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Modelling of vacuum osmotic dehydration of food
~~zl~nuf ofFood Enaineerina 22 (19941313-328 8 1594 El&x Scieke Limited Printed in Great Britain. All rights reserved ~26~-S~~41~4lS~.~~ ELSEVIER
Modelling of Vacuum Osmotic Dehydration of Food Pedro Fito Departamento
de Tecnologia de Alimentos, Universidad Politkxica Camino de Vera 14, Valencia, Spain
de Valencia,
ABSTRACT Vacuum osmotic dehydration leads to some advantagesas compared with atmospheric osmotic dehydration. The influence of vacuum treatment is very important on the kinetics of the mass transferphenomena, especially concerning water loss and weight reduction of food during osmotic treatment. This effect of vacuum application cannot be explained only on the basis of di~sional and osmotic tra~porr mechanist. So, a hydrodynamic mechanism has been proposed and experimentally ana~ysed. Taking this new mechanism into account, a more accurate approach to the modelling of the vacuum osmotic dehydration operation may be done.
INTRODUCTION In the last few years, osmotic dehyration (OD) of food, especiahy of fruits and vegetables, has been studied in many tests (Le Maguer, 1988; Mata, 1991; Raoult-Wack, 1991). There are some recent pub~cations which show the OD advantages and disadvantages and some important efforts have been made to model the operation through the analysis of its mass transfer phenomena, especially inside the food (Tyree, 1970; Toupin & Le Maguer, 1989; Toupin et al., 1989; Marcotte & Le Maguer, 1991; Marcotte et al., 1991; Raoul-Wack, 1991; Marcotte & Le Maguer, 1992; Fito & Pastor, 1993). Most of these studies were done at atmospheric pressure. However, some vacuum studies prove that under these conditions quicker dehydration kinetics are obtained (Zozulevich & D’yachenko, 1969; Hawkes & Flink, 1978; DalIa Rosa et al., 1982; Mata, 1991; Pastor et&., 1992a, b). 313
Pedro Fito
314
Figures 1 to 4 show, as an example, the results obtained in the osmotic dehydration of apple slices (var: Granny Smith) corresponding to experimental work done in the Departamento de Tecnolo@a de Alimentos of Universidad Politecnica de Valencia (Mata, 1991; Mata & Fito, 1992; Pastor et al., 1992a, b). The results of water loss and solutes gain correspond to experiments done with apple slices 8 mm thick, using a 65% saccharose solution working at 50 and 60°C and with pressures of 1030, 176 and 120 mbars (the last two are the steam pressures at each tested temperature). Note that vacuum-wor~g significantly increased the water loss rate compared to that obtained at atmospheric pressure at the same temperature. Thus, the lower the working pressure was, the more spoilt the difference was. However, the solutes gain did not seem to be affected by the working pressure. This increase of mass transfer rate when vacuum-working is difficult to explain using classical, diffusional and osmotic mechanisms. Even the traditional approach of a capillary mechanism cannot correctly explain the dependence between transfer rate and work pressure. For this reason, a vacuum mass transfer mechanism, which occurs when vacuum-work~g, was described in a previous work (Fito & Pastor, 1993). This was called a ‘hydrodynamic mechanism’ (HDM). In this work, the study of the HDM in the case of fruits is expanded and the possib~ity that the HDM knowledge leads to a better vacuum osmotic
0 Fig.
1.
2 5OA
4 ---Q---
6
Sov
Water loss in apple slices in OD at 50°C; atmospheric (Vi.
8
10 time(b
)
pressure (A), vacuum
315
Modelring of vacuum osmotic dehydration of food
dehydration (VOD) model is analysed. Better knowledge of the mass transfer mecha~sms and their relation to the food ~crost~cture permits not only improvement of the existing processes, but also the use of vacuum food impregnation as an implement for the development of new products.
0
2
--Q--WY\
Fig. 2.
4 ---_o__
6
8
10
time(h
60”
Water loss in apple slices in Or) at 60°C; atmosp~e~c 0.9.
)
pressure {A), vacuum
70 x -t m
60
so
40
30
20 10
ot 0
2 ’
---3--
Fig. 3.
SOA
----t
time(h
) lo
5ov
Sugar gain (Brix) of apple slices in OD at 50°C; atmospheric vacuum (V 1.
pressure
(A),
316
Pedro Fito
0
v
Fig. 4.
2 6oA
4 --+--
6
10
8
time@
&Iv
Sugar gain (Brix) of apple slices in OD at 60°C; atmospheric vacuum (v).
INFLUENCE
OF STRUCTURE
)
pressure
(A),
ON MASS TRANSFER
The porous food structure plays a basic role in the mass transfer that takes place in the vacuum operations on porous food. Therefore, the study of pores should be included in the work plan of any research on the subject (Aguilera & Stanley, 1991). The presence of pores in food can be caused by multiple factors. In some fruit such as apples, the presence of intercellular spaces (ICS) is characteristic in the parenchymatical tissue (Trakoontivakorn et al., 1988). This kind of study was done on different fruits and the ~terrelation between structure, structural parameters and operational variables in VOD (Domingo & Lluch, 1991; Mata, 1991; Puig, 1992a,b) were quantified. Figure 5 shows a portion of apple tissue where an ICS can be observed. In general, this study will concern pores and, therefore, will refer to the structural elements, occupied by gas, that form the porous structure of food.
HDM MOD~LIZA~~N In a previous study, Fito and Pastor ( 1993) showed that the mass transfer produced by driving forces due to pressure gradients (capillary and/or
Modeling of vacuum osmotic dehydration offood
Fig. 5.
317
Scanning electron micrograph of apple tissue where an ICS may be observed.
I+....___________.__.
sdutian
z . . . . . . . . .._...~... Gas -----YP*FP*
-2 --
kIlOtiC
Sdid
I
i
4
i
Liquid
i pa=p*+p
Shation at t=O pio+=w
Fig. 6.
The HDM in an ideal pore.
imposed) could be calculated according to a model named the hydrodynamic mechanism, which is described as follows. Figure 6 schematically shows an ideal situation in which a pore is represented by a cylinder of constant diameter I) and length z. The interior of the pore is assumed to be occupied by gas at pressure pi while in the exterior a liquid exists at pressure p,. This last pressure is equal to the system pressure p2 plus the capillary pressure pC, which can be calculated
318
Pedro Fito
by the Young-Lap~ace
equation:
where cris the surface tension. En a simplified form, the penetration of the liquid into the pore, as an effect of the pressure gradient, can be calculated by 32~~ -Api-----DZ
dx, x”z=O
(2)
where p is the liquid viscosity, and the penetration depth of the liquid into the pore has been expressed as a function of the volume fraction of the pore occupied by the liquid (x,). The increase in pressure or driving force will progressively diminish as a consequence of the pi increase when the gas is compressed. Assuming an isothermal compression:
where pi0 is the initial value of gas pressure. From eqns (2) and (3): Pi0
”
l-x,
+3Qz* D’
dx, X, ---0 dt
(4
The equilibrium condition is reached when pressures become equal, and
From eqns (4) and (5) the x, value at equilibrium can be deduced:
and substituting:
Hence:
Pe=Pz+Pc
(7)
PiO”Pl
(8)
Model@
of vacuum osmotic dehydration offood
319
=(P2fPc-Pl)
x ”
(P2
PC)
+
When there are no pressure gradients imposed on the system, p, =p2 and the single driving force is p,. In this case:
xv =(p2P;pJ
(W
Equation (9) can now be written in a more simplified way such as
(11) where r is the actual compression
ratio:
r=(P2+Pc)= Pl
p2 + fi Pl 00
PI
(12)
It can be defined:
R,pz
(13)
PI
where R is the apparent compression
ratio, and
pr& Pl
(14)
where pr is the reduced capillary pressure. This will result in r=
R+p,
(15)
In many cases, pr is much smaller than R and it may be accepted that Y= R. Once an x, mean value is calculated, the calculation can be extended to the total food volume, multiplying it by the effective porosity ( EJ, which is defined as the fraction of the food total volume which is occupied by gas. Therefore, the volumetric fraction of the liquid (x) transferred by the HDM will be X=&X e ”
(16)
320
Pedro Fito
Figure 7 shows X, values calculated with eqn (12) as a function of R and pr The curve corresponding to R = 1 only describes the capillary effect, without imposed pressure gradients. It can be noted that, for low pr values, the X, values were small. Nevertheless, when increasing pr (e.g. working at low pressures) the X, value considerably increased. There was a great increase when external pressure gradients (R> 1) were imposed as can be seen in the corresponding set of curves.
HDM EXPERIMENTAL
VERIFICATION
With the same experimental method described in a previous paper (Fito & Pastor, 1993), the HDM behaviour in eight different fruits was studied (And& & Fito, 1992). Isotonic saccharose solutions from 1030 to 50 mbars were also used. The fruits studied were: papaya, mango, peach, apricot, banana, pear, pineapple and apple. In Fig. 8 the experimental values achieved in each case were shown against 1 - l/r, according to eqn ( 11); it has been assumed that R = r since no data on the mean values of the pore diameter were available, and therefore p, could not be calculated. It could be observed that in many cases it was only possible to adjust a line in the low pressure range as the theory predicts when p, was discarded.
0.6
Fig. 7.
-
R=20
-
R=IO
-
R=X
-
R=6
-
R=4
-
R=2 -
Values of x, from eqn (11) for different p, and R values.
R=I
321
Mudelling of vacuum usmoric dehydration offood
In the case of predicting E,, this function was adjusted in all cases: x=K i
l-1r
1 +x0
(17)
The K and x0 parameter values, as well as the x,,, experimental value at atmospheric pressure, are shown in Table 1. The E, values for each of the experiments done was calculated by the equation: x e,=-
l-1 i
r
1
5
0 0.0
0.2
0.4
0.6
0.8
1.0
l-l/r
Fig. 8.
Expe~ment~ values of x against 1-l/r for the different fruits tested.
TABLE 1 Xa,,, X0and K Parameter Values for Each One of the Tested Fruits
Papaya Mango Peach Apricot Banana Pear Pineapple Apple
2.567 0.606 1.505 1.453 0+571 1.767 0.001 2.280
2675 - 8.770 - 12.456 -0.159 0.496 -0.615 -0851 - 1-721
1.989 23.794 26.027 4.96 1 18.336 14,724 6.796 2 1.248
Pedro Fito
322
in which the x and Yexperimental values were used in each case. Figure 9 shows the results obtained for ail tested fruits, compared with the pressures used. For pressures below 600 mbars, the E, experimental values kept practically constant as expected. An increase in effective porosity (E,) was noticed only for mango and peach when pressure decreases. It was possibly due to a loss of native liquid during the expansion and release stage of the gas occluded in the pores. This loss will cause an increase in the inner volume of pores which was available for the gas phase, TYPICAL STEPS IN A MASS TRANSFER OPERATION BETWEEN A POROUS FOOD AND A LIQUID UNDER VACUUM CONDITION For a good understanding of how and when the mass transfer mena are produced by the HDM as well as their importance, it esting to analyse the typical steps that take place in a process in porous solid was immersed in a liquid under vacuum conditions food rehydration, vacuum impregnation, etc.) These steps are: Step Step Step Step
1 2 3 4
phenois interwhich a (VOD,
The solid was immersed in the liquid at atmospheric pressure. The working pressure was applied to the system (p < p,,). The system was held at working pressure for a time of t. The system was placed at atmospheric pressure again. The solid was removed from the liquid.
Figure 10 shows schematically what would happen in a food pore (simplified as a cylinder) along the stages mentioned above. In order to
Fttpya -
Mango
-
Peach
-
Apncnt
-w -pear
0 i
0
I
xl0
$
1
400
600
-t-
Pineapple
-
Apple
P(mb)
Fig. 9.
Effective porosity values at different pressures for each fruit.
~odelling o~vacu~m osmotic dehydration Osgood
323
t=o Pore with gas No liquid InsIde
HDM (P=l030mb) Only capillarity xv= O-018
P change to 7OOmb Gas expands and flow out.
HDM (P=l OOmb) Only capillarity XV= 0.15
Atmosfenc pressure restored. HDM Capillanty and external pressure as drivmg forces xv= 0.9 solld
Fig. 10.
m
gas a
llquld
H
E
Typical steps in a mass transfer operation between a porous food immersed in a liquid at vacuum conditions. Situation of an ideal pore.
the effects produced by the HDM, on the right of each figure there are the X, values that would appear if the food were an apple of the Granny Smith variety {p, = 19 mbars, I) = 160 ,um and &e= O-22). The first stage described would cause the situations represented by the Fig. 10(A) and (B), with a penetration of liquid due to a capillary effect of only X, = 0.018. In terms of total volume fraction of the fruit, this only represented a value of 0.396%. The second stage (Fig. 10(C) and (D)) would produce, in the first place, an expansion of the gas occluded in the pores. In some cases it could take away some of the food native liquid (if there was any). Once the gas pressure was made equal to the system pressure, the HDM would be produced which, this time, according to eqn (11) and assuming a work pressure of 100 mbars, will result in a value of xY= O-15. It is important to notice that just the fact of decreasing the work pressure has increased the x, value more than eight times. This would be the situation of the system during the third stage, although the situation would be frequently complicated by the structural
quantify
324
Pedro Fit5
changes occurring during the process (shrinkage). All this explained why the mass transfer kinetics was quicker when working at vacuum for OD operations. In the first place, the HDM contributes to a total transport in a much more important way when vacuum working. Secondly, the other mechanisms (diffusional and osmotic) have a larger interface surface available because of a greater occupation of the internal surface of the pores. When the atmosphe~c pressure finally returned to the system, the HDM acted again, this time as an effect of the pressure gradients imposed when changing the external pressure (Fig. 10(E)). The effect was now much more important; x, = 0.9. It means an amount of liquid was transported to the interior of food. It was, in the case of apple, 19.8% of the total fruit volume. It is important to indicate that this value depends on the working pressure (eqn (11)). Therefore, this phenomenon can be controlled and is, in a way, reversible.
HDM APP~~ATI~~S As has been said, the net mass flows transferred in the vacuum operations between porous foods and a liquid in which they are immersed were the result of the contribution of several mechanisms (osmotic, diffusion, etc.). Among them, the HDM may play an important role in terms of total amount of transferred mass. Experimental results as those of Figs 1 and 4 are difficult to understand if the HDM contribution is ignored. In this sense it is very useful for the interpretation of the experimental results of VOD to calculate the net flows of water and solutes produced by the HDM (through eqn ( 11) and those follow~g) and to analyse the water loss and solutes gain kinetics, discounting the HDM contribution. Figures 11, 12 and 13 show the values corrected in this way for the water loss and solutes gain of the same experiments shown in Figs 1 to 4. In this case, the differences between the experiments done in vacuum and those done at atmospheric pressure can be observed especially the gain and solutes that were not seen before the HDM effect was corrected. As regards the water loss values, the differences between atmospheric pressure and vacuum were even greater when discoun~g the HDM since this is a mechanism that transfers an osmotic solution at 65% of saccharose inside the food. It consequently produces a decrease in the humidity of the sample. The main advantage of the VOD against the OD atmospheric pressure lies in the mass transfer due to the HDM and to the corresponding
325
Modelling of vacuum osmotic dehydration offood
1 2
..._.....+f__
......I....\ .................“j .....................
q
soToveInli~lo6s
l
wc!wa!$lomnDMdimmctd
l
twcovcniuwatcrlars
0
0 Fig.
11.
s
4
f
I
6
a
Time(h)
Water loss of apple slices at 50 and 60°C during VOD, discounting contribution.
0 Fig. 12.
I 2
600~ Water loss HDH d&comted
2
4
6
a
Sugar gain of apple slices at 50°C during VOD, discounting tribution.
”
the HDM
Time(h)
”
the HDM con-
increment produced in the solid-liquid inter-facial surface. The obstacle is basically the higher cost of the equipment. Considering that (Fig 10(E)) the most important HDM effect is very quick and occurs just when the system is placed at atmospheric pressure again, a new procedure was designed to carry out the VOD, which is called pulsed vacuum osmotic dehydration (P-VOD) {Fito et al., 1992). Through this procedure, short periods (e.g. 5 mm) of vacuum ~~tment
Pedro Fito
326 0.25
q
. ... -0.05
1 0
Fig. 13.
“_i .................... ... 2
i .. .
..i 1 4
l
j I
sugar Gain
SugarGain
HDMdimted I
6
Time(h)
8
Sugar gain of apple slices at 60°C during VOD, discounting tribution.
Water
loss
A
4OT,normal 35T,vacuum
fresh
A
35”C,pulse vacuum 35T,normal
pressure
(Kg/Kg
fresh
0
WC,normal
l
35T,vacuum
o
35T,pulse
’
35”C,normal pressure
Water loss and sugar gain of apricot halves at different pressures, (OD, VOD and P-VOD).
fruit)
pressure
0
gain
lo
the HDM con-
(Kg/Kg
IJ
Sugar
Fig. 14.
overall
..____ ~_‘_._...._~
fruit)
pressure
vacuum
temperatures
and
were applied to the product, while it was immersed in the osmotic solution. After that, the products undergo normal osmotic dehydration at atmospheric pressure. In this way, the filling of the food pores with the same osmotic solution was induced at the beginning of the treatment. It brings with it most of the VOD advantages. However, the treatment was carried out most of the time in an atmospheric pressure installation. This procedure is being studied at present and offers very good prospects.
Modelling of vacuum osmotic dehydration offood
327
Figure 14 shows the results achieved using apricot, at different temperatures and pressures. It is interesting to compare the results of water loss and solute gain at 40°C and vacuum (70 mb). The values obtained through the P-VOD procedure (a 5 min pulse at 70 mb follo.wed by the rest of the atmospheric pressure treatment) are only slightly inferior to those achieved by the VOD procedure, but very superior to those obtained at atmospheric pressure.
CONCLUSIONS The HDM analysed in this study offers a better understanding of the mass transfer phenomenon produced in the vacuum operations of porous food impregnation with liquids. The proposed equations permit the calculation of the volumes of liquid transferred through this mechanism and explain the influence of pressure and of the microstructural characteristics of food. Therefore, using this mechanism it is possible to model the operations better and to improve them.
REFERFNCES Aguilera, J. M. & Stanley, D. W. (1990). Microstructural Principles of Food Processing and Engineering. Elsevier Applied Science, London, 343 pp. Andres, A. & Fito, P. (1992). The hydrodynamic penetration mechanism in some fruits. In 1sopO W- V Valencia, Spain. Dalla Rosa, M., Pinnavaia, G. & Lerici, C. R. (1982). La disidratazione della frutta median& osmosi diretta. Notta II. Esperienze di laboratorio su alcumi generi di frutta. Industri~ Consewe, 57,3-7. Domingo, L. & Lluch, M. A. (1991). Estudio de las modifi~aciones microestructurales de la ma~ana Malus Comunis L. ‘Granny Smith sometida a deshidratacion osmotica. Anales de Investigation de1 Master en Ciencia e Ingenieria de Alimentos. Vol. 1; SPUPV. Valencia, Spain, pp. 709-32. Fito, P. & Pastor, R. (1993). Non diffusional mechanisms occurring during vacuum osmotic dehydration. J. Food Eng., 2 1,5 13- 19. Fito, P., Shi, X. Q., Chiralt, A., Acosta, E. & Andres, A. (1992). Vacuum osmotic dehydration of fruits. In ISOPO W-V Valencia, Spain. Hawkes, J. & Flink, J. M. (1978). Osmotic concentration of fruits slices prior to freeze dehydration. J. FoodProc. Pres., 2,26.5-84. Le Maguer, M. ( 1988 ). Osmotic dehydration: review and future directions. In Proc. symposium on Progress in Food Prese~~tio~ Processes, Vol. 1. Gentre for Education and Research of Food and Chemical Industries, Brussels, pp. 183-309. Marcotte, M. & Le Maguer, M. (1992). Mass transfer in cellular tissues; part 2. Computer simulations vs: experimental data. J. Food Eng., 17, 177.
328
PedroFito
Marcotte, M., Toupin, C. J. & LeMaguer, M. (1991). Mass transfer in cellular tissues. Part 1. The mathematical model. J. Food Eng., 13, 199. Mata, M. (1991). Aportacion al desarrollo de un proceso de deshidratacion osmotica a vacio de alimentos. PhD, U~versidad Politecnica de Valencia, Spain. Mata, M. & Fito, P. ( 1992). Vacuum osmotic dehyration of foods (VOD) I: Design and evaluation of a pilot plant. In ISOPOW-k’, Valencia, Spain, 260 PP. Pastor, R., Mata, M., Fito, P. (1992~). Deshidratacion Osmotica de manzana. Anales de Investigation de1 Master en Ciencia e Ingenieria de Alimentos. Vol. 1, SPUPV. Valencia, Spain, pp. 857-74. Pastor, R., Mata, M. & Fito, P. (19923). Vacuum osmotic dehydration of foods (VOD) II. Introduction to modelization of transfer phenomena in apple (Granny Smith} drying. In 1&SOPO W-I/. Valencia, Spain. Puig, A. (1992~). Effect of atmospheric and vacua osmotic dehydration on microst~cture of pineapple (a~a~as combo L; var; Cayena Lisa). In ISOPOW-V. Vaiencia, Spain. Puig, A. (19923). Effect of atmospheric and vacuum osmotic dehydration on microstructure of mango (Mangifka indica L; var. Haden). In ISOPO W-V, Valencia, Spain. Raoult-Wack, A. ( 199 1). Les procedes de Deshydratation-Impregnation par imnersion dans des solutions concentrees (DII). Etude experimentale et modelisation des transfer@ d’eau et de solute sur gel modele. PhD, Universite Montpellier II France, 150 pp. Toupin, C. J., LeMaguer, M. ( 1989). Osmotically induced mass transfer in plant storage tissues: a mathematical model Part 2. J. Food Eng., 10,97- 121. Toupin, C. J., Marcotte, M. & LeMaguer, M. (1989). Osmotically induced mass transfer in plant storage tissues: a ma~ematical model Part 1. J. Food Eng., 10,13-38.
Trakoontivakorn, G., Patterson, M. E., Swansoo, B. G. (1988). Scanning electron microscopy of cellular structure of Granny Smith and Red Delicious apples. Food Microstructure, 7,205- 12. Tyree, M. T. (1970). The symplast concept. A general theory of symplastic transport according to the thermodynamics of irreversible processes. J. Theor. Biol., 26,181-9.
Zozulevich, B. V. & D’yachenko, E. N. ( 1969). Osmotic dehydration of fruits. Konservn. Ovoshches~ch. Prom., 7,32-42.
Modelling of Vacuum Osmotic Dehydration of Food Pedro Fito Departamento
de Tecnologia de Alimentos, Universidad Politkxica Camino de Vera 14, Valencia, Spain
de Valencia,
ABSTRACT Vacuum osmotic dehydration leads to some advantagesas compared with atmospheric osmotic dehydration. The influence of vacuum treatment is very important on the kinetics of the mass transferphenomena, especially concerning water loss and weight reduction of food during osmotic treatment. This effect of vacuum application cannot be explained only on the basis of di~sional and osmotic tra~porr mechanist. So, a hydrodynamic mechanism has been proposed and experimentally ana~ysed. Taking this new mechanism into account, a more accurate approach to the modelling of the vacuum osmotic dehydration operation may be done.
INTRODUCTION In the last few years, osmotic dehyration (OD) of food, especiahy of fruits and vegetables, has been studied in many tests (Le Maguer, 1988; Mata, 1991; Raoult-Wack, 1991). There are some recent pub~cations which show the OD advantages and disadvantages and some important efforts have been made to model the operation through the analysis of its mass transfer phenomena, especially inside the food (Tyree, 1970; Toupin & Le Maguer, 1989; Toupin et al., 1989; Marcotte & Le Maguer, 1991; Marcotte et al., 1991; Raoul-Wack, 1991; Marcotte & Le Maguer, 1992; Fito & Pastor, 1993). Most of these studies were done at atmospheric pressure. However, some vacuum studies prove that under these conditions quicker dehydration kinetics are obtained (Zozulevich & D’yachenko, 1969; Hawkes & Flink, 1978; DalIa Rosa et al., 1982; Mata, 1991; Pastor et&., 1992a, b). 313
Pedro Fito
314
Figures 1 to 4 show, as an example, the results obtained in the osmotic dehydration of apple slices (var: Granny Smith) corresponding to experimental work done in the Departamento de Tecnolo@a de Alimentos of Universidad Politecnica de Valencia (Mata, 1991; Mata & Fito, 1992; Pastor et al., 1992a, b). The results of water loss and solutes gain correspond to experiments done with apple slices 8 mm thick, using a 65% saccharose solution working at 50 and 60°C and with pressures of 1030, 176 and 120 mbars (the last two are the steam pressures at each tested temperature). Note that vacuum-wor~g significantly increased the water loss rate compared to that obtained at atmospheric pressure at the same temperature. Thus, the lower the working pressure was, the more spoilt the difference was. However, the solutes gain did not seem to be affected by the working pressure. This increase of mass transfer rate when vacuum-working is difficult to explain using classical, diffusional and osmotic mechanisms. Even the traditional approach of a capillary mechanism cannot correctly explain the dependence between transfer rate and work pressure. For this reason, a vacuum mass transfer mechanism, which occurs when vacuum-work~g, was described in a previous work (Fito & Pastor, 1993). This was called a ‘hydrodynamic mechanism’ (HDM). In this work, the study of the HDM in the case of fruits is expanded and the possib~ity that the HDM knowledge leads to a better vacuum osmotic
0 Fig.
1.
2 5OA
4 ---Q---
6
Sov
Water loss in apple slices in OD at 50°C; atmospheric (Vi.
8
10 time(b
)
pressure (A), vacuum
315
Modelring of vacuum osmotic dehydration of food
dehydration (VOD) model is analysed. Better knowledge of the mass transfer mecha~sms and their relation to the food ~crost~cture permits not only improvement of the existing processes, but also the use of vacuum food impregnation as an implement for the development of new products.
0
2
--Q--WY\
Fig. 2.
4 ---_o__
6
8
10
time(h
60”
Water loss in apple slices in Or) at 60°C; atmosp~e~c 0.9.
)
pressure {A), vacuum
70 x -t m
60
so
40
30
20 10
ot 0
2 ’
---3--
Fig. 3.
SOA
----t
time(h
) lo
5ov
Sugar gain (Brix) of apple slices in OD at 50°C; atmospheric vacuum (V 1.
pressure
(A),
316
Pedro Fito
0
v
Fig. 4.
2 6oA
4 --+--
6
10
8
time@
&Iv
Sugar gain (Brix) of apple slices in OD at 60°C; atmospheric vacuum (v).
INFLUENCE
OF STRUCTURE
)
pressure
(A),
ON MASS TRANSFER
The porous food structure plays a basic role in the mass transfer that takes place in the vacuum operations on porous food. Therefore, the study of pores should be included in the work plan of any research on the subject (Aguilera & Stanley, 1991). The presence of pores in food can be caused by multiple factors. In some fruit such as apples, the presence of intercellular spaces (ICS) is characteristic in the parenchymatical tissue (Trakoontivakorn et al., 1988). This kind of study was done on different fruits and the ~terrelation between structure, structural parameters and operational variables in VOD (Domingo & Lluch, 1991; Mata, 1991; Puig, 1992a,b) were quantified. Figure 5 shows a portion of apple tissue where an ICS can be observed. In general, this study will concern pores and, therefore, will refer to the structural elements, occupied by gas, that form the porous structure of food.
HDM MOD~LIZA~~N In a previous study, Fito and Pastor ( 1993) showed that the mass transfer produced by driving forces due to pressure gradients (capillary and/or
Modeling of vacuum osmotic dehydration offood
Fig. 5.
317
Scanning electron micrograph of apple tissue where an ICS may be observed.
I+....___________.__.
sdutian
z . . . . . . . . .._...~... Gas -----YP*FP*
-2 --
kIlOtiC
Sdid
I
i
4
i
Liquid
i pa=p*+p
Shation at t=O pio+=w
Fig. 6.
The HDM in an ideal pore.
imposed) could be calculated according to a model named the hydrodynamic mechanism, which is described as follows. Figure 6 schematically shows an ideal situation in which a pore is represented by a cylinder of constant diameter I) and length z. The interior of the pore is assumed to be occupied by gas at pressure pi while in the exterior a liquid exists at pressure p,. This last pressure is equal to the system pressure p2 plus the capillary pressure pC, which can be calculated
318
Pedro Fito
by the Young-Lap~ace
equation:
where cris the surface tension. En a simplified form, the penetration of the liquid into the pore, as an effect of the pressure gradient, can be calculated by 32~~ -Api-----DZ
dx, x”z=O
(2)
where p is the liquid viscosity, and the penetration depth of the liquid into the pore has been expressed as a function of the volume fraction of the pore occupied by the liquid (x,). The increase in pressure or driving force will progressively diminish as a consequence of the pi increase when the gas is compressed. Assuming an isothermal compression:
where pi0 is the initial value of gas pressure. From eqns (2) and (3): Pi0
”
l-x,
+3Qz* D’
dx, X, ---0 dt
(4
The equilibrium condition is reached when pressures become equal, and
From eqns (4) and (5) the x, value at equilibrium can be deduced:
and substituting:
Hence:
Pe=Pz+Pc
(7)
PiO”Pl
(8)
Model@
of vacuum osmotic dehydration offood
319
=(P2fPc-Pl)
x ”
(P2
PC)
+
When there are no pressure gradients imposed on the system, p, =p2 and the single driving force is p,. In this case:
xv =(p2P;pJ
(W
Equation (9) can now be written in a more simplified way such as
(11) where r is the actual compression
ratio:
r=(P2+Pc)= Pl
p2 + fi Pl 00
PI
(12)
It can be defined:
R,pz
(13)
PI
where R is the apparent compression
ratio, and
pr& Pl
(14)
where pr is the reduced capillary pressure. This will result in r=
R+p,
(15)
In many cases, pr is much smaller than R and it may be accepted that Y= R. Once an x, mean value is calculated, the calculation can be extended to the total food volume, multiplying it by the effective porosity ( EJ, which is defined as the fraction of the food total volume which is occupied by gas. Therefore, the volumetric fraction of the liquid (x) transferred by the HDM will be X=&X e ”
(16)
320
Pedro Fito
Figure 7 shows X, values calculated with eqn (12) as a function of R and pr The curve corresponding to R = 1 only describes the capillary effect, without imposed pressure gradients. It can be noted that, for low pr values, the X, values were small. Nevertheless, when increasing pr (e.g. working at low pressures) the X, value considerably increased. There was a great increase when external pressure gradients (R> 1) were imposed as can be seen in the corresponding set of curves.
HDM EXPERIMENTAL
VERIFICATION
With the same experimental method described in a previous paper (Fito & Pastor, 1993), the HDM behaviour in eight different fruits was studied (And& & Fito, 1992). Isotonic saccharose solutions from 1030 to 50 mbars were also used. The fruits studied were: papaya, mango, peach, apricot, banana, pear, pineapple and apple. In Fig. 8 the experimental values achieved in each case were shown against 1 - l/r, according to eqn ( 11); it has been assumed that R = r since no data on the mean values of the pore diameter were available, and therefore p, could not be calculated. It could be observed that in many cases it was only possible to adjust a line in the low pressure range as the theory predicts when p, was discarded.
0.6
Fig. 7.
-
R=20
-
R=IO
-
R=X
-
R=6
-
R=4
-
R=2 -
Values of x, from eqn (11) for different p, and R values.
R=I
321
Mudelling of vacuum usmoric dehydration offood
In the case of predicting E,, this function was adjusted in all cases: x=K i
l-1r
1 +x0
(17)
The K and x0 parameter values, as well as the x,,, experimental value at atmospheric pressure, are shown in Table 1. The E, values for each of the experiments done was calculated by the equation: x e,=-
l-1 i
r
1
5
0 0.0
0.2
0.4
0.6
0.8
1.0
l-l/r
Fig. 8.
Expe~ment~ values of x against 1-l/r for the different fruits tested.
TABLE 1 Xa,,, X0and K Parameter Values for Each One of the Tested Fruits
Papaya Mango Peach Apricot Banana Pear Pineapple Apple
2.567 0.606 1.505 1.453 0+571 1.767 0.001 2.280
2675 - 8.770 - 12.456 -0.159 0.496 -0.615 -0851 - 1-721
1.989 23.794 26.027 4.96 1 18.336 14,724 6.796 2 1.248
Pedro Fito
322
in which the x and Yexperimental values were used in each case. Figure 9 shows the results obtained for ail tested fruits, compared with the pressures used. For pressures below 600 mbars, the E, experimental values kept practically constant as expected. An increase in effective porosity (E,) was noticed only for mango and peach when pressure decreases. It was possibly due to a loss of native liquid during the expansion and release stage of the gas occluded in the pores. This loss will cause an increase in the inner volume of pores which was available for the gas phase, TYPICAL STEPS IN A MASS TRANSFER OPERATION BETWEEN A POROUS FOOD AND A LIQUID UNDER VACUUM CONDITION For a good understanding of how and when the mass transfer mena are produced by the HDM as well as their importance, it esting to analyse the typical steps that take place in a process in porous solid was immersed in a liquid under vacuum conditions food rehydration, vacuum impregnation, etc.) These steps are: Step Step Step Step
1 2 3 4
phenois interwhich a (VOD,
The solid was immersed in the liquid at atmospheric pressure. The working pressure was applied to the system (p < p,,). The system was held at working pressure for a time of t. The system was placed at atmospheric pressure again. The solid was removed from the liquid.
Figure 10 shows schematically what would happen in a food pore (simplified as a cylinder) along the stages mentioned above. In order to
Fttpya -
Mango
-
Peach
-
Apncnt
-w -pear
0 i
0
I
xl0
$
1
400
600
-t-
Pineapple
-
Apple
P(mb)
Fig. 9.
Effective porosity values at different pressures for each fruit.
~odelling o~vacu~m osmotic dehydration Osgood
323
t=o Pore with gas No liquid InsIde
HDM (P=l030mb) Only capillarity xv= O-018
P change to 7OOmb Gas expands and flow out.
HDM (P=l OOmb) Only capillarity XV= 0.15
Atmosfenc pressure restored. HDM Capillanty and external pressure as drivmg forces xv= 0.9 solld
Fig. 10.
m
gas a
llquld
H
E
Typical steps in a mass transfer operation between a porous food immersed in a liquid at vacuum conditions. Situation of an ideal pore.
the effects produced by the HDM, on the right of each figure there are the X, values that would appear if the food were an apple of the Granny Smith variety {p, = 19 mbars, I) = 160 ,um and &e= O-22). The first stage described would cause the situations represented by the Fig. 10(A) and (B), with a penetration of liquid due to a capillary effect of only X, = 0.018. In terms of total volume fraction of the fruit, this only represented a value of 0.396%. The second stage (Fig. 10(C) and (D)) would produce, in the first place, an expansion of the gas occluded in the pores. In some cases it could take away some of the food native liquid (if there was any). Once the gas pressure was made equal to the system pressure, the HDM would be produced which, this time, according to eqn (11) and assuming a work pressure of 100 mbars, will result in a value of xY= O-15. It is important to notice that just the fact of decreasing the work pressure has increased the x, value more than eight times. This would be the situation of the system during the third stage, although the situation would be frequently complicated by the structural
quantify
324
Pedro Fit5
changes occurring during the process (shrinkage). All this explained why the mass transfer kinetics was quicker when working at vacuum for OD operations. In the first place, the HDM contributes to a total transport in a much more important way when vacuum working. Secondly, the other mechanisms (diffusional and osmotic) have a larger interface surface available because of a greater occupation of the internal surface of the pores. When the atmosphe~c pressure finally returned to the system, the HDM acted again, this time as an effect of the pressure gradients imposed when changing the external pressure (Fig. 10(E)). The effect was now much more important; x, = 0.9. It means an amount of liquid was transported to the interior of food. It was, in the case of apple, 19.8% of the total fruit volume. It is important to indicate that this value depends on the working pressure (eqn (11)). Therefore, this phenomenon can be controlled and is, in a way, reversible.
HDM APP~~ATI~~S As has been said, the net mass flows transferred in the vacuum operations between porous foods and a liquid in which they are immersed were the result of the contribution of several mechanisms (osmotic, diffusion, etc.). Among them, the HDM may play an important role in terms of total amount of transferred mass. Experimental results as those of Figs 1 and 4 are difficult to understand if the HDM contribution is ignored. In this sense it is very useful for the interpretation of the experimental results of VOD to calculate the net flows of water and solutes produced by the HDM (through eqn ( 11) and those follow~g) and to analyse the water loss and solutes gain kinetics, discounting the HDM contribution. Figures 11, 12 and 13 show the values corrected in this way for the water loss and solutes gain of the same experiments shown in Figs 1 to 4. In this case, the differences between the experiments done in vacuum and those done at atmospheric pressure can be observed especially the gain and solutes that were not seen before the HDM effect was corrected. As regards the water loss values, the differences between atmospheric pressure and vacuum were even greater when discoun~g the HDM since this is a mechanism that transfers an osmotic solution at 65% of saccharose inside the food. It consequently produces a decrease in the humidity of the sample. The main advantage of the VOD against the OD atmospheric pressure lies in the mass transfer due to the HDM and to the corresponding
325
Modelling of vacuum osmotic dehydration offood
1 2
..._.....+f__
......I....\ .................“j .....................
q
soToveInli~lo6s
l
wc!wa!$lomnDMdimmctd
l
twcovcniuwatcrlars
0
0 Fig.
11.
s
4
f
I
6
a
Time(h)
Water loss of apple slices at 50 and 60°C during VOD, discounting contribution.
0 Fig. 12.
I 2
600~ Water loss HDH d&comted
2
4
6
a
Sugar gain of apple slices at 50°C during VOD, discounting tribution.
”
the HDM
Time(h)
”
the HDM con-
increment produced in the solid-liquid inter-facial surface. The obstacle is basically the higher cost of the equipment. Considering that (Fig 10(E)) the most important HDM effect is very quick and occurs just when the system is placed at atmospheric pressure again, a new procedure was designed to carry out the VOD, which is called pulsed vacuum osmotic dehydration (P-VOD) {Fito et al., 1992). Through this procedure, short periods (e.g. 5 mm) of vacuum ~~tment
Pedro Fito
326 0.25
q
. ... -0.05
1 0
Fig. 13.
“_i .................... ... 2
i .. .
..i 1 4
l
j I
sugar Gain
SugarGain
HDMdimted I
6
Time(h)
8
Sugar gain of apple slices at 60°C during VOD, discounting tribution.
Water
loss
A
4OT,normal 35T,vacuum
fresh
A
35”C,pulse vacuum 35T,normal
pressure
(Kg/Kg
fresh
0
WC,normal
l
35T,vacuum
o
35T,pulse
’
35”C,normal pressure
Water loss and sugar gain of apricot halves at different pressures, (OD, VOD and P-VOD).
fruit)
pressure
0
gain
lo
the HDM con-
(Kg/Kg
IJ
Sugar
Fig. 14.
overall
..____ ~_‘_._...._~
fruit)
pressure
vacuum
temperatures
and
were applied to the product, while it was immersed in the osmotic solution. After that, the products undergo normal osmotic dehydration at atmospheric pressure. In this way, the filling of the food pores with the same osmotic solution was induced at the beginning of the treatment. It brings with it most of the VOD advantages. However, the treatment was carried out most of the time in an atmospheric pressure installation. This procedure is being studied at present and offers very good prospects.
Modelling of vacuum osmotic dehydration offood
327
Figure 14 shows the results achieved using apricot, at different temperatures and pressures. It is interesting to compare the results of water loss and solute gain at 40°C and vacuum (70 mb). The values obtained through the P-VOD procedure (a 5 min pulse at 70 mb follo.wed by the rest of the atmospheric pressure treatment) are only slightly inferior to those achieved by the VOD procedure, but very superior to those obtained at atmospheric pressure.
CONCLUSIONS The HDM analysed in this study offers a better understanding of the mass transfer phenomenon produced in the vacuum operations of porous food impregnation with liquids. The proposed equations permit the calculation of the volumes of liquid transferred through this mechanism and explain the influence of pressure and of the microstructural characteristics of food. Therefore, using this mechanism it is possible to model the operations better and to improve them.
REFERFNCES Aguilera, J. M. & Stanley, D. W. (1990). Microstructural Principles of Food Processing and Engineering. Elsevier Applied Science, London, 343 pp. Andres, A. & Fito, P. (1992). The hydrodynamic penetration mechanism in some fruits. In 1sopO W- V Valencia, Spain. Dalla Rosa, M., Pinnavaia, G. & Lerici, C. R. (1982). La disidratazione della frutta median& osmosi diretta. Notta II. Esperienze di laboratorio su alcumi generi di frutta. Industri~ Consewe, 57,3-7. Domingo, L. & Lluch, M. A. (1991). Estudio de las modifi~aciones microestructurales de la ma~ana Malus Comunis L. ‘Granny Smith sometida a deshidratacion osmotica. Anales de Investigation de1 Master en Ciencia e Ingenieria de Alimentos. Vol. 1; SPUPV. Valencia, Spain, pp. 709-32. Fito, P. & Pastor, R. (1993). Non diffusional mechanisms occurring during vacuum osmotic dehydration. J. Food Eng., 2 1,5 13- 19. Fito, P., Shi, X. Q., Chiralt, A., Acosta, E. & Andres, A. (1992). Vacuum osmotic dehydration of fruits. In ISOPO W-V Valencia, Spain. Hawkes, J. & Flink, J. M. (1978). Osmotic concentration of fruits slices prior to freeze dehydration. J. FoodProc. Pres., 2,26.5-84. Le Maguer, M. ( 1988 ). Osmotic dehydration: review and future directions. In Proc. symposium on Progress in Food Prese~~tio~ Processes, Vol. 1. Gentre for Education and Research of Food and Chemical Industries, Brussels, pp. 183-309. Marcotte, M. & Le Maguer, M. (1992). Mass transfer in cellular tissues; part 2. Computer simulations vs: experimental data. J. Food Eng., 17, 177.
328
PedroFito
Marcotte, M., Toupin, C. J. & LeMaguer, M. (1991). Mass transfer in cellular tissues. Part 1. The mathematical model. J. Food Eng., 13, 199. Mata, M. (1991). Aportacion al desarrollo de un proceso de deshidratacion osmotica a vacio de alimentos. PhD, U~versidad Politecnica de Valencia, Spain. Mata, M. & Fito, P. ( 1992). Vacuum osmotic dehyration of foods (VOD) I: Design and evaluation of a pilot plant. In ISOPOW-k’, Valencia, Spain, 260 PP. Pastor, R., Mata, M., Fito, P. (1992~). Deshidratacion Osmotica de manzana. Anales de Investigation de1 Master en Ciencia e Ingenieria de Alimentos. Vol. 1, SPUPV. Valencia, Spain, pp. 857-74. Pastor, R., Mata, M. & Fito, P. (19923). Vacuum osmotic dehydration of foods (VOD) II. Introduction to modelization of transfer phenomena in apple (Granny Smith} drying. In 1&SOPO W-I/. Valencia, Spain. Puig, A. (1992~). Effect of atmospheric and vacua osmotic dehydration on microst~cture of pineapple (a~a~as combo L; var; Cayena Lisa). In ISOPOW-V. Vaiencia, Spain. Puig, A. (19923). Effect of atmospheric and vacuum osmotic dehydration on microstructure of mango (Mangifka indica L; var. Haden). In ISOPO W-V, Valencia, Spain. Raoult-Wack, A. ( 199 1). Les procedes de Deshydratation-Impregnation par imnersion dans des solutions concentrees (DII). Etude experimentale et modelisation des transfer@ d’eau et de solute sur gel modele. PhD, Universite Montpellier II France, 150 pp. Toupin, C. J., LeMaguer, M. ( 1989). Osmotically induced mass transfer in plant storage tissues: a mathematical model Part 2. J. Food Eng., 10,97- 121. Toupin, C. J., Marcotte, M. & LeMaguer, M. (1989). Osmotically induced mass transfer in plant storage tissues: a ma~ematical model Part 1. J. Food Eng., 10,13-38.
Trakoontivakorn, G., Patterson, M. E., Swansoo, B. G. (1988). Scanning electron microscopy of cellular structure of Granny Smith and Red Delicious apples. Food Microstructure, 7,205- 12. Tyree, M. T. (1970). The symplast concept. A general theory of symplastic transport according to the thermodynamics of irreversible processes. J. Theor. Biol., 26,181-9.
Zozulevich, B. V. & D’yachenko, E. N. ( 1969). Osmotic dehydration of fruits. Konservn. Ovoshches~ch. Prom., 7,32-42.