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www.ingentaselect.com=titles=09603085.htm Trans IChemE, Part C, March 2004
Food and Bioproducts Processing, 82(C1): 44–48
MASS TRANSFER DURING OSMOTIC DEHYDRATION
Determination of Moisture and Solute Diffusion
Coefficients from Concentration Profiles
N. K. RASTOGI and K. S. M. S. RAGHAVARAO*
Department of Food Engineering, Central Food Technological Research Institute, Mysore, India
M
ass transfer during osmotic dehydration was studied. The effective diffusion
coefficients for water and solute diffusion were determined assuming osmotic
dehydration to be governed by Fickian diffusion. Solution of Fick’s law for
unsteady-state mass transfer was used to estimate the effective diffusion coefficients. The
average effective diffusion coefficients (De) obtained by this method could predict the moisture
(r2 ¼ 0.95) and solid (r2 ¼ 0.96) content to a sufficient accuracy. A high degree of correlation
was observed between predicted and experimental values of moisture and solid content.
Keywords: mass transfer; osmotic dehydration; diffusion; laminate.
INTRODUCTION (Torreggiani, 1993). It also increases sugar to acid ratio, and
improves texture and stability of the pigment during dehy-
Osmotic dehydration is a process for the partial removal of dration and storage (Raoult-Wack, 1994). It is effective even
water from plant tissues by immersion in an aqueous at ambient temperature, so heat damage to texture, colour
concentrated solution of soluble solutes. A driving force and flavour of food are minimized (Torreggiani, 1993).
for the diffusion of water from the tissue into the solution is Mass transfer during osmotic treatment occurs through
provided by the difference in osmotic pressure between the semi-permeable cell membranes present in biological mate-
food and surrounding osmotic solution. The diffusion of rials, which offer the dominant resistance to the process. The
water is accompanied by the simultaneous counter diffusion state of the cell membrane can change from being partially
of solute from the osmotic solution into the tissue. Since the permeable to being totally permeable and this can lead to
membrane responsible for osmotic transport is not perfectly significant changes in tissue architecture (Rastogi et al.,
selective, other solutes present in the cells can also be 2000a).
leached into the osmotic solution (Dixon and Jen, 1977; There are a number of methods reported in the literature
Lerici et al., 1985; Giangiacomo et al., 1987). The rate of (such as solution of Fick’s law, short time solution of Fick’s
diffusion of water from any material made up of such tissues law and slope method) for the calculation of effective
is reported to be dependent on several factors such as diffusion coefficients for water as well as solute during
temperature and concentration of the osmotic solution, the osmotic dehydration considering steady state mass transfer
size and geometry of the material, the solution to material (Rastogi and Raghavarao, 1995, 1997b) as well as unsteady
mass ratio and the level of agitation of the solution (Raoult- state approach (Rastogi et al., 1997, 2002; Rastogi and
Wack et al., 1992; Torreggiani, 1993; Raoult-Wack, 1994; Raghavarao, 1997a, b; Convey et al., 1983; Beristain et al.,
Rastogi and Raghavarao, 1994, 1995, 1997a, b; Rastogi 1990; Azuara et al., 1992; Rastogi and Niranjan, 1998). Recent
et al., 1997, 2002). advances in osmotic dehydration have been reported by
Osmotic dehydration is generally used as an upstream Barat et al. (2001), Ferrando and Spiess (2001), Kowalaska
step for the dehydration of foods before they are subjected to and Lenart (2001) and Scalzo et al. (2001). The aim of the
further processing such as freezing (Ponting, 1973), freeze present work is to study the mechanism of mass transfer
drying (Hawkes and Flink, 1978), vacuum drying (Dixon during osmotic dehydration and to determine the moisture
and Jen, 1977) and air-drying (Nanjundaswamy et al., and solute diffusion coefficients during osmotic dehydration
1978). Osmotic dehydration is used as a pretreatment to based on moisture and solute concentration profiles.
many processes and improves nutritional, sensorial and
functional properties of food without changing its integrity
MATERIALS AND METHODS
*Correspondence to: Dr. K.S.M.S. Raghavarao, Department of Food Raw Material Preparation
Engineering, Central Food Technological Research Institute, Mysore
570 013, India. Fresh potatoes were purchased locally in large quantities
E-mail: raghava@cscftri.ren.nic.in and stored at low temperature (8–10 C) in order to have
44
MASS TRANSFER DURING OSMOTIC DEHYDRATION 45
uniformity of raw material. The potatoes were cut into circular The solution of equation (4) for relative distance (x=l) can be
pieces of diameter 3.5 cm and thickness 1.0 cm. The average written for diffused moisture (Mr) and solute ratio (Sr)
moisture content of the potato was found to be 86.5% on a wet (Crank, 1975):
basis. Commercial sucrose was used as the osmotic agent.
ðm m 1 Þ 4 X 1
(1)n
Mr ¼ t ¼
mo m1 p n¼0 2n þ 1
Osmotic Dehydration
The potato pieces taken from the same potato were D (2n þ 1)2 p2 t (2n þ 1)px
exp ew cos (7)
blotted with tissue paper to remove external moisture. 4l 2 2l
These pieces were pre-weighed, tied with coloured thread
(for identification purposes) and subjected to osmotic dehy- and
dration in a vessel containing osmotic solution of concen- ð s s1 Þ
tration 50 B. Temperature was maintained at 25 C in a Sr ¼ t
so s1
constant temperature stirred water bath. Ratio of the volume
of the sample to that of osmotic solution was maintained at
4X 1
(1)n D (2n þ 1)2 p2 t
1:25, in order to ensure that the concentration of osmotic ¼ exp es
solution did not change significantly during the experiment. p n¼0 2n þ 1 4l 2
At the end of 1, 2, 3, 4 and 5 h immersion time, the samples
were withdrawn, rinsed quickly in a stream of water to (2n þ 1)px
cos (8)
remove adhering osmotic solution, blotted gently with tissue 2l
paper and then weighed. A potato slice after osmotic where Mr and Sr are the moisture and solute ratio; the
treatment was cut longitudinally into 10–12 slices. The subscripts o, 1 and t represent the corresponding con-
samples were then dried in a vacuum oven at 70 C for centrations at initial conditions, at equilibrium, and at any
about 18 h. All the experiments were carried out in triplicate time, respectively; Dew and Des are the effective diffusivities
and the average value was taken. of water and solute, respectively, considering infinite flat
The moisture and solute content were expressed in terms sheet configuration, ‘l’ the characteristic length and ‘x’
of kg of water=kg of initial dry solids and kg of solids=kg of varies between l < x < þl.
initial dry solids, respectively. The weight loss during Fourier numbers for water, Fow, and solute, Fos, diffusion
osmotic dehydration can be expressed by the following are given by the following equations (Perry et al., 1984;
relation (Rastogi and Raghavarao, 1997a): Rastogi and Raghavarao, 1997a, b):
weight loss ¼ water loss + solid gain (1) Dew t
Fow ¼ (9)
The moisture and solid content on dry basis (kg of water=kg of l2
dry solids) at any time can be calculated as follows: D t
Fos ¼ es (10)
l2
moisture content (kg=kg)
Substituting the values from equations (9) and (10) in to
(initial water present water lost) equations (7) and (8) resulted in the following equations:
¼ (2)
initial dry solids ðm m 1 Þ 4 X 1
(1)n
Mr ¼ t ¼
solid content (kg=kg) mo m1 p n¼0 2n þ 1
(initial dry solids þ solid gain) (2n þ 1)2 p2 (2n þ 1)px
¼ (3) exp Fow cos (11)
initial dry solids 4 2l
and
Determination of Water and Solute Diffusivities
during Osmotic Dehydration ð s s1 Þ 4 X 1
(1)n
Sr ¼ t ¼
Fick’s unsteady state diffusion equation can be written as so s1 p n¼0 2n þ 1
(Crank, 1975):
(2n þ 1)2 p2 (2n þ 1)px
@C @2 C exp Fos cos (12)
¼ De 2 (4) 4 2l
@t @x
where C is the concentration, De is the effective diffusion The values of diffused moisture (Mr) and (Sr) ratios for
coefficient, x is the diffusion path and t is the time. different x=l values were experimentally estimated over a
For an infinite slab being subjected to osmotic dehydration period of time (t). Using equations (11) and (12), the Fourier
from both the major faces with the assumptions (a) uniform numbers for moisture and solute diffusion were obtained
initial moisture distribution, (b) negligible external resistance (for a particular x=l value) corresponding to different values
to mass transfer and (c) no shrinkage during osmotic dehy- of diffused moisture and solute ratios, respectively. The
dration; and the following initial and boundary conditions value of Fourier numbers for moisture and solute diffusion,
C ¼ Co l < x < þl t¼0 (5) thus obtained, for different values of immersion time (t)
were plotted according to equations (9) and (10) and the
C ¼ C1 x¼l t>0 (6) effective diffusion coefficient (De) values were inferred from
Trans IChemE, Part C, Food and Bioproducts Processing, 2004, 82(C1): 44–48
46 RASTOGI and RAGHAVARAO
the slope. (Rastogi and Raghavarao, 1997b; Rastogi et al., of osmotic dehydration are shown in Figure 2 (a, b). As
2000b, 2002). relative distance (x=l ) is increased from 0 to 1, the moisture
content decreases and solid content increases for all immer-
sion times. Similarly, at the centre of the material (x=l ¼ 0),
RESULTS AND DISCUSSION moisture content decreases and solid content increases as the
The mechanisms of osmotic dehydration in cellular osmotic dehydration proceeds.
biological materials can be explained with the help of In order to calculate diffusion coefficients for moisture
schematic diagram shown in Figure 1. At first, water is and solid, the moisture and solid ratios (Mr and Sr) were
diffused from the outer layer of the sample to the osmotic calculated and shown in Figure 3 (a, b). The values of
solution, thereby increasing the osmotic pressure at the Fourier number of water (Fow) as well as solid diffusion
surface. As the osmotic pressure reaches a critical value (Fos) were obtained for different relative distances as per
(1.95 105 Pa, Rastogi et al., 2000a), the cell membranes equations (11) and (12). These values of Fourier numbers,
rupture and shrink, which in turn results in more porous thus obtained, were plotted against the corresponding values
cells and loss of water as well as gain of solid by the of immersion times as shown in Figure 4 [as per equations
material (Figure 1a and b). (9) and (10)]. The diffusion coefficients for moisture (Dew)
As osmotic dehydration proceeds, the dehydration front as well as solute (Des) at different relative distances were
moves into the product (towards the centre of the material); calculated from the slopes of these plots.
it results in cell membrane disintegration in the dehydrated The values of diffusion coefficients for moisture (Dew)
region and water is transported across three different regions as well as solute (Des) were plotted against relative distances
such as diffusion of water from the core of the material to (x=l ) as shown in Figure 5. The values of moisture as well as
the dehydration front, diffusion of water across the front and solute diffusion coefficients remained constant up to a relative
diffusion of water through the osmotically dehydrated distance of 0.5, beyond which it increased with increase in
material into the surrounding medium. Owing to cell relative distance. This indicates that for the present condition
permeabilization during progressive osmotic dehydration, of osmotic treatment, cells were not disintegrated up to a
diffusion of solid from osmotic solution also occurs into the relative distance of 0.5, beyond which cell disintegration
material. increased (increasing the porosity) with relative distance,
Since the moisture and solid content vary at each point which resulted in increase in diffusion coefficients (Figure 5).
with time due to osmotic dehydration, it results in onset of It may be noted that, although the De values are increasing
moisture as well as solute profiles (Figure 1). The increase in with an increase in distance (x=l), they are constant with
immersion time results in decrease in moisture content and
increase in solid content towards the centre of the material.
The solid and moisture profiles obtained during the course
Figure 2. (a) Variation of moisture and (b) solid content with time for
different relative distances during osmotic dehydration of potato sample.
Slice thickness, 1.0 cm; osmotic solution concentration and temperature,
Figure 1. Schematic diagram showing the mechanisms of osmotic dehydra- 50 B and 25 C, respectively. (Osmotic dehydration time: ¼ 1 h; j ¼ 2 h;
tion in cellular biological materials. r ¼ 3 h; m ¼ 4 h; s ¼ 5 h.)
Trans IChemE, Part C, Food and Bioproducts Processing, 2004, 82(C1): 44–48
MASS TRANSFER DURING OSMOTIC DEHYDRATION 47
Figure 5. Variation of effective diffusion coefficient for water (Dew) and
solute (Des) with relative distance (j ¼ for water diffusion ¼ for solid
diffusion).
respect time for any given relative distance (x=l) as long as
there is no change in the physical properties of the sample.
The average moisture and solute diffusion coefficients
[(Dew)av and (Des)av] were calculated as per the following
equation proposed by Crank (1975) considering food mate-
rial as laminate.
l1 l l l l
þ 2 þ 3 þ þ n ¼
(Dew )1 (Dew )2 (Dew )3 (Dew )n (Dew )av
Figure 3. (a) Moisture and (b) solid concentration profiles developed during (13)
osmotic dehydration. Slice thickness, 1.0 cm; osmotic solution concentra-
tion and temperature, 50 B and 25 C, respectively. (Osmotic dehydration l1 l l l l
time: ¼ 1 h; j ¼ 2 h; r ¼ 3 h; m ¼ 4 h; s ¼ 5 h.) þ 2 þ 3 þ þ n ¼
(Des )1 (Des )2 (Des )3 (Des )n (Des )av
(14)
(Dew)i and (Des)i are the moisture and solute diffusion
coefficients for respective distances li.
The average moisture (Dew)av and solute diffusion coeffi-
cients (Des)av were found to be 0.66 0.02 109 m2 s1
and 0.41 0.03 109 m2 s1, respectively. Based on these
average diffusion coefficients the moisture and solid content
for whole piece was calculated as per the following equations
for a well-agitated unlimited volume of osmotic solution
(Rastogi and Raghavarao, 1997a, b; Rastogi et al., 2002).
ðm m 1 Þ 8X 1
1
Mr ¼ t ¼ 2 2
mo m1 p n¼0 ð2n þ 1Þ
2
p Dew t
exp ð2n þ 1Þ2 ; (15)
l2
and
ð s s1 Þ 8X1
1
Sr ¼ t ¼ 2
so s1 p n¼0 ð2n þ 1Þ2
2
2 p Des t
exp ð2n þ 1Þ (16)
l2
The theoretical and experimental values for moisture as
well as for solid content with immersion time are shown in
Figure 6. The experimental determined moisture (r2 ¼ 0.95)
Figure 4. Variation of Fourier number of moisture as well as solid diffusion with and solid (r2 ¼ 0.96) content are in good agreement with the
immersion time (relative distance ¼ 0; j ¼ 0.5; r ¼ 0.7; m ¼ 0.8; s ¼ 0.9). theoretical values.
Trans IChemE, Part C, Food and Bioproducts Processing, 2004, 82(C1): 44–48
48 RASTOGI and RAGHAVARAO
Convey, J., Castaigne, F., Picaroift, G. and Vovan, X., 1983, Mass transfer
consideration in the osmotic dehydration of apples, Can Inst Food Sci
Technol J, 16: 25–29.
Crank, J., 1975, The Mathematics of Diffusion (Clarendon Press, Oxford, UK).
Dixon, G.M. and Jen, J.J., 1977, Changes of sugar and acid in osmovac dried
apple slices, J Food Sci, 42: 1126–1131.
Ferrando, M. and Spiess, W.E.L., 2001, Cellular response of plant tissue
during osmotic treatment with sucrose, maltose, and trehalose solutions,
J Food Eng, 49: 115–128.
Giangiacomo, R., Torreggiani, D. and Abbo, E., 1987, Osmotic dehydration
of fruit. Part I: Sugar exchange between fruit and extracting syrup, J Food
Process Preserv, 11: 183–195.
Hawkes, J. and Flink, J.M., 1978, Osmotic concentration of fruit slices prior
to freeze dehydration, Int J Food Sci Technol, 2: 265–284.
Kowalska, H. and Lenart, A., 2001, Mass exchange during osmotic
pretreatment of vegetables, J Food Eng, 49: 137–140.
Figure 6. Comparison of theoretical [equations (15) and (16)] and Lerici, C.L., Pinnavaia, G., Dalla Rosa, M. and Bartolucci, L., 1985,
experimental values of moisture and solid content during osmotic dehydra- Osmotic dehydration of fruit: Influence of osmotic agents on drying
tion. Symbols represent the experimental values and solid lines represent behaviour and product quality, J Food Sci, 50: 1217–1219.
theoretical values. Arrows point to respective axes. Nanjundaswamy, A.M., Radhakrishnaiah Setty, G., Balachandran, C.,
Saroja, S. and Murthy Reddy, K.B.S., 1978, Studies on development of
new categories of dehydrated product from indigenous fruits, Ind Food
Packer, 22: 91–93.
It is revealed from the study that moisture as well as solid Perry, R.H., Green, D.W. and Maloney, J.O., 1984, Perry’s Chemical Engi-
profiles can be used for the prediction of the values of neer’s Handbook, 6th edn (McGraw-Hill, New York, USA), pp. 20.11–
diffusion coefficients. 20.14.
Ponting, J.D., 1973, Osmotic dehydration of fruits—recent modifications
and applications, Process Biochem, 8: 18–20.
Raoult-Wack, A.L., 1994, Advances in osmotic dehydration, Trends Food
CONCLUSION Sci Technol, 5: 255–260.
Mass transfer during osmotic dehydration of was studied. Raoult-Wack, A.L., Lenart, A. and Guilbert, S., 1992, Recent advances
during dewatering through immersion in concentrated solution, in Drying
Moisture and solute diffusion coefficients during osmotic of Solids, Majumdar, A.S. (ed.) (International Science Publisher,
dehydration were determined based on moisture and solute New York, USA), pp. 21–51.
concentration profiles. The average effective diffusion coeffi- Rastogi, N.K. and Niranjan, K., 1998, Enhanced mass transfer during
cients calculated from this method could predict the mois- osmotic dehydration of high pressure treated pineapple, J Food Sci,
63(3): 508–511.
ture (r2 ¼ 0.95) and solid (r2 ¼ 0.96) content to a sufficient Rastogi, N.K. and Raghavarao, K.S.M.S., 1994, Effect of temperature and
accuracy. Such predictions are expected to be useful in concentration of osmotic dehydration of coconut, Lebens Wiss Technol,
optimizing the osmotic dehydration process conditions. 27: 264–567.
Rastogi, N.K. and Raghavarao, K.S.M.S., 1995, Kinetics of osmotic
dehydration of coconut, J Food Process Eng, 18: 187–197.
Rastogi, N.K. and Raghavarao, K.S.M.S., 1997a, Water and solute diffusion
NOMENCLATURE coefficients of carrot as a function of temperature and concentration,
J Food Eng, 34: 429–440.
C concentration at any time, kg m3; moisture content on a dry
Rastogi, N.K. and Raghavarao, K.S.M.S., 1997b, Mass transfer during
basis at any time, kg kg1
osmotic dehydration of carrot: Comparison of different methods for the
C1 bulk concentration, kg m3
estimation of effective diffusion coefficients, in Proceedings of 7th
Co initial concentration, kg m3; initial moisture content on a dry
International Congress on Engineering and Food (ICEF), Brighton,
basis, kg kg1
Vol. 2, pp. G73–76.
Des effective diffusion coefficient of solute, m2 s1
Rastogi, N.K., Raghavarao, K.S.M.S. and Niranjan, K., 1997, Mass transfer
Dew effective diffusion coefficient of water, m2 s1
during osmotic dehydration of banana: Fickian diffusion in cylindrical
Fos fourier number of solute diffusion
configuration, J Food Eng, 31: 423–432.
Fow fourier number of water diffusion
Rastogi, N.K., Angersbach, A. and Knorr, D., 2000a, Evaluation of mass
l half thickness of potato piece, m
transfer mechanisms during osmotic treatment of plant materials, J Food
m moisture content at t ¼ t, kg kg1
Sci, 65(6): 1016–1021.
m1 moisture content at t ¼ 1 , kg kg1
Rastogi, N.K., Angersbach, A., Niranjan, K. and Knorr, D., 2000b, Rehy-
mo initial moisture content at t ¼ 0, kg kg1
dration kinetics of high pressure treated and osmotically dehydrated
s solid content at t ¼ t, kg kg1
pineapple, J Food Sci, 65(5): 838–841.
s1 solid content at t ¼ 1 , kg kg1
Rastogi, N.K., Raghavarao, K.S.M.S., Niranjan, K. and Knorr, D., 2002,
so initial solid content at t ¼ 0, kg kg1
Recent developments in osmotic dehydration: methods to enhance mass
t immersion time, h
transfer, Trends Food Sci Technol, 13(2), 58–69.
T temperature of osmotic solution, K
Scalzo, R.L., Papadimitriu, C., Bertolo, G., Maewstrelli, A. and
x length of diffusion path, m
Torreggiani, D., 2001, Influence of cultivar and osmotic dehydration
time on aroma profiles of muskmelon (Cucumis melo, cv reticulatus
Naud.) spheres, J Food Eng, 49: 261–264.
REFERENCES Torreggianni, D., 1993, Osmotic dehydration in fruits and vegetable proces-
sing, Food Res Int, 26: 59–68.
Azuara, E., Cortes, R., Garcia, H.S. and Bristain, C.I., 1992, Kinetic model
for osmotic dehydration and its relationship with Fick’s second law, Int J
Food Sci Technol, 27: 409–418. ACKNOWLEDGEMENT
Barat, J.M., Fito, P. and Chiralt, A., 2001, Modelling of simultaneous
mass transfer and structural changes in fruit tissues, J Food Eng, 49: Thanks are due to Mr N. Venkateswara Rao for his help for some of the
77–86. experiments.
Beristain, C.I., Azuara, E., Cortes, R. and Garcia, H.S., 1990, Mass transfer
during osmotic dehydration of pineapple rings, Int J Food Sci Technol, 25: The manuscript was received 30 May 2003 and accepted for publication
576–582. after revision 9 January 2004.
Trans IChemE, Part C, Food and Bioproducts Processing, 2004, 82(C1): 44–48
