FOAM-MAT FREEZE-DRYING OF APPLE JUICE PART 1: EXPERIMENTAL DATA AND ANN SIMULATIONS

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FOAM-MAT FREEZE-DRYING OF APPLE JUICEPART 1: EXPERIMENTAL DATA AND ANN SIMULATIONS

NARINDRA RAHARITSIFA1,3 and CRISTINA RATTI2

1Département des Sciences des Aliments et de Nutrition

2Département des sols et de génie agroalimentaireFaculté des Sciences de l’Agriculture et de l’Alimentation

Université LavalQuébec G1K 7P4, Canada

Accepted for Publication March 8, 2009

ABSTRACT

Freeze-drying of foamed and nonfoamed apple juice was studied in orderto assess if there is a reduction in process time due to foaming. Foams wereprepared by whipping apple juice with methylcellulose or egg albumin atdifferent concentrations. Foamed and nonfoamed juice samples having differ-ent thickness and different initial weight were frozen at -40C and then freeze-dried at 20C during 48 h under vacuum. Sample weight loss and temperaturewere followed at different process times. A mathematical model based onartificial neural networks was developed to represent foam kinetics and tem-perature curves during freeze-drying. Foaming reduced process time if thecomparison was done at equal sample thickness. However, lower density offoamed materials decreases weight load to the dryer. Unfortunately, the opti-mization of the process did not permit the determination of a practical minimalfoam sample thickness to enhance both drying rate and dryer throughput.

PRACTICAL APPLICATIONS

Fruit juice powders have a large application in the food and nutraceuticalindustries. These powders are used as instant beverages, ingredients for bakeryor extruded products and to incorporate in pharmaceutical tablets. Freeze-drying is an excellent process to obtain a high-quality fruit juice powderbecause it offers extraordinary nutritional, structure and sensorial qualitieswhen compared with products of alternative drying process: air, vacuum,microwave and osmotic drying. However, the process cost is expensive due to

3 Corresponding author. TEL: 604-755-3153; FAX: 418-656-3723 (c/o C. Ratti); EMAIL:[email protected]

Journal of Food Process Engineering 33 (2010) 268–283. All Rights Reserved.© 2009 Wiley Periodicals, Inc.DOI: 10.1111/j.1745-4530.2009.00400.x

268

the long drying times under vacuum. Process acceleration through optimiza-tion is therefore necessary in order to obtain high quality in the final productsbut at lower costs. This study aims to decrease the cost of the freeze-dryingprocess by using foaming prior to processing to increase the drying rate.

INTRODUCTION

Freeze-drying is usually used to manufacture dehydrated products withexcellent final quality due to the low temperatures required in the process andthe direct passage of water from solid to vapor states. Organoleptic quality andrehydration capacity decrease significantly during most of dehydration process(Nijhuis et al. 1998). In freeze-drying process, however, structure and shapeare maintained; the original flavor and aroma are retained, as well as vitaminsand minerals (Ratti 1994, 2001). Freeze-dried products present higher solu-bility, longer shelf life, higher reduction in weight and the possibility toperform rehydration at any level. The process is largely used to dry thermal-sensitive products such as antibiotics, bacteria, pharmaceutical products, foodingredients or those with high value-added such as coffee, herbs or nutraceu-ticals (Wolff and Gibert 1988; Palmfeldt et al. 2003). However, the energyconsumption to maintain vacuum during the long processing times involved infreeze-drying is highly expensive, which constitutes the main disadvantage ofthis technique. Researchers in the food area such as Sharma and Arora (1995)found that the decrease in sample thickness helps reduce the sublimation timeand the exposure time of the dry layer to higher temperatures. Thickness isthus an important parameter to control the process.

On the other hand, some researchers successfully used foaming todecrease processing times during conventional hot-air drying of liquids andpastes (Morgan et al. 1961; Karim and Wai 1999a). In this technique called“foam-mat drying,” a liquid is whipped to form stable foam, and then dehy-drated by thermal means. The larger surface area exposed to the drying airseemed to be the cause of moisture removal acceleration (Brygidyr et al.1977). Other researchers, however, pointed out capillarity as the main moisturemovement within the product during foam-mat drying (Sankat and Castaigne2004). Many studies concerning physical and organoleptic characteristicswere undertaken on the application of this process to mango (Cooke et al.1976), tamarind juice (Vernon-Carter et al. 2001), star fruit puree (Karim andWai 1999b), whole egg (Muhammad et al. 1988; Satyanarayana Rao andMurali 1988) or ripe bananas (Sankat and Castaigne 2004). Other studies weredone concerning the application of foaming to the food industry (Prud’hommeand Khan 1996; Piazza et al. 2008). No work has, however, focused on thestudy of foaming application before freeze-drying.

FOAM-MAT FREEZE-DRYING OF APPLE JUICE 269

The present work brings into play foam-mat with freeze-drying process tostudy the possibility of acceleration of drying kinetics. Drying rate and heatingrate are the two main factors to be managed during foam-mat freeze-drying.When the drying progresses too rapidly, the dried product can be blown out bythe escaping water vapor. Moreover, a too high heating rate may generatemelting or collapse of the product (Bellows and King 1973; Roos 1995). Thesephenomena produce physical and structural changes, giving an unattractiveproduct which is difficult to reconstitute. It is thus gainful to develop amathematical model to predict the moisture content and the temperatureduring the foam-mat freeze drying at diverse conditions in order to improve thedrying rate but avoiding long manipulations.

Artificial neural networks (ANN) are nonlinear set of equations inspiredon a simplified model of the human brain function. It has the capability toself-adapt in order to relate complex nonlinear relationships between input andoutput variables. It has been successfully used in different areas such as drying(Huang and Mujumdar 1993), prediction of shrimp growth (Yu et al. 2006) orfor food processes optimization (Mittal and Zhang 2002; Torrecilla et al.2005).

The present work proposes to study the application of foaming prior tothe freeze-drying process in order to accelerate drying kinetics. The objectivesare (1) to study experimentally freeze-drying of foamed and nonfoamed applejuice; (2) to develop a model by ANN to predict the moisture content andtemperature during freeze-drying; and (3) to determine the optimum thicknessto accelerate the process throughput.

MATERIALS AND METHODS

Materials

Clarified apple juice (Del Monte, Nabisco, Ontario, Canada) having pH3.5 was purchased from a local supermarket and stored at -4C until use.Foaming and stabilizing agents used to form foams out of apple juice wereegg white (EW) powder (Newly Weds, Quebec, Canada) and methylcellulose(MC; Methocel 65HG, Fluka BioChemika 64670, Buchs SG, Switzerland).

Foam Preparation

Proper amounts of apple juice and foaming agent were weighed to givefinal concentrations of 1% (w/w) MC and 3% (w/w) EW. These concentrationshave been previously found to be appropriate in order to form stable foams ofapple juice (Raharitsifa et al. 2006).

270 N. RAHARITSIFA and C. RATTI

Freeze-Drying

Foams were poured carefully with a spatula into beakers (68 ¥ 88 mm,VWR International, Mississauga, Ontario, Canada) at four thickness levels (1,4, 6 and 8 cm). Nonfoamed apple juice at the same thicknesses was used ascontrol. Foamed and nonfoamed juice samples were first frozen at -40C andthen freeze-dried in a Unitop 400 L freeze-drier (VIRTIS, Gardinier, NY) at20C and at a total pressure of less than 4 Pa during 48 h. Temperature of theproduct was followed as a function of time with a thermocouple (MVP Probes,Omega Engineering Inc., Stamford, CT) carefully placed before freezing at1 mm from the sample bottom.

Moisture Content

Moisture content (dry basis) data were obtained by weighing the samplesafter 1, 3, 5, 7, 9, 12, 18, 24 and 48 h of freeze-drying at 20C, in a balance(Mettler AE 200, Grefensee, Zürich, Switzerland) with 0.0001 g accuracy.Samples were then transferred to a vacuum oven at 50C for 48 h to obtain thedried weight (AOAC 1990). Drying curves were expressed in terms of thedimensionless relative moisture content (X/Xo):

X XW t W

W Wod

i d

=( ) −

−(1)

where W(t) is the moisture content at time t, Wd is the dried weight and Wi isthe initial weight.

Neural Network Modeling

The neural network modeling of moisture content and product tempera-ture was based on the following equation (Eq. [2]):

Y f LW f IW p b b= +( )[ ] +{ }2 2 1 1 1 1 1 2, , (2)

where p is a column vector containing the input variables (thickness and time),Y is the network response containing the output variables (moisture content andtemperature), IW1,1 is the weight matrix between the input layer and the hiddenlayer, LW2,1 is the weight matrix between the hidden layer and the output layer,b1 is the bias of the hidden layer; b2 is the bias of the output layer; f1 refers tothe logarithmic transfer function and f2 refers to the linear transfer function.

Matlab 7.3.0 software with the Neural Network Toolbox 4 (The Math-works, Inc., Natick, MA) was used for ANN modeling of product water


content and temperature. A hyperbolic tangent was chosen as the transferfunction for the hidden layer with 10 hidden neurons. One hidden layer issufficient to approximate any continuous nonlinear function. In addition, alinear transfer function was employed in the output layer. The back-propagation network training function was that of Levenberg–Marquardt.Experimental data at 1, 4 and 6 cm thickness were used for the training.Supervised training was ended when the mean square error, which comparedthe target value to an estimated output, was less than 0.0001.

In order to asses the prediction capabilities of the ANN model, moisturecontent curves for 8 cm-thickness foam and juice were obtained experimen-tally and compared with the model predictions.

Statistics

Experimental measurements were done at least in duplicate, and tripli-cated when the coefficient of variation was higher than 10%. Data weresubjected to statistical analysis by the general linear model procedure of SAS(SAS Institute Inc., Cary, NC), and a least significant difference test with aconfidence interval of 95% was used to compare the means.

RESULTS AND DISCUSSION

Moisture Content

Product thickness, as well as the freeze-dryer heating plate temperatureand total pressure are variables that should be controlled in the freeze-dryingprocess. Thus, samples at equal thickness are compared to assess drying rates.Figure 1 shows the freeze-drying curves of 4 cm-thickness foamed and non-foamed apple juice. Foamed juice freeze-drying rate is much faster thannonfoamed juice at 4 cm thickness. For instance, the time to reach X/Xo = 0.1for the nonfoamed juice, MC and EW foamed apple juice (at 4 cm thickness)was 41, 12 and 8 h, respectively, showing that not only foaming but also thefoaming agent has an impact on drying rate. The reason why EW foamed applejuice freeze-dries faster than the MC one could be explained by the fact that toachieve efficient heat and mass transfer in drying, small bubble size has anadvantage in terms of having large surface to volume ratio (Moy 1971).Hertzendorf and Moshy (1970) stated in their microflake process research thatdrying time was found to be proportional to the square root of the bubble size.In our case, previous research showed that 3% EW foamed apple juice presentssmaller bubble size than those with 1% MC (Raharitsifa et al. 2006), thussustaining the faster drying rate found experimentally. On the other hand, the


strong interaction between water and MC (Hatakeyama et al. 2000) can alsocontribute to slow down its drying rate.

Unfortunately, the lower density of foamed materials as compared withnonfoamed ones (0.159, 0.113 and 1.065 g/cm3 for 1% MC and 3% EW foamsand juice, respectively; Raharitsifa et al. 2006) decreases the weight load ofthe dryer, undermining the potential economical benefits of foaming beforefreeze-drying. It is thus desirable to explore the possibility of finding condi-tions for which foamed juice has not only higher drying rate but also a higherdrying throughput than nonfoamed juice. In the case of foam-mat hot-airdrying, many authors have reported that, at the same thickness, foam exhibitedshorter drying time in comparison with nonfoamed mango pulp (Rajkumaret al. 2007), tamarind pulp (Vernon-Carter et al. 2001) or juice (Hertzendorfand Moshy 1970). However, not in many of these cases, the dryer throughputwas actually increased.

As said previously, product thickness is an important variable duringfreeze-drying. Figures 2–4 show the freeze-drying curves of foamed (MC andEW) and nonfoamed apple juice samples, respectively, at different thickness.As can be seen, thickness has a significant impact (P < 0.01) on both foamedand nonfoamed juice freeze-drying curves. However, the effect of thickness ismore pronounced for the nonfoamed samples (juice). For instance, the time fora nonfoamed sample having 4-cm thickness to reach X/Xo = 0.1 is four times

Time (h)

0 10 20 30 40 50

X/X

o

0,0

0,2

0,4

0,6

0,8

1,01%MC 3% EW Juice

FIG. 1. FREEZE-DRYING CURVE OF NONFOAMED AND FOAMED APPLE JUICEAT 4-CM THICKNESSES

MC, methylcellulose; EW, egg white.


Time (h)

0 5 10 15 20 25

X/X

o

0,0

0,2

0,4

0,6

0,8

1,06cm4cm1cm

FIG. 2. FREEZE-DRYING CURVE OF 1% METHYLCELLULOSE FOAMED APPLE JUICE ATDIFFERENT THICKNESS

Time (h)

0 5 10 15 20 25

X/X

o

0,0

0,2

0,4

0,6

0,8

1,0

6cm4cm1cm

FIG. 3. MOISTURE CONTENT OF 3% EGG WHITE FOAMED APPLE JUICE ATDIFFERENT THICKNESS


higher than that for 1 cm, but just two times higher if the product is foamed.Thickness could be thus a good optimization variable to increase drying rate aswell as dryer throughput.

Figures 5–7 show the product temperature during freeze-drying offoamed (MC and EW) and nonfoamed apple juice samples, respectively. Theshape of the curves is similar to the ones obtained for most of the productsduring the freeze-drying process (Sagara and Ichiba 1994). The initial tem-perature of both the heating plate and product after freezing was -40C. As thetemperature of the heating plate increases to reach 20C, product temperatureincreases with a delay corresponding to the sublimation time. The duration ofthe sublimation step had a good correlation with the foam thickness (e.g., 1 hfor 1 cm, 5 h for 4 cm and 8 h for 6 cm for 3% EW foam in Fig. 6). After allthe ice sublimated, the temperature increased gradually to reach the heatingplate temperature.

A simplified energy balance for the frozen region can be estimated bysupposing a lumped parameter approach due to the higher thermal conductiv-ity of frozen materials:

m CT

tQ H Ni pi input s w

∂∂

= − Δ (3)

where mi and Cpi are the mass and the specific heat of frozen material,respectively, Qinput is the heat that gets into the frozen control volume by

Time (h)

0 10 20 30 40 50

X/X

o

0,0

0,2

0,4

0,6

0,8

1,0

6cm4cm1cm

FIG. 4. MOISTURE CONTENT OF NONFOAMED JUICE AT DIFFERENT THICKNESS


Time (h)

0 10 20 30 40 50

Tem

pera

ture

(°C

)

-50

-40

-30

-20

-10

0

10

20

30

6cm4cm1cm

FIG. 5. EXPERIMENTAL AND ARTIFICIAL NEURAL NETWORKS PREDICTEDTEMPERATURE VALUES DURING FREEZE-DRYING OF 1% METHYLCELLULOSE

FOAMED APPLE JUICE AT DIFFERENT THICKNESS

Time (h)

0 5 10 15 20 25

Tem

pera

ture

(°C

)

-50

-40

-30

-20

-10

0

10

20

30

6cm4cm1cm

FIG. 6. EXPERIMENTAL AND ARTIFICIAL NEURAL NETWORKS PREDICTEDTEMPERATURE VALUE DURING FREEZE-DRYING OF 3% EGG WHITE FOAMED APPLE

JUICE AT DIFFERENT THICKNESS


conduction, DHs is the sublimation heat and Nw is the water flux due tosublimation. In Eq. (3), if all the heat received in the control volume is used forsublimation, then ∂T/∂t = 0 and, consequently, T is constant. In this case,neither heat nor mass transfer can be considered separately as the controllingstep. EW foamed apple juice samples at 4-cm thickness (Fig. 6) and non-foamed juice at 1 cm thickness (Fig. 7) presented this behavior. On the otherhand, the process can be considered to be mass transfer limited when Nw valueis small; thus, the derivative ∂T/∂t in Eq. (3) is positive. It is the case of juicesamples at 4- and 6-cm thickness for which temperature curves are above-40C (initial temperature). Thus, in most cases, juice freeze-drying seems tobe mass transfer controlled. To end, limited heat transfer occurs in a situationwhere the derivative in Eq. (3) is negative. It is the case for EW foamed juiceat 6-cm thickness (Fig. 6) and for MC at 4- and 6-cm thickness (Fig. 5).

Low thermal conductivity of foams (0.026 W/m C from Shamaeva et al.1987) compared with that of juice (2.214 W/m C from Mattea et al. 1986)makes foamed systems to be heat transfer controlled during freeze-drying.To confirm this, freeze-drying curves (Figs. 2–4) and temperature curves(Figs. 5–7) showed that in the case of foams, the time to reach low watercontents was smaller than the time to attain the final temperature, and thecontrary for the juice samples.

In summary, thickness is an important parameter in freeze-drying havingdifferent degrees of impact depending on the state (foamed or nonfoamed) ofthe material. Thus, there could be a thickness for which foamed juice may

Time (h)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Tem

pera

ture

(°C

)

-50

-40

-30

-20

-10

0

10

20

30

6cm4cm1cm

FIG. 7. EXPERIMENTAL AND ARTIFICIAL NEURAL NETWORKS PREDICTEDTEMPERATURE VALUE DURING JUICE FREEZE-DRYING AT DIFFERENT THICKNESS


present not only higher drying rate but also higher dryer throughput thannonfoamed during freeze-drying. The determination of such optimal thicknessmust accomplish the following relationship:

t

tnonfoamed

foamed

nonfoamed

foamed

≥ρρ

(4)

where tnonfoamed and tfoamed are the freeze-drying times of non-foamed andfoamed materials, respectively, and rnonfoamed and rfoamed are the density ofnonfoamed and foamed materials.

Modeling and Optimization

ANN was used to simulate moisture content and temperature during theprocess. The network structure associated with the present ANN model ispresented in Fig. 8. Training of the model was done using experimental data ofdimensionless water content as a function of time during freeze-drying of thedifferent foamed and nonfoamed products having thicknesses of 1, 4 and 6 cm.In Figs. 1–7, experimental data are marked with symbols while the ANNpredictions are marked with solid lines. As can be seen, the ANN values agreed

Output layer Hidden layer Input layer

Temperature

Moisture

Time

Thickness

Bias 1 Bias 2

iw{1,1} lw{2,1}

FIG. 8. STRUCTURE OF ARTIFICIAL NEURAL NETWORK (2/10/2)


closely to experimental data for all products at all the thicknesses. As anexample, Fig. 9 shows the excellent correlation for 1% MC foamed apple juiceat 6-cm thickness, for which R2 = 0.9996. The R2 values for the other foodsystems were always higher or equal to 0.9990.

Experimental data on freeze-drying of foamed and nonfoamed 8-cmthickness samples were used to test the prediction capabilities of the ANNmodel. As an example, Fig. 10 shows the prediction of the ANN modelcompared with the data for foamed (1% MC foams) and non foamed juicehaving 8-cm thickness. The comparison showed an excellent agreement con-firming what some researchers found concerning the superiority of ANN topredict drying process (Yu et al. 2006; Goñi et al. 2008) and demonstratingthe capability of the ANN to learn and simulate with an excellent accuracya physical problem from experimental data, without solving any complexnumerical model.

The ANN model was then used to predict drying times for foamed andnonfoamed juice samples in order to find the minimal thickness required tosatisfy (Eq. 4). Table 1 shows the results of the ratio of drying times fornonfoamed to foamed samples from the ANN predictions together with thedensity relationship shown in (Eq. 4) between nonfoamed and foamedsamples. This relationship was found to be 6.60 and 9.29 for 1% MC and 3%EW, respectively (Raharitsifa et al. 2006). As can be seen, as the samplethickness increases, the time ratio also increases. However, up to 8-cm thick-ness, the ratio was never bigger than the density ratio, as required for process

Predicted value

0,0 0,2 0,4 0,6 0,8 1,0

Exp

erim

enta

l val

ue

0,0

0,2

0,4

0,6

0,8

1,0

Y=0.9994X+1.912.10-4

R2=0.9996

2 hidden layers10 neurons

FIG. 9. CORRELATION BETWEEN MOISTURE CONTENT EXPERIMENTAL ANDPREDICTED VALUE OF 1% METHYLCELLULOSE FOAMED APPLE JUICE AT 6 CM


optimization. Thus, minimal thicknesses would probably be too big for apractical increase of the dryer throughput, both for foams made with MC andEW at the tested concentrations.

CONCLUSIONS

Foaming reduced freeze-drying time if the comparison was done at equalsample thicknesses. However, lower density of foamed materials decreases

Time (h)

0 10 20 30 40 50 60 70 80 90 100 110

X/X

o

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1MC JuiceANN

FIG. 10. COMPARISON OF METHYLCELLULOSE FOAMED APPLE JUICE ANDNONFOAMED JUICE FREEZE-DRYING CURVE AT 8 CM THICKNESS

TABLE 1.THICKNESS OPTIMIZATION FOR 1% MC AND 3% EW FOAMS FROM ANN PREDICTIONS

Thickness (cm) 1% MC 3% EW

rnonfoamed/rfoamed tnonfoamed/tfoamed rnonfoamed/rfoamed tnonfoamed/tfoamed

1 6.6 1.819 9.21 3.1564 3.858 5.5356 4.344 6.1008 4.671 6.328

MC, methylcellulose; EW, egg white.


mass load to the dryer. This study revealed that freeze-drying of foamedmaterials is limited by heat transfer, while for nonfoamed ones, by masstransfer. It was shown that the insulation property characteristic of foams wasmore significant in slowing down the freeze-drying process than the increasedsurface area available for mass transfer due to foaming. ANN can be used toobtain excellent predictions of moisture content and temperature during thefreeze-drying process. No practical minimal thickness could be found for 1%MC or 3% EW foams in order to increase dryer throughput.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support of FondsQuébécois de la Recherche sur la Nature et les Technologies (Québec,Canada), as well as Olivier Quirion-Blais and Monica Araya-Fariàs for theirvaluable assistance during this study.

REFERENCES

AOAC. 1990. Official Methods of Analysis, Association of Official AnalyticalChemists, Washington, DC.

BELLOWS, R.J. and KING, C.J. 1973. Product collapse during freeze-dryingof liquid foods. AIChE Symp. Ser. 69(132), 31.

BRYGIDYR, A.M., RZEPECKA, M.A. and MCCONNELL, M.B. 1977.Characterization and drying of tomato paste foam by hot air and micro-wave energy. J. Can. Inst. Food Sci. Technol. 10(4), 313–319.

COOKE, R.D., BREAG, G.R., FERBER, C.E.M., BEST, P.R. and JONES, J.1976. Studies of mango processing I. The foam-mat drying of mangopuree. J. Food Technol. 11, 463–473.

GOÑI, S.M., ODDONE, S., SEGURA, J.A., MASCHERONI, R.H. and SAL-VADORI, V.O. 2008. Prediction of foods freezing and thawing times:Artificial neural networks and genetic algorithm approach. J. Food Eng.84(1), 164–178.

HATAKEYAMA, T., NAKAMURA, K. and HATAKEYAMA, H. 2000.Vaporization of bound water associated with cellulose fibres. Thermo-chim Acta 352–353, 233–239.

HERTZENDORF, M.S. and MOSHY, R.J. 1970. Foam mat drying in the foodindustry. Crit. Rev. Food Technol. 1, 25–70.

HUANG, B. and MUJUMDAR, A.S. 1993. Use of neural network to predictindustrial dryer performance. Drying Technol. 11(3), 525–541.


KARIM, A.A. and WAI, C.C. 1999a. Foam-mat drying of starfruit (Averrhoacarambola L.) purée. Stability and drying characteristics. Food Chem.64, 337–343.

KARIM, A.A. and WAI, C.C. 1999b. Characteristics of foam prepared fromstarfruit puree by using methylcellulose. Food Hydrocolloids 13, 203–210.

MATTEA, M., URBICAIN, M.J. and ROTSTEIN, E. 1986. Prediction ofthermal conductivity of vegetable foods by the Effective Medium Theory.J. Food. Sci. 51, 113–134.

MITTAL, G.S. and ZHANG, J. 2002. Prediction of food thermal processevaluation parameters using neural networks. Int. J. Food Microbiol. 79,153–159.

MORGAN, A.I., GRAHAM, R.P., GINNETTE, L.P. and WILLIAMS, G.S.1961. Recent developments in foam-mat drying. Food Technol. 15(1),37–39.

MOY, J.H. 1971. Vacuum-puff freeze-drying of tropical fruit juices. J. FoodSci. 36(6), 906–910.

MUHAMMAD, N., ANWAR, M., AFZAL, M., EHTESHAMUDDIN, A. andJAMIL, M. 1988. Egg powder by foam-mat drying. Pak. J. Sci. Ind. Res.31, 303–306.

NIJHUIS, H.H., TORRINGA, H.M., MURESAN, S., YUKSEL, D., LEGRIT,C. and ET KLOEK, W. 1998. Approaches to improving the quality ofdried fruit and vegetables. Food Sci. Technol. 9, 13–20.

PALMFELDT, J., RÅDSTRÖM, P. and HAHN-HÄGERDAL, B. 2003. Opti-misation of initial cell concentration enhances freeze-drying tolerance ofPseudomonas chlororaphis. Cryobiology, 47(1), 21–29.

PIAZZA, L., GIGLI, J. and BULBARELLO, A. 2008. Interfacial rheologystudy of espresso coffee foam structure and properties. J. Food Eng. 84,420–429.

PRUD’HOMME, R.K. and KHAN, S.A. 1996. Foams-Theory, Measurements,and Applications, p. 511, Marcel Dekker Inc., New York, NY.

RAHARITSIFA, N., GENOVESE, D.B. and RATTI, C. 2006. Characteriza-tion of apple juice foams for foam-mat drying prepared withEgg white protein and methylcellulose. J. Food Sci. 71(3), E142–E151.

RAJKUMAR, P., KAILAPPAN, R., VISWANATHAN, R. and RAGHAVAN,G.S.V. 2007. Drying characteristics of foamed alphonso mango pulp in acontinuous type foam mat dryer. J. Food Eng. 79(4), 1452–1459.

RATTI, C. 1994. Shrinkage during drying of foodstuffs. J. Food Eng. 23(1),91–105.

RATTI, C. 2001. Hot air and freeze-drying of high-value foods: A review.J. Food Eng. 49(4), 311–319.


ROOS, Y.H. 1995. Phase Transitions in Foods, Academic Press, San Diego,CA.

SAGARA, Y. and ICHIBA, J. 1994. Measurement of transport properties forthe dried layer of coffee solution undergoing freeze drying. DryingTechnol. 12(5), 1081–1103.

SANKAT, C.K. and CASTAIGNE, F. 2004. Foaming and drying behaviour ofripe bananas. Lebensm.-Wiss. Technol. 37, 517–525.

SATYANARAYANA RAO, T.S. and MURALI, H.S. 1988. Changes in lipidsof spray dried, freeze-dried and foam-mat dried, whole egg powdersduring storage. Lebensm.-Wiss. Technol. 22(5), 217–221.

SHAMAEVA, A.P., TOLSTYAKOV, D.N. and FEDOROVA, F.G. 1987.Water-content dependence of the thermal conductivity for a phenolicfoam plastic composite. Translated from Izmeritel″naya Tekhnika. MeasTech. 30(5), 464–465.

SHARMA, N.K. and ARORA, C.P. 1995. Influence of product thickness,chamber pressure and heating conditions on production rate of freeze-dried yoghurt. Int. J. Refrig. (UK) 18(5), 297–307.

TORRECILLA, J.S., OTERO, L. and SANZ, P.D. 2005. Artificial neuralnetworks: A promising tool to design and optimize high-pressure foodprocesses. J. Food Eng. 69(3), 299–306.

VERNON-CARTER, E.J., ESPINOSA-PAREDES, G., BERISTAIN, C.I. andROMERO-TEHUITZIL, H. 2001. Effect of foaming agents on the sta-bility, rheological properties, drying kinetics and flavour retention oftamarind foam-mats. Food Res. Intern. 34, 587–598.

WOLFF, E. and GIBERT, H. 1988. Développements technologiques nou-veaux en lyophilisation. J. Food Eng. 8(2), 91–108.

YU, R., LEUNG, P.S. and BIENFANG, P. 2006. Predicting shrimp growth:Artificial neural network versus nonlinear regression models. Aquac.Eng. 34(1), 26–32.


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FOAM-MAT FREEZE-DRYING OF APPLE JUICE PART 1: EXPERIMENTAL DATA AND ANN SIMULATIONS