Journal of Food Engineering 64 (2004) 81–87 www.elsevier.com/locate/jfoodeng
Moisture diffusivity and transfer modelling in dry biscuit Valerie Guillard a,b, Bertrand Broyart c, Stephane Guilbert d, Catherine Bonazzi c, Nathalie Gontard a,* a
UMR IATE (Ing enierie des Agropolymeres et des Technologie Emergentes), Universit e Montpellier II, cc023, place Eugene Bataillon 34095 Montpellier cedex 5, France b CTCPA, 11 rue Marcel Lucquet, 32000 Auc France c UMR G enie Industriel Alimentaire, ENSIA-INRA, 1 avenue des olympiades, 91744 Massy cedex, France d UMR IATE, ENSAM-INRA, 2 place Pierre Viala, 34060 Montpellier cedex 1, France Received 3 June 2003; accepted 13 September 2003
Abstract Experimental moisture transfer at 20 C within a biscuit was evaluated using water vapour sorption kinetics or moisture migration experiments in a two compartment 0.99 aw agar gel/biscuit system. In each case, moisture transfer was successfully modelled using mathematical models based on Fick’s second law. The model for moisture transfer in composite food was successfully validated with a lower agar gel aw (0.90) and also with an acetylated monoglycerides film at the interface of biscuit and agar gel. Diffusivity estimated from sorption kinetics was found to increase till a moisture content close to the monolayer value, and then, to decrease at higher moisture content. Diffusivity estimated from moisture migration experiments in an agar gel/biscuit system varied in the same way but was found about two fold higher than diffusivity values estimated from sorption kinetic. This difference in diffusivity values could be partially explained by the significant influence of an external resistance to moisture transfer (evaluated to about 0.018 m/s) at the air/biscuit interface during sorption kinetics. 2003 Elsevier Ltd. All rights reserved. Keywords: Moisture transfer; Dry cereal-based food; Effective diffusivity; External transfer resistance; Simulations
1. Introduction Due to the high consumer demand for ready-to-eat foods with good nutritional and organoleptic qualities and a sufficient shelf-life, recent trends in the food industry are the development of composite foods associating a dry crispy compartment with a soft filling containing limited sugar and lipids. Moisture transfer from the ‘‘wet’’ to the ‘‘dry’’ compartment is a common problem in such composite foods, because for the crispy cereal-based product, the loss of crispness is strongly correlated to moisture content changes (Roudaut, Dacremont, & Le Meste, 1998). Moisture transfer modelling is of particular interest for predicting shelf-life of composite foods. But despite of its high interest as compared to long and laborious experimental studies, moisture transfer modelling in composite foods has received little attention. Among these rare studies, Hong, *
Corresponding author. Tel.: +33-4-67-14-33-61; fax: +33-4-67-1449-90. E-mail address:
[email protected] (N. Gontard). 0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2003.09.014
Bakshi, and Labuza (1986) described a model for predicting moisture transfer in dried fruits and almonds mixture, Karathanos and Kostaropoulos (1995) discussed water diffusion in dough/raisin system and Guillard, Broyart, Bonazzi, Guilbert, and Gontard (2003a) validated a model for predicting moisture transfer in agar gel/sponge-cake composite food. Except for the study of Hong et al. (1986), all the models developed deal with intermediate or high aw products and cylindrical, non commercial food geometries. It would be interesting to validate such models on more realistic geometries with low aw products. The transport (diffusivity) and equilibrium (sorption isotherm) of water for each compartment are important parameters required in any modelling purposes. Contrary to water sorption isotherm, moisture diffusivity values cannot be directly obtained from experimental measurements. Authors, thus, resort to estimation of diffusivity from experimental data, using a mathematical model and an optimisation procedure. The sensitivity of diffusivity to moisture content is well documented and widely accepted. There is no
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generally accepted model expressing the influence of moisture content on diffusivity. Authors, thus, choose a diffusivity model a priori and adjust its parameters to moisture distribution profiles obtained from drying or sorption experiments (Zogzas, Maroulis, & Marinos Kouris, 1994). The resulting estimated diffusivity values contain all the deviation from ideality due to experimental errors and analytical treatment. As a consequence, a high number of models, often not consistent to each other, are found for a same product (Zogzas, Marousis, & Marinos Kouris, 1996). More realistic models of diffusivity versus moisture content can be obtained through sorption kinetics. During sorption experiments, the product being studied is placed in constant temperature and fixed relative humidity atmospheres and mass changes of the product are monitored till aw equilibrium between air and product is reached. For each RH level of low amplitude, assumed constant diffusivity value could be estimated. Diffusivity changes with moisture content are thus obtained. This method has been investigated by Leslie et al. (1991) on starch mixtures and by Guillard, Broyart, Bonazzi, Guilbert, and Gontard (2003b) on sponge-cake. Diffusivity models determined by these authors were then tested in drying kinetics and moisture migration experiments in agar gel/sponge-cake composite food respectively. Adjustment of parameters was required for a best fit of experimental data. The application of a diffusivity model obtained in a particular system, to a different system is sometimes difficult, since different mechanisms of water transport between these systems could occur (Guillard et al., 2003a). Moreover, in drying or sorption kinetics, where the product being studied is placed in a surrounding atmosphere, some studies have stated the importance of taking into account both external and internal (diffusivity) resistances to mass transfer for estimating accurate diffusivity values (Ni, Datta, & Torrance, 1999; Simal, Sanchez, Bon, Femenia, & Rossello, 2001). The objectives of the present study were to validate the model developed by Guillard et al. (2003a, 2003c) in a food system with a more realistic geometry, a lower aw cereal-based compartment (dry biscuit), including the effect of an edible barrier film at the interface. The large water content range variation of biscuit should allow analysis and validation of the evolution of diffusivity values in the entire range of moisture content.
prepare agar gels of 0.900 aw , 64 g/100 g of glucose syrup (D.E. ¼ 67, moisture content ¼ 12.0 g/100 g wet basis (w.b.); Chamtor, 51110 Bazincourt, France) was added to a mixture of 3 g of agar powder and 33 g of water. The agar solution was left for 1 h at 100 C in a water bath until the solution became transparent. A total of 0.4 g of sodium azide was then added in the solution in order to limit microbial development in the agar gel. The agar gel solution was poured into a plate for electrophoresis (20 · 20 cm) in order to obtain agar gels of 0.35 cm height. The gels were put into storage at 20 C in a controlled relative humidity jar, where the relative humidity was adjusted by using pure water or saturated salt solution of BaCl2 ðaw ¼ 0:92Þ according to the initial aw of gels. 2.2. Biscuit The cereal-based compartment was a laminated dry cookie, a Petit Brun (Danone, 92300 Levallois–Perret, France) composed of wheat flour, sugar, vegetable fat, glucose syrup, ammonium and sodium carbonate, citric acid, bisodium biphosphate, salt, lactose and milk proteins. The biscuit has a 5 · 3 cm area, a 0.5 cm height, a 2% (wet basis) moisture content, a 0.18 aw , an average weight of 6.31 ± 0.1 g and a density of 350.8 kg of dry matter/m3 of bulk volume. 2.3. Acetylated monoglyceride film-forming technique An acetylated monoglyceride, TSED619 (Guillard, Broyart, Bonazzi, Guilbert, & Gontard, 2003c), was used as material for film forming. Material was melted at 70 C for 10 min, laminated using a film-making apparatus (Braive Instruments, 41000 Checy, France) adjusted to 0.4 mm thickness onto a hot steel plate (70 C) that was previously covered with greaseproof paper sheets and solidified at room temperature. After solidifying, the film was removed from the paper and the thickness was measured at room temperature with a hand-held micrometer (Braive Instrument) having a sensitivity of 0.001 mm. Measurements were made at different places (at least five) of the film and an average value was calculated. Before the experiment, the film was conditioned at 20 C in a 75% RH atmosphere (saturated salt solution of NaCl) for 7 days. 2.4. Sorption isotherm and effective diffusivity
2. Materials and methods 2.1. Preparation of agar gels The agar solution for gel preparation was prepared by adding 3 g of agar powder to 97 g of water with vigorous stirring to homogenise the solution. In order to
The water vapour sorption kinetic at 20 C of Petit Brun biscuit was determined (two replicates) for aw varying from 0 to 0.97 using a controlled atmosphere microbalance as detailed previously (Guillard et al., 2003b). The experimental water sorption isotherm was plotted from equilibrium moisture content for each aw level investigated,. The Ferro Fontan equation [Eq. (1)]
V. Guillard et al. / Journal of Food Engineering 64 (2004) 81–87
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was used to model the sorption isotherm curve for water activity between 0.70 and 1 c a 1 X ¼ ln ð1Þ aw b
ues by the following empirical model (Tong & Lund, 1990): ! n X i ai X ð6Þ Deff ðX Þ ¼ D0 exp
where X is the moisture content in g/g (dry basis) and a, b and c are empirical parameters. Values of Ferro Fontan parameters were determined by minimising the sum of squared error between experimentally measured and predicted values of moisture content using Levenberg–Marquardt algorithm (Gill, Murra, & Wright, 1981) and MATLAB software. Diffusivity values within biscuit were estimated from transient-state moisture contents of the sorption kinetics, using the optimisation procedure (Levenberg–Marquardt algorithm) and a diffusion model. Two mathematical models were developed, taking into account or not the effect of an external resistance to moisture transfer at the interface air/biscuit. In both cases, for each aw level investigated, the transient-state diffusion of water within biscuit assumed normal to biscuit surface, is expressed by Fick’s second law, the diffusivity value is assumed constant and biscuit swelling is considered negligible. Assuming, first, that external resistance to mass transfer is negligible, as compared to the internal resistance (diffusivity), an analytical solution for linear diffusion [Eq. (2)] in an infinite slab of L thickness (m) was used (Crank, 1975):
where Deff ðX Þ indicates the diffusivity model as a function of moisture content, X is the average moisture content, i values are constants ranging from 1 to n which is an integer value, and D0 (m2 /s) and ai are empirical parameters. Values for n ranging from 1 to 5 were successively tested in order to obtain the best fit of Deff as a function of moisture content using the Levenberg–Marquardt algorithm for optimisation procedure. In order to study the effect of an external resistance to moisture transfer on diffusivity estimation, a second diffusion model was developed assuming that the external resistance to moisture transfer at the interface air/ biscuit could not be neglected. Therefore, Eq. (5) is replaced by the following boundary condition (Datta & Ni, 2002):
1 X X X0 8 ¼1 2 2 X1 X0 n¼0 ð2n þ 1Þ p ( ) 2 Deff ð2n þ 1Þ p2 t exp 4L2
ð2Þ
i¼0
Deff q
X ðx; 0Þ ¼ X0
ð3Þ
oX ðL; tÞ ¼0 ox
ð4Þ
X ð0; tÞ ¼ X1
ð5Þ
Using the Levenberg–Marquardt algorithm for optimisation procedure, estimation of diffusivity values was conducted for each aw level by minimising the sum of squared error between experimentally measured and predicted values obtained with [Eq. (2)] as described by Guillard et al. (2003b). Diffusivity variations with moisture content (arithmetic mean between initial and equilibrium moisture content for the aw step) were tentatively modelled in biscuit from the previously estimated diffusivity val-
ð7Þ
where q is the density of dry matter in the bulk solid (kg/ m3 ), k is the mass transfer coefficient (m/s), cs is the water vapour content (kg/m3 ) at the product surface and ca is the water vapour content of the surrounding air (kg/m3 ). Assuming surrounding air as perfect gas, water vapour contents are correlated to water vapour partial pressure using the perfect gas low and then, to water activity as follows: Deff q
where X , X0 and X1 are the average, initial and equilibrium moisture contents (g/g d.b.) respectively of the sample at time t for the aw level investigated and Deff is the constant effective diffusivity (m2 /s). The initial and boundary conditions are
oX ð0; tÞ ¼ kðcs ca Þ ox
oX ð0; tÞ kMw Pvsat ¼ ðaw ðX Þ awair Þ ox RT
ð8Þ
where Pvsat is the saturated vapour pressure at the temperature of the study (2337 Pa at 20 C) T is the surface temperature of the solid (293 K), Mw is the molecular mass of water (18 kg/kmol), R is the perfect gas constant (8314.3 J/kmol/K) and aw ðX Þ and awair are, respectively, the water activity at the product surface and in the surrounding air. Fick’s second law with initial and boundary conditions (3), (4) and (8) was solved numerically using a explicit finite-difference method (Ozisik, 1994). All equations are solved simultaneously using MATLAB software. Explicit method is stable provided that [Eq. (9)] is always verified. 2
r ¼ DDt=ðDxÞ < 0:5
ð9Þ
where Dt and Dx are the time and space step, respectively. An application-specific function proposed in MATLAB Optimisation Toolbox was used (Anonymous, 2000) which adjusts Dt value at each iteration in order to keep r < 0:5.
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2.5. Moisture migration experiments and simulations
3. Results and discussion
A 5 · 3 cm surface of agar gel was stamped out from electrophoresis plate and placed in contact with the biscuit. The two-compartment food (agar gel/biscuit) was then hermetically packaged in a high moisture barrier impermeable aluminum-based film and was kept at a constant temperature chamber (20 ± 0.1 C). Three-compartments foods were realised in a same manner with an additional 5 · 3 cm TSED 619 film at the interface between the agar gel and the biscuit. Experimental moisture content variations of each compartment, agar gel, biscuit and film, versus time were measured in three replicates through weight changes before and after complete desiocation (24 h in an oven at 103 C) for different storage time and initial agar gel aw . For each experiment, the average of 95% confidence interval of all the replicates represented the experimental error (in g/100 g wet basis). The models used for modelling moisture transfer in a two- or three-compartment system were developed and discussed by Guillard et al. (2003a, 2003c). Equations and hypothesis on boundary and initial conditions and the numerical solving of these equations remained identical, except size of time step that was decreased to 60 s in order to be able to represent the rapid moisture changes in the biscuit. Initial parameters for simulations are, for each compartment, constants of Ferro Fontan model for sorption isotherm, initial moisture content and density. These parameters are given previously for agar gel (Guillard et al., 2003a) and acetylated monoglycerides films (Guillard et al., 2003c). Effective diffusivity within acetylated monoglycerides film was constant and equal to 2.1 · 1011 m2 /s. Parameters of biscuit diffusivity model [Eq. (6)] were obtained from experimental moisture content evolution with time using the optimisation procedure and the model for moisture transfer in a composite food. Since the optimisation method was not self-starting, parameters of diffusivity model within biscuit obtained from the water vapour sorption kinetics were used as initial guessed values. The root mean square error (RMSE) was used to estimate the quality of model fitting and was calculated as follows:
Water sorption and diffusivity are two important water properties governing moisture transfer rate in food and are, thus, required for modelling purposes.
ð10Þ
A sorption isotherm of the tested biscuit at 20 C for aw varying from 0 to 0.97 is shown in Fig. 1 (symbols). Ferro Fontan equation [Eq. (1)] with 1.0813, 0.0638 and )1/0.8256 values for a, b and c parameters, respectively, was successful to model sorption curves with correlation coefficient of 0.998 (Fig. 1, continuous curve). High equilibrium water uptake was observed for aw between 0.7 and 1 with, for example, a moisture content of 14 g/ 100 g w.b. at 0.8 aw . Similar results at 0.8 aw were observed by Palou, Lopez-Malo, and Argaiz (1997) in various cookies and corn snacks and by Arogba (2001) in biscuit with equilibrium moisture content, respectively, of 20 g/100 g (w.b.) at 25 C and 15 g/100 g w.b. at 31 C. Diffusivity values within biscuit were obtained from the transient-state moisture contents of the sorption kinetics using the optimisation procedure and analytical solution [Eq. (2)] for modelling moisture sorption. The resulting Deff values at 20 C are plotted in Fig. 2 (black diamonds) against the corresponding moisture contents. The effective diffusivity increased sharply from 3.53 to 6.59 · 1010 m2 /s as the moisture content of the biscuit increased from 1.7% to 10.0% then decreased gradually as the moisture content of the biscuit increased further 10.0%, to reach a minimal value of 0.63 · 1010 m2 /s for 32.3%. These values are in the same range with those reported by Tong and Lund (1990) for biscuit (from 8.6 40 35 Moisture content (g/100g wb)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð^y yÞ RMSE ¼ ðN pÞ
3.1. Water vapour sorption isotherm and diffusivity in the biscuit
30 25 20 15 10 5 0
where y and ^y are respectively the experimental and predicted moisture content values (g/100 g d.b.), N is the number of moisture content measurements and p is the number of identified parameters.
0.0
0.2
0.4 0.6 Water activity
0.8
1.0
Fig. 1. Water sorption isotherm of a biscuit at 20 C: experimental data (symbols) and Ferro Fontan prediction (continuous curve).
V. Guillard et al. / Journal of Food Engineering 64 (2004) 81–87
100.0
1.6E-09 1.4E-09
Moisture content (g/100 g w.b.)
1.2E-09 1.0E-09 8.0E-10
(1)
6.0E-10 4.0E-10 2.0E-10 0.0E+00 0
Agar gel
90.0
(2)
10 20 30 Moisture content (g/100g wet basis)
40
Fig. 2. Moisture diffusivity in biscuit at 20 C as a function of moisture content identified either from (1) water vapour sorption kinetics (r Deff value for each aw level obtained from Eq. (2) and (––) Deff values calculated from Eq. (6)) or from (2) moisture migration experiments in a two-compartment system ( ).
to 11.0 · 1010 m2 /s for moisture content varying from 9.0% to 44.4%), using isothermal convective drying at 20 C. Modelling diffusivity as a function of moisture content was obtained by using Eq. (6). Best fit was obtained for n ¼ 4. Parameters’ values are given in Table 1 and resulting predicted Deff are presented in Fig. 2 (continuous black curves). Eq. (6) succeeded in modelling Deff variations with correlation coefficient of 0.989. 3.2. Moisture content evolution in the composite cerealbased food and modelling The drastic moistening of the biscuit, placed in direct contact with high aw agar gel was experimentally observed through measurements of moisture content evolution with time in both biscuit and agar gel for initial agar gel aw of 0.999 (Fig. 3) and 0.900 (Fig. 4). Considering a critical moisture content of 10% w.b. (Roudaut et al., 1998) for crispy cereal-based foods, loss of texture within biscuit was reached rapidly in a few hours whatever the agar gel water activity. Moistening of biscuit was tentatively reduced by placing an edible film of acetylated monoglycerides, chosen for its interesting barrier properties (Guillard et al., 2003c), at the interface between biscuit and agar gel. Such a film of 316.1
80.0 70.0 60.0 50.0 40.0 Biscuit
30.0 20.0 10.0 0.0 0
2 4 Storage time (hours)
6
Fig. 3. Comparison between experimental (symbols) and predicted (continuous curves) moisture content evolution with time at 20 C of a biscuit in direct contact with an agar gel of 0.999 initial aw . Experimental error was too low compared to the symbol size for being represented and was, thus, not shown on the graph. Dotted lines represent predictive errors.
45.0 Agar gel Moisture content (g/100g wet basis)
Moisture diffusivity (m²/s)
85
40.0 35.0 30.0 Biscuit
25.0 20.0 15.0 10.0 5.0 0.0 0.0
10.0 20.0 Storage time (days)
30.0
Fig. 4. Comparison between experimental (symbols) and predicted (curves) moisture content evolution with time at 20 C of a biscuit in direct contact with an agar gel of 0.900 initial aw . Vertical bars and dotted lines represent, respectively, experimental and predictive errors.
(±14.5) lm thickness delayed the loss of crispness for more than 3 days (Fig. 5), confirming the potential
Table 1 Parameters of biscuit diffusivity model at 20 C [Eq. (6)] determined either from water vapour sorption kinetic of biscuit or from moisture migration experiments in a two-compartment system agar gel/biscuit Parameters of Eq. (6) D0 (m2 /s) Sorption kinetic Moisture migration experiments
10
1.49 · 10 3.06 · 1010
a1
a2
a3
a4
)639.92 )628.30
746.52 733.33
)292.81 )287.94
37.60 36.96
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45.0 Agar gel
Moisture content (g/100g wet basis)
40.0 35.0 30.0 25.0
Biscuit
20.0 15.0 10.0
Film
5.0 0.0 0.0
10.0 20.0 Storage time (days)
30.0
Fig. 5. Comparison between experimental (symbols) and predicted (curves) moisture content evolution with time at 20 C of a biscuit separated from an agar gel of 0.900 initial aw by a 316.1 lm acetylated monoglycerides (AMG) film. Experimental error was too low compared to the symbol size for being represented and was, thus, not shown on the graph.
interest of using acetylated monoglycerides films to control moisture transfer in composite cereal-based foods. Modelling of moisture transfer was first studied in a two-compartment system: agar gel of initial aw of 0.999, in contact with biscuit using the following procedure: optimisation was started with initial guessed parameters for biscuit diffusivity model obtained from sorption kinetics (Table 1). Ferro Fontan model for sorption isotherms, initial moisture content and density required in the model were evaluated in this study for biscuit and in Guillard et al. (2003a) for agar gel. Parameters of biscuit diffusivity model should be adjusted for a best fit to the moisture content evolution profile with time. Additional diffusivity models (linear, exponential, . . .) were unsuccessfully tested with unacceptable RMSE values. Only Eq. (6) was able to model the moisture content evolution with time in biscuit confirming the Deff variations already observed using sorption kinetics. The resulting estimated parameters are given in Table 1. The model successfully fitted the experimental biscuit and agar gel moisture content evolution with time (Fig. 3) with a RMSE value of ±1.0 g/100 g w.b., consistent with experimental error of ±0.7 g/100 g w.b. The model validity with identified parameters for Deff ðX Þ model within biscuit was tested by comparing predicted and experimental moisture content evolution with time in 2 other independent experiments with varying initial conditions: either lower aw agar gel (0.90, Fig. 4) or an acetylated monoglycerides barrier film at the interface of the two compartments (Fig. 5). In both cases, the model successfully predicted experimental moisture content evolution profile with RMSE values of
±2.2 and ±1.1 g/100 g w.b., slightly higher but consistent with experimental errors of ±1.4 and ±0.8 g/100 g w.b. for Figs. 4 and 5, respectively. The model can be thus considered as an adequate tool for predicting moisture content evolution profile with time for biscuit and various aw agar gels in direct contact or separated by an edible film. 3.3. Diffusivity evaluation Fig. 2 shows the diffusivity variations within biscuit evaluated using two different methods: water vapour sorption kinetic of biscuit or moisture migration experiments in agar gel/biscuit system. Comparing the two methods, diffusivity variations were found qualitatively identical with a peak of diffusivity not far from the monolayer value (6.2 ± 1.8 g/100 g w.b.) as evaluated by fitting the GAB model to experimental sorption data. Similar behaviour was previously observed for spongecake (Guillard et al., 2003b) with a peak of diffusivity around the monolayer value (9.3 g/100 g w.b.) and for porous starch mixtures (Karathanos, Villalobos, & Saravacos, 1990; Marousis, Karathanos, & Saravacos, 1989) with a maximum of diffusivity around 10 g/100 g w.b. The increasing Deff in sponge-cake for moisture content below 10% was related to the saturation of the monolayer and the decreasing diffusivity at moisture content above 10% to the decrease in vapour-phase diffusion contribution to the overall water transport because of a reduction of apparent degree of porosity. In biscuit, saturation of the monolayer value but also high porosity should influence the Deff increase for moisture content below 10%. Then, as for sponge-cake, decreasing influence of vapour-phase diffusion to the water flow due to porosity changes should explain the Deff decrease at moisture content above 10%. Diffusivity values estimated from moisture migration experiments in agar gel/biscuit system were found twofold higher (varying from 1.35 to 13.60 · 1010 m2 /s) than diffusivity values from sorption kinetic (varying from 0.63 to 6.59 · 1010 m2 /s). These significant differences between estimated Deff values as regard the experimental method used could reflect too restrictive assumptions in the model formulation [Eq. (2)], when estimating diffusivity from sorption kinetics, such as no external resistance to moisture transfer at the interface air/biscuit, no volume changes, mono-directional water flow etc. Among these assumptions, the influence of external resistance to moisture transfer on diffusivity identification could be evaluated. A second diffusion model for modelling sorption kinetics was developed taking into account the external resistance to moisture transfer [Eq. (8)]. Using the numerical solution of Fick’s second law with Eqs. (3), (4) and (8) as initial and boundary conditions, estimation of mass transfer coefficient ðkÞ was conducted from transient-state moisture
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contents of each sorption kinetics step by fixing the corresponding diffusivity with the value obtained from moisture migration experiment. The resulting k values were found increasing from 0.0072 to 0.0184 m/s for moisture content ranging from 0% to 10 % (w.b.) and then constant and equal to 0.0184 m/s for moisture content above 10% (w.b.). This last value was in accordance with the values of 0.018 m/s reported by Datta and Ni (2002) and Ni et al. (1999) for microwave heating of porous product. A growing effect of external resistance (inversely correlated to mass coefficient) with diffusivity was observed. These relevant mass transfer coefficients at the interface air/biscuit could explain the difference observed between diffusivity identified from either sorption kinetic or moisture migration experiments in agar gel/biscuit system. However, these values should be treated cautiously since several other hypotheses have not been confirmed and should interfere with the effect of external resistance. For example, swelling which is not taken into account in the model formulation may cause biscuit surface area to be dependent on the moisture content and may yield a discrepancy of the estimated diffusivity values. Swelling remains, therefore, very difficult to evaluate during sorption kinetics measurement without perturbing the measure. In biscuit, the different mechanisms of water transport encountered may also contribute to explain the higher Deff values determined from moisture content evolution profile. For example, an additional flux of water resulting from capillary action could occur in the cereal-based food in contact with high moisture content agar gel as already suggested for sponge-cake (Guillard et al., 2003a). This additional flux would not take place in water vapour adsorption experiments. Taking into account simultaneously both external and internal resistances to moisture transfer appeared as a good approach to identify diffusivity value from sorption kinetics. However, difficulties generally encountered to determine accurate values of mass transfer coefficients and several interfering phenomena (swelling, different mechanisms of water transport, . . .) made difficult the direct transposition of sorption kinetics diffusivity values to moisture transfer in composite foods. Anyway, identification of diffusivity values from sorption kinetic seemed to be a good means to assess diffusivity changes with moisture content and to provide diffusivity model and initial guessed parameters for modelling moisture transfer in the composite food, even if this diffusivity model should be quantitatively adjusted to apply to moisture migration experiments modelling.
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