 ¼ k12ð _Vc � _VpÞ � þk12

g12F12 ð20Þ

The equation of motion obtained by summing these forces will thendescribe the volume change that is contained by the cell wall (Vc).We can assume that the mass of the cell wall is very small so thatwe can neglect inertia effects. In that case F12 ¼ �F11 � F21. Aftersome algebra we find that the time derivative of the cell volumecan be written as

_Vc ¼ðk11 � k12Þ _Vp þ k12

g12F12

k11 � k12 � k21ð21Þ

Eqs. (14) and (21) form a set of 2 coupled ordinary differential equa-tions (ODE) that can be solved numerically applying the appropriateboundary conditions. The relaxation time of the system is equal to:

srel ¼ g12k21 þ k12 � k11

k21k12 þ k11k12ð22Þ

Initially, at time t = 0, it is assumed that the volume of the cell(Vc0) is known and is equal to that of the protoplast (Vp0). The ini-tial amount of sucrose present in the protoplast can be derivedfrom the initial solute molar fraction (x0), the initial volume ofthe protoplast (Vp0) and the sucrose density (qs).

2.5.1.3. Change of intercellular air volume due to OD. For the non-impregnated samples it was found from comparison of the modeloutcome and experimental results that the volume of the air pores(Va) decreased during osmotic dehydration. This was modeled asfollows:

Va ¼ uV0 ð23Þ

u ¼ u1 � ðu1 �u0Þ expðkutÞ ð24Þ

where V0 is the initial volume of the sample [m3], u = ut is the timedependent porosity, u0 is the porosity at time t = 0, u1 is the poros-ity at time t =1, ku is the rate constant [1/s], and t is the time [s].

2.5.1.4. Intercellular liquid volume. Because (1) the intercellular li-quid volume Vl is small with respect to volume of the cell andair, (2) it is more or less constant during the OD, (3) has a minoreffect on the simulation outcome, and (4) the available experimen-tal data is not accurate enough to distinguish well between cell andintercellular volume, we neglected the intercellular liquid volumein the calculations and assumed Vl = 0

2.5.1.5. Comparison experiment and model simulation. The modelparameters are estimated by comparing the experimental datawith the model outcome. The measured parameters during the os-motic dehydration and relaxation process are the mass (m) andvolume (V), the total water mass (mw), and the sugar mass fractionXss of the apple sample, which is considered equal to soluble sol-utes content of the samples. These experimental parameters are re-lated to the model parameters as follows:

m ¼ ðmw;p þms;pÞ þ ðmw;i þms;iÞ þ ðmw;l þms;lÞ þmX ð25Þ

mw ¼ mw;p þmw;i þmw;l ð26Þ

Xss ¼ ms;p þms;i þms;l

mð27Þ

where mw,p is the mass of the water in the protoplast [g], ms,p is themass of the sucrose in the protoplast [g], mw,l is the mass of water inthe region between the cell wall and the protoplast [g], ms,l is themass of sucrose in the region between the cell wall and the proto-plast [g], mw,i is the mass of water in the intercellular space [g], ms,i

is the mass of sucrose in the intercellular space [g], and mX is themass of the cell wall and other compounds in the sample [g].

The mass of the water and sucrose in the protoplast are calcu-lated using the above described equations and ODE’s. The massof the water and sucrose in the region between the cell wall andthe protoplast can be calculated from the volume Vi = Vc � Vp andthe sucrose mass fraction which is here equal to the outside xO.The intercellular liquid volume is assumed to be constant whileits sucrose mass fraction is allowed to vary according to Eq. (25).The mass of the cell wall and other compounds in the apple are as-sumed to be constant.

Calculations are performed using Matlab (Mathworks). Fittingwas performed using the Levenberg–Marquardt algorithm.


3. Results and discussion

3.1. Study of sample evolution to the equilibrium stage

During the operation of osmotic dehydration, fluxes of waterand soluble solids cause a change in the total mass and in the com-position of the tissue and consequently in the total volume of thesample. The net change of the mass (Dmt), water (Dmw,t), solublesolutes (Dms,t) and volume (DVt) of the apple slice were calculatingfor each treatment according to the following equations

Dmt ¼ðmt �m0Þ

m0ð28Þ

Dmw;t ¼ðmt � Xw

t �m0 � Xw0 Þ

m0ð29Þ

Dms;t ¼mt � Xss

t �m0 � Xss0

� �m0

ð30Þ

0 0.5 1 1.5 2 2.5

x 104

-0.6

-0.4

-0.2

0

0.2

0.4

no VI

t (min)

ΔM

o t, ΔM

w t, Δ

Mss t

, ΔV

o t

0 0.5 1 1.5 2 2.5

x 104

-0.6

-0.4

-0.2

0

0.2

0.4

VI: Sucrose

t (min)

ΔM

o t, ΔM

w t, Δ

Mss

-t, Δ

Vo t

0 0.5 1 1.5 2 2.5

x 104

-0.6

-0.4

-0.2

0

0.2

0.4

t (min)

ΔM

o t, ΔM

w t, Δ

Ms s t, Δ

Vo t

VI: Trehalose

Fig. 2. Experimentally determined relative change of the apple slice mass (DMot , j), wa

samples and samples impregnated with sucrose and trehalose during OD in a 55�Brix sufigures in the right side show only the first period. Each point represents the average valuindicate standard deviations.

DV t ¼ðV t � V0Þ

V0ð31Þ

Fig. 2 shows the measured evolution of net change of mass,water, solutes and volume for non impregnated samples and sam-ples impregnated with sucrose and trehalose during OD in a55�Brix sucrose solution at 40 �C. The right panels zoom in onthe first time period. These results corroborate the existence oftwo periods in cellular tissues equilibration for all the treatments.In the first period the apple shrinks and mass decreases due towater flux from the protoplast to the outside environment whilein the second period the apple expands and mass increases againdue to the relaxation of the cell wall towards its original shape.The change from shrinkage to expansion is between 420 and1440 min for all treatments.

In the first period, the gradient of chemical potential betweenthe hypertonic solution and the intracellular liquid phase is thedriving force for water removal and solute gain. This water loss

0 500 1000 1500

-0.6

-0.4

-0.2

0

0.2

no VI

t (min)

ΔM

o t, ΔM

w t, Δ

Mss t

, ΔV

o t

0 500 1000 1500

-0.6

-0.4

-0.2

0

0.2

VI: Sucrose

t (min)

ΔM

o t, ΔM

w t, Δ

Mss t

, ΔV

o t

0 500 1000 1500

-0.6

-0.4

-0.2

0

0.2

t (min)

ΔM

o t, ΔM

w t, Δ

Ms s t, Δ

Vo t

VI: Trehalose

ter (DMwt , N), soluble solutes (DMss

t , d) and volume (DVot , h) for non impregnated

crose solution at 40 �C. Figures at the left side show the whole treatment, while thee of triplicates. The dotted line represents the limit between two periods. Error bars

-0.7

-0.5

-0.3

-0.1

0.1

0.3

0.5no VIVI: SUCVI: TRE

-0.7

-0.5

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-0.1

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0.3

0.5no VIVI: SUCVI: TRE

ΔMot ΔMw

t ΔVot

ΔMsst

ΔMot

ΔMwt ΔVo

t

ΔMsst

a

b b

a

b b

a a a

aa a

a

b b

a ab b

a

b b

a a a

no VIVI: SUCVI: TRE

no VIVI: SUCVI: TRE

ΔMot ΔMw

t ΔVot

ΔMsst

ΔMot

ΔMwt ΔVo

t

ΔMsst

a

b b

a

b b

a a a

aa a

a

b b

a ab b

a

b b

a a a

no VIVI: SUCVI: TRE

Δ Δ Δ

Δ

ΔMot

ΔMwt ΔVo

t

ΔMsst

a

b b

a

b b aa a

a

b b

a ab b

a

b b

a a a

Fig. 3. Experimentally determined net change of mass, water soluble solutes andvolume at the end of the first (top) and second period (bottom). Different lettersshow statistically significant differences between means at P < 0.05.


and the soluble solids uptake result in a moisture content decreaseand a soluble solids content increase.

The outflow of water from the protoplast results in cell volumedecrease and cell wall deformation. Due to the visco-elastic prop-erties of the cell, the deformation of the cell wall involves accumu-lation of (elastic) free energy in the system as mechanical stress aswell as instant relaxation. In fact, the transmembrane transport,the structural shrinkage and relaxation occur simultaneously;however, they have different rates. Moreover, the relaxation of vis-co-elastic cell walls promotes bulk flux of osmotic solution (Baratet al., 1999). In the first period of osmotic dehydration, transmem-brane transport and structural shrinkage is faster than the struc-tural relaxation. Therefore, mass fluxes in the system involvedconsiderable weight and volume losses since the characteristicrelaxation time and the subsequence bulk flux are larger thanthe characteristic transmembrane transport.

The rate of transmembrane transport decreases as the gradient ofwater and solute activity between the intracellular liquid phase andthe osmotic solution is reduced. Therefore, bulk flux of osmotic solu-tion due to structural relaxation becomes significant. This explainsthe mass and volume gain observed during the second period.

Fig. 2 shows that the application of impregnation treatment af-fects the evolution of the samples during osmotic dehydration. Thenon impregnated samples presented greater maximum mass andvolume change as well as greater mass and volume recovery. Thisdifference shows that the application of a vacuum impregnationpre-treatment influences on the mechanisms acting in the osmoticdehydration process. The vacuum impregnation promotes the bulkflux of impregnating solution into the porous of the sample, thusaffecting transport mechanisms. As reported by other authors (Bar-rera et al., 2004, 2009; Escriche et al., 2000; Fito et al., 2001), vac-uum impregnation with isotonic solutions promotes effectivediffusion in the intercellular liquid phase.

In the second period, the impregnated samples reached the con-stant mass earlier (t � 1.4�104 min) than the non-impregnatedsamples (t > 2 � 104 min; Fig. 2). The later increase of mass innon-impregnated samples may be attributed to replacement ofgas that remained in the intracellular space (Barat, 1998), oncethe bulk flux of osmotic solution into the fruit tissue by relaxationof the structure may finish.

The sample volume variation show the same trend as the sam-ple mass variation: decreasing to a minimum value in the first per-iod and increasing in the second one.

Fig. 3 shows the statistical analysis of the effect of the differenttreatments on net change of mass, water, soluble solutes and vol-ume at the end of the first and second period. The multiple analysisof variance (P < 0.05) revealed that the application of impregnationtreatment affects the change of mass. This effect becomes moreapparent in the second period. In the first period, the non-impreg-nated samples show more water loss than the impregnated ones.However, the solid gain does not present significant differencesin this first period. The multiple analysis of variance revealed alsothat the substitution of sugar in the vacuum impregnation step didnot have a significantly effect on the change of mass. The change ofvolume does not present significant differences

Fig. 4 shows the measured solute mass fraction of the liquidphase of the apples. This is assumed to be equal to the sugar massfraction of the protoplast. From the figure it is seen that the solutemass fraction of the protoplast approaches equilibrium, corre-sponding to the situation when it is equal to the solute concentra-tion of the environmental osmotic solution. It is noted that thesolute content of the osmotic solution, which was periodically con-trolled and kept at 55�Brix, was measured at 40 �C. However, thesolute concentration of the fruit liquid phase was measured at20 �C. In Fig. 4 the solute content of the osmotic solution correctingthe effect of the temperature is also plotted.

In a previous study, Barat et al. (2007) reported that by the timethat the samples reached the maximum mass and volume varia-tion, solute concentration of the fruit liquid phase was higher thanthat of the osmotic solution. These authors suggest that a gradientof osmotic pressure should appear to balance the stress accumu-lated in the solid matrix during fruit concentration. We think thatthis interpretation might be wrong. If there would be a stress onthe protoplast due to its shrinkage, it is expected that it opposesthe shrinkage so that the equilibrium solute concentration wouldbe lower than the outside one.

3.2. Model fitting

The proposed model describes the physical and biologicalmechanisms during osmotic dehydration, like the shrinkage ofthe protoplasm and cell due to the osmotic dehydration, relaxationof the cell wall, and loss of intercellular air volume in a number ofmodel parameters.

The volume of air plays an important role in the relation be-tween the mass and the volume (Barat et al., 2001). It is assumedthat the loss of air from the intercellular space during the osmoticdehydration is due to the shrinkage of the cells that causes thatalso the capillary pores change in size, which in turn causesthat some air can escape from the sample. Therefore, we assumethat the volume of the air in the pores (Va) decreases during

0 0.5 1 1.5 2 2.5

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

t (min)

Zss (g

sol

uble

sol

ids/

g liq

uid

phas

e)

20°C

40°C

Fig. 4. Evolution of solute mass fraction in the product liquid phase for eachtreatment (no VI (N), Sucrose (s), Trehalose (h)). The dotted line represents thesolute mass fraction of the environmental sucrose solution at 20 �C. The continuousline represents the solute mass fraction of the environmental sucrose solution at40 �C. Each point represents the average value of triplicates, error bars indicatestandard deviations.


osmotic dehydration at the same rate as the protoplast shrinks.This rate was estimated by fitting an exponential function to theexperimental data shown in Fig. 4

0 2 4 6 8 10

x 105

0.006

0.008

0.01

0.012

0.014Mass sample

t (s)

m (k

g)

0 2 4 6 8 10

x 105

0

0.002

0.004

0.006

0.008

0.01

0.012

t (s)

mi (k

)

Mass

0 t (s) 1 x 105

0 t (s) 1 x 105

Fig. 5. Best results of the model compared with the experimental data of a sample impre40 �C. Total mass evolution, top left; and volume sample evolution, top right. The dots a(experimental data (s), and modelled data (—)), sucrose mass evolution (experimental da(h), and modeled data (��)), bottom left; and water mass fraction evolution (expe(experimental data (d), and modeled data (——)), bottom right. The insets show a blow-ularge figure.

Zss ¼ Zss1 � ðZ

ss1 � Zss

0 Þ expð�k/ � tÞ ð32Þ

with Zss0 and Zss

1 the value of solute mass fraction in product liquidphase (Zss) at t = 0 and t =1, respectively; k/ is the rate constant[1/s], and t is the time [s]. This resulted for the rate of air volumedecrease k/ = 10�4 1/s (see Eq. (23)).

Preliminary comparisons of the model outcome with the exper-imental data show that the mechanical parameters are correlatedand that the available experimental data was not (accurate) en-ough to get a unique set of values for the parameters. To overcomethis and to be able to compare the mechanical parameters betweendifferent treatments, we assume that the inherent elasticity of thecell wall (k21) does not depend on the application of vacuumimpregnation with isotonic solutions. Therefore, the parameterk21 was fitted against the experimental data of the non impreg-nated samples and considered constant for all the studied cases(k21 = 10�7 N/m3).

The equilibrium value of the volume of the cells at t =1 (Vc,1) iscontrolled by the parameters k11 and k21. It is given by

Vc;1 ¼k11Vp1 þ k21V c0

k11 þ k21ð33Þ

with Vp1 is the volume of the protoplast at t =1. In various cases, thefinal volume of the samples is measured to be smaller than the initialone, indicating k11 – 0. The final mass of the samples might be largerthan the initial one due to the higher density of the liquid phase ofthe osmotic solution with respect to that of the isotonic one. In thecalculations the final mass was set to be equal to the experimentallyderived value. The value of k11 can be estimated from Eq. (33) andthe fit-parameter k21. Vc and Vp1 were determined according toEqs. (3) and (19). The estimated k11 were (8 ± 2) � 10�9 N s/m3 fornon-impregnated samples, (2 ± 0.4) � 10�8 N s/m3 for samples

0 2 4 6 8 10

x 105

0.6

0.8

1

1.2

1.4x 10

-5 Volume sample

t (s)

V (m

3 )

0 2 4 6 8 10

x 105

0

0.2

0.4

0.6

0.8

1Mass fraction

t (s)

x i (kg

i/kg

)

0 t (s) 1 x 105

0 t (s) 1 x 105

gnated with sucrose and dehydrated osmotically with a 55�Brix sucrose solution atre experimental data and lines correspond to modelled data. Water mass evolutionta (d), and modeled data (——)) and solid matrix mass evolution (experimental data

rimental data (s), and modeled data (—)), and sucrose mass fraction evolutionp of the dehydration at the first period; the units in the y-axis are equal to that of the

0

1

2

3

4

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6

7

(N/m

3 )

no VIVI SUCVI TRE

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)

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)

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3 )

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a

a

a

x10-8 x10-7

aa

a

x10-2

a

ba

x10-5

a

b

a

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no VIVI SUCVI TRE

10

no VIVI SUC

VI TRE

no VIVI SUCVI TRE

a

a

a

aa

a

a

ba

a

b

a

no VIVI SUC

VI TRE

no VIVI SUCVI TRE

a

a

a

aa

a

a

ba

L k12

η 21 τ

Fig. 6. Estimated cell permeability L (top left), estimated k12 (top right), estimated g12 (bottom left) and estimated srel (bottom right). Different letters indicate significantdifferences (P 6 0.05).

Fig. 7. Schematic diagram of the evolution of one cell during osmotic dehydrationprocess (OD) and osmotic dehydration process with impregnation pre-treatment(VI + OD). x is the solute fraction inside the protoplast, xO is the solute fraction of theenvironment, Jw is the transmembrane water outflow, Jos is the bulk osmoticsolution flux.


impregnated with sucrose and (1 ± 0.2) � 10�8 N s/m3 for samplesimpregnated with trehalose.

The only unknowns in the model are now the parameters k, k21,k12 and g12. These are estimated from fitting simultaneously themodeled values of the total mass (m), total volume (V), water mass

(mw), solute mass (ms), and water and solute mass fraction (Xw andXss, respectively) of the sample against the measured values. Seealso the section ‘‘Comparison experiment and model calculation’’.Fig. 5 shows typical examples for the best simulated results ofthe model compared with experimental data. In general, the modelis able to simulate the evolution of the mass and volume, as well asthe composition of the sample.

The cell permeability (L) was determined according to Eq. (15)once the value of k was obtained. Fig. 6 shows that there are no sig-nificant differences in the water cell permeability for the appliedtreatments. This suggests that the usage of the isotonic solutionsof sucrose and trehalose does not affect the cell permeability. How-ever, some authors (Atarés et al., 2009; Ferrando and Spiess, 2001)suggested that the use of different sugars as osmotic agent has aneffect in the cell permeability. The estimated cell permeability val-ues ((7 ± 2) � 10�8 s/m) correspond well with reported values ofwater permeability for plant cells, which is between 10�9 and10�8 s/m (Ferrier and Dainty, 1978; Green et al., 1978; Hüskenet al., 1978).

The effect of the applied vacuum impregnation process on theparameters k12 and g12 (including relaxation time srel = k12/g12)that describe the mechanical properties of the cell are shown inFig. 6. The elastic (k12), visco-elastic (g12) modulus, and therelaxation time (srel) are lower for the impregnated samples. Thedifferences in elastic and visco-elastic modulus may explainthe different structural responses for impregnated and non-impregnated samples during osmotic dehydration observed


previously (Barat et al., 1999). In the case of impregnated samples,the water loss causes that the protoplast retracts from the periph-eral layers of the cell towards the middle pulling away from thecell wall. In the case of impregnated samples, the water loss causedthat the protoplast detaches from the cell wall with scarce defor-mation of the cell wall. This is depicted in Fig. 7 and is in line withthe values we find for the mechanical parameters. The higher theelastic and visco-elastic modulus, the stronger the interaction be-tween cell wall and protoplast. In the case of non impregnatedsamples, the higher elastic and visco-elastic modulus causes thatthe cell wall will deform more than in the case of the impregnatedsamples, where the elastic and visco-elastic modulus is lower. Thisis also in line with the observed faster relaxation for non-impreg-nated samples than for the impregnated ones, as can be seen inthe bottom-right panel of Fig. 6.

Differences among the two impregnation treatments might berelated to the integrity of the interaction between cell wall andprotoplast and its tolerance to stretching. Ferrando and Spiess(2001) reported the protective effect of trehalose on plasma mem-brane in onion epidermis cells during osmotic dehydration. Theseauthors suggested that the trehalose favours a high formation ofHechtian strands, and therefore the ability of the protoplast toshrink, maintaining their linkage to the cell wall. This will be re-flected in the higher visco-elastic modulus that the samplesimpregnated with trehalose present.

4. Conclusions

During the equilibration of plant tissue in hypertonic solutionstwo periods were differentiated. The relative importance of trans-membrane transport and relaxation phenomena was different ateach period. In the first period the volume of the sample decreasesbecause water loss due to the transmembrane transport is largerthan water gain due to structural relaxation of the cell wall, whilein the second period this was opposite.

A mathematical model was developed and proposed in thiswork that was able to simulate the experimentally observedbehaviour during short and long term osmotic dehydration well.Good quantitative correspondence was obtained between mea-sured and calculated volume, mass, water content and concentra-tion of soluble solids of apple samples that are not impregnatedand impregnated with isotonic solution of sucrose or trehalose.Obtained values of the cell permeability correspond well withtabulated values. Furthermore, also the obtained values of theparameters describing the mechanical properties of the cell walland Hectian strands seem to reflect the observed structuraldevelopment of these structures for the different treated sampleswell.

Acknowledgements

The authors would like to thank Cargill Benelux B.V for supply-ing trehalose.

The author L. Oliver acknowledges Conselleria d’Educació (Gen-eralitat Valenciana) for her FPI grant (BFPI06/504) and the financialsupport for the stage in The Netherlands (BEFPI/2008/005, BEFPI/2009/014, and BEFPI/2010/013).

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