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Original article
The mathematical modelling of the osmotic dehydration
of shark fillets at different brine temperatures
Saheeda Mujaffar & Clement K. Sankat*
Department of Mechanical Engineering, Faculty of Engineering, The University of the West Indies, St Augustine, Trinidad
and Tobago, West Indies
(Received 1 July 2004; Accepted in revised form 11 May 2005)
Summary The effect of brine temperature (20, 30, 40 and 50 C) on the osmotic drying behaviour of
shark slabs (10 5 1 cm) in saturated (100) brine was investigated. The parameters
investigated were weight reduction, water loss, salt gain and water activity. Salt uptake and
moisture data were analysed using various mathematical solutions based on Ficks Law of
Diffusion and the effective diffusion coefficients were predicted after considering the
process variables. The expressions presented by Azuara et al. (1992), based on the model
presented by Crank (1975), were successfully used to predict the equilibrium point and tocalculate diffusion coefficients at not only the initial stages of dehydration, but also at
different times during the osmotic process.
Keywords Diffusion coefficient, Ficks Law, mass transfer, salting.
Introduction
The salting of fish is essentially an osmotic
dehydration process. It involves two major mass
transfer flows: water flow out of the fish and a
simultaneous transfer of salt into the fish. In orderto have a comprehensive overview of the salting
process and to design an optimum-salting regime,
it is first necessary to investigate the mass transfer
changes (salt uptake and water removal), which
occur during the process, as well as to describe and
predict these changes via mathematical modelling.
While the literature abounds with information
on general salting and drying techniques, as well as
numerous works concerning important chemical,
nutritional and microbiological aspects, fewer
articles have been dedicated to the scientific study
of the process and the basic mechanisms involvedin the production of dried salted fish. Most of the
studies on the salting and drying of fish have
involved the splitting of fish followed by dry or
wet salting and sun drying. Where salting and
drying variables are considered, they are done
from the perspective of how quickly the process is
completed or the overall quality.
There are very few reports on the calculation of
drying rate constants and diffusion coefficients forthe processes of salt uptake and water loss (WL)
during the osmotic dehydration of fish. The main
body of knowledge that is referenced is based
upon the early work of researchers such as Beatty
& Fougere (1957); Jason (1958); Burgess et al.
(1967); Del Valle & Nickerson (1967a,b,1968);
Zugarramurdi & Lupin (1976,1977,1980) for
temperate fish and later reviews by Wheaton &
Lawson (1985) and Ismail & Wooton (1992).
More recent studies include the work of Berhim-
pon et al. (1991) who investigated the process
requirements for the salting of whole, split orfilleted (with skin on) Yellowtail fish, Deumier
et al. (1997), who described and experimentally
checked a system for continuous determination of
mass transfers based on the loss of buoyancy
during the brining of whole herring, and Medina-
Vivanco et al. (1998) who investigated the salting*Correspondent: Fax: +1 868 662 4414;
e-mail: [email protected]
International Journal of Food Science and Technology 2006, 41, 405416 405
doi:10.1111/j.1365-2621.2005.01086.x
2006 Institute of Food Science and Technology Trust Fund
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behaviour of filleted Tilapia (without skin). Barat
et al. (2002) investigated the effect of increasing
brine concentration in the cod-salting process
(using de-boned cod fillets) with a view to
increasing process yield.
This study was undertaken to investigate and
mathematically model the osmotic dehydration of
locally available Shark (Carcharhinus leucas,
Muller and Henle). Shark is underutilized as fresh
fish and therefore available and relatively inexpen-
sive. Shark is an ideal fish model because it can be
filleted to give many small fillets of uniform size.
Additionally, reports indicate that salted fish
produced from shark and other species with white
or light-coloured flesh is similar in appearance to
the costly imported salted cod, with comparable
protein and fat contents (IDC, 1986). The specific
objectives of this study were:
1 To determine the effect of immersion time andbrine temperature on WL and salt gain (SG) in
shark slabs during osmotic dehydration.
2 To mathematically model mass transfer during
osmotic dehydration using various transient
solutions to Ficks Law and to calculate the
diffusion coefficients for SG and moisture loss
for the osmotic process using these models.
Theoretical considerations
The mathematical models used to describe mass
transfer during osmotic dehydration are usually
based upon various solutions to Ficks Law of
Diffusion. The solution given by Crank (1975) has
been applied to the osmotic dehydration of fruits
and vegetables (Hawkes & Flink, 1978; Favetto
et al., 1981; Magee et al., 1983) but has also been
used to describe salt uptake of sliced and whole fish
(Del Valle & Nickerson, 1967b; Zugarramurdi &
Lupin, 1977; Medina-Vivanco et al., 1998). The
solution applies to unsteady one-dimensional trans-
fer between a plane sheet and a well-stirred solution
with a constant surface concentration, that is,
infinite or semi-infinite medium. Rate constants
and diffusion coefficients for the initial stages of theprocess are determined from plots ofXt/X vs. t
1/2:
Xt
X1 Kt1=2 1
where K 2(D/pL2)1/2, Xt is the amount solute
entering/water leaving the sample at time t; X
,
amount solute entering/water leaving the sample
at equilibrium; D, diffusion coefficient for solute/
water flow; L, half-thickness of slab; t, time.
Based on this model (Crank, 1975) and
Azuara et al. (1992) presented an expression
from which the diffusion coefficient can be
calculated at different times during the osmotic
process, not just only for the initial stages of
dehydration:
D pL2
4t
St
1 St
X1model
X1 experimental
22
where S is the constant related to the rate of WL/
SG; X model, theoretical equilibrium value for
WL/SG; X experimental, experimental equilibrium
value for WL/SG.
The theoretical equilibrium value (X model),
and the constant, S, are estimated using the
experimental data (Xt) and linear regression:
t
Xt
1
SX1model
t
X1model: 3
The expression presented by Azuara et al.
(1992) was tested using previously reported data
on the osmotic treatment of apple, pineapple and
beef. Medina-Vivanco et al. (1998) used the
regression equation to determine equilibrium salt
content (SC) in tilapia.
Materials and methods
Sample preparation
Shark was obtained from a local supplier. Upon
capture, fish were cleaned, gutted and skinned
before being split in half and filleted along the
direction of the muscle fibres (Riley, 1973). The
layer of dark, subepidermal flesh was trimmed.
The fillets were transported to the Processing
Laboratory (University of the West Indies, St
Augustine, Trinidad) in an iced box, where they
were immediately cut into smaller pieces of the
required size (10 5 cm). These pieces were then
carefully placed in reclosable plastic freezer bagsand stored overnight at )30 C in a chest type
home freezer. The following day, fillets were
allowed to thaw partially to allow for easy cutting
and accurately cut to the desired thickness (1 cm)
using a Hobart food slicer (Model 1612E; Hobart
Corporation, Troy, OH, USA).
Osmotic dehydration of shark fillets S. Mujaffar and C. K. Sankat406
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Osmotic medium
Saturated brine, made from food-grade sodium
chloride (NaCl) dissolved in distilled water, was
used as the osmotic medium. Saturated brine
contains 26.5% salt (w/v) and has a specific
gravity of 1.19 at 15 C (Gould & Gould, 1988).
At ambient tropical temperatures, this corre-
sponds to approximately 360 g of salt in 1 L
solution (Clucas, 1981). The specific gravity of the
brine was checked using a hydrometer (Woolf
Thermo-Hydrometer SPGR; American Beverage
and Supply Company, Indianapolis, IN, USA)
and brine saturation was maintained by suspend-
ing a fine nylon mesh containing solid salt in the
solution [United Nations Development Fund for
Women (UNIFEM), 1988]. A total of 10 L of
brine was used for each osmotic run. The
weight:volume ratio of solution to samples wasat least 20:1, to avoid significant dilution of the
medium (by the absorbed salt) and subsequent
decrease in the (osmotic) driving force during the
process (Lazarides & Mavroudis, 1996).
Experimental design
The brine solution and the samples were contained
in temperature-controlled (0.1 C) stainless-steel
water-baths with water circulators and digital
temperature display (BlueM Constant Tempera-
ture Water-bath, Model WB1110A; Asheville,
NC, USA). Solutions were constantly circulated
at a flow rate of 200 mL s)1. This improved mass
transfer allowed for closer control of the brine
(Lazarides et al., 1995). Osmotic trials were done
at four brine temperatures: 20, 30 (ambient), 40
and 50 C. It is recognized that temperatures of
40 C and 50 C may not be of practical import-
ance to fish osmotic dehydration because of
microbial contamination. However there is poten-
tial application at these temperatures for other
products such as fruits and vegetables. Tempera-
tures above 50 C were not used as this is the
temperature reported as the upper limit beyondwhich cooking of fish flesh occurs (FAO, 1981).
Use of low temperatures (below 20 C) increases
the viscosity of the osmotic medium and prohibits
thorough mixing and satisfactory mass transfer of
brine (Lazarides et al., 1995). To facilitate osmotic
dehydration at 20 C, the water-bath was placed
in a refrigerated room (1.77 2.36 2.29 m) set
at 20 C (1.5 C).
Experimental treatment
The experiments were designed to investigate the
effect of brine temperature (20, 30, 40, 50 C) on
the salting of shark fillets (10 5 1 cm) in
saturated brine. Saturated brine (360 g L)1) was
used throughout because preliminary experiments
revealed that spoilage occurred when slabs were
immersed in a 210 g L)1 salt solution (60%
saturation) at all temperatures. Slabs immersed
in a 270 g L)1 salt solution (80% saturation) at
20 C were shown to reabsorb water after an
initial loss while the mass transfer changes at 30
50 C were generally similar to those that occurred
in slabs in a saturated solution (36% w/v).
Therefore, as a matter of convenience the satur-ated solution was chosen for osmotic trials as the
salt concentration in saturated brine is easier to
maintain.
Sampling procedure
Each osmotic trial consisted of placing the shark
slabs (10 5 1 cm) in 100brine at a fixed
temperature for a maximum immersion time of
32 h. At the start of the experiment, fish samples
were immersed completely in the brine. At speci-
fied time intervals, samples were removed from the
solution and weight, moisture content (MC), SC
and water activity measured. For weight measure-
ment, the same five samples were used throughout
each osmotic trial. These samples were separated
from the other slabs using a fine nylon mesh. For
moisture and salt analysis, duplicate samples were
quickly rinsed with water to remove any surface
salt and excess moisture blotted off using house-
hold tissue paper (Favetto et al., 1981; Heng et al.,
1990; Lazarides et al., 1997). For water activity
determination, duplicate samples were removed
from the solution and excess moisture blotted off
before measurement.
Analytical methods and calculations
Two important mass transfers occur during the
osmotic process: water flow out of the sample into
the surrounding medium and solute transfer from
Osmotic dehydration of shark fillets S. Mujaffar and C. K. Sankat 407
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the medium into the sample. To consider the
changing solute content during the osmotic pro-
cess, moisture and SC data were expressed on a
non-salt dry matter basis. Non-salt dry matter was
calculated as the sample weight minus the weight
of water and the weight of absorbed salt (Del Valle
& Nickerson, 1967a,b; Zugarramurdi & Lupin,
1980; Favetto et al., 1981; Berhimpon et al.,
1991):
Non-salt dry matter Sample weight (g)
Water (g)
Absorbed salt (g) 4
Del Valle & Nickerson (1967a) noted that
expressing moisture and salt data on a non-salt
solids basis instead of the total solids basis is
preferable as this is the only parameter that
remains constant during the process as loss of
soluble material is small. Favetto et al. (1981)
added that for an osmotic process, the non-solute
dry matter is a measure of the true dry matter of
the sample.
Sample weight in grams (g) was measured using
an Ohaus Galaxy (110) Analytical Balance (Ohaus
Scale Corporation, New Jersey, NJ, USA). Weight
reduction (WR) was calculated as the change from
the original fresh weight (FWt ) FW0) and
expressed on an initial non-salt dry matter basis
(g g DM)1):
WR
FWt FW0
DM : 5
Moisture content was determined by an oven-
drying method (FAO, 1981). Samples were dried
for 24 h at 105 C in a Gallenkamp Size One BS
Oven (Loughborough, England, UK). MC was
expressed on a non-salt dry weight basis (g H2O g
DM)1):
MC H2Ot
DM: 6
Water loss (WL), which represents the total
amount of moisture lost by the slabs from the
beginning of the process up to that sampling
interval, was also expressed on a non-salt dry
matter basis (g H2O g DM)1):
WL H2O0 H2Ot
DM: 7
Salt (NaCl) content of the fillets was determined
titrimetrically using silver nitrate solution (FAO,
1981). SC was expressed as the weight of salt in the
sample on a non-salt dry weight basis (g NaCl g
DM)1):
SC NaClt
DM: 8
Salt gain (SG), which represents the totalamount of salt absorbed by the slabs from the
beginning of the process up to that sampling
interval, was also expressed on a non-salt dry
matter basis (g NaCl g DM)1):
SG NaClt NaCl0
DM: 9
The salt : water ratio (S/W) was calculated as
SC divided by the MC of the sample:
S=W SC
MC: 10
Water activity (aw) was measured using a water
activity meter (Rotronic Hygroskop DT; Rotronic
Instrument Corp., Huntington, VA, USA) and
calculated as the equilibrium relative humidity
divided by 100 (Labuza et al., 1976; Gould &
Gould, 1988).
Statistical analysis
Data analysis consisted of simple regression
analysis using Microsoft Excel 97 to examine the
data for good fit. Further regression analysis and
anova were carried out by using Genstat Statis-
tical Software (Lawes Agricultural Trust, 1996).
Results and discussion
Quality changes
Slabs immersed in 100brine at 20 and 30 C had a
good colour, odour and texture. Increasing the
brine temperature to 40 C resulted in shrinkage
and discolouration of slabs. A cooking effect was
observed at 50 C, whereby slabs became translu-
cent in colour and developed the aroma of cookedfish. While the use of high temperatures can
increase the rate of osmotic dehydration, high
temperatures may result in undesirable changes in
the food piece. For example, in the osmotic
treatment of apple chips using a sugar solution,
the rate of dehydration increases as temperature
Osmotic dehydration of shark fillets S. Mujaffar and C. K. Sankat408
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increases from 22 to 40 C (Ponting et al., 1966).
However, enzymatic browning and flavour deteri-
oration occur above 49 C. Similarly for fish, the
higher the temperature, up to a certain limit, the
quicker the salt uptake (Burgess et al., 1967;
Clucas & Sutcliffe, 1981). However, at higher
temperatures, spoilage and protein denaturation
become the limiting factors for fish and meat.
Doe et al. (1982) reported that changes in cod
flesh occur when it is heated to 31.5 C. At this
temperature some of the tissue water become less
strongly bound to protein and appears as free
fluid. At about 43 C, the fish flesh becomes
somewhat more translucent followed by an
increase in opacity because of the precipitation
of thermally denatured sarcoplasmic proteins,
which begins at about 45 C. It is therefore usually
safer to keep fish cool during salting. Ordinarily,
in the tropics, the process is, for convenience, atroom temperature (Burgess et al., 1967).
Weight reduction
Weight reduction in shark slabs was calculated
from the weight data using eqn 5. WR was
significantly affected by immersion time and brine
temperature (P 0.001). All slabs showed an
increase in WR (Fig. 1) and increasing brine
temperature increased the weight loss. This means
that the higher the temperature, the higher the
reduction in weight for the 24 h of dehydration.
Weight loss values after 24 h of dehydration
averaged 0.18, 0.36, 0.54 and 0.95 g g DM)1 for
slabs dehydrated at 20, 30, 40 and 50 C,
respectively.
Moisture content and water loss
The MC of shark slabs was calculated on a dry
matter basis using eqn 6. MC was significantly
affected by immersion time and brine temperature
(P 0.001). All slabs showed a decrease in MC
(Fig. 2). MC values declined rapidly during the
first 2 h of dehydration and more gradually after.
The higher the temperature, the more rapid the
initial decline in MC. Initial moisture values
averaged 2.76 g H2O g DM)1 (73.4% wb). Values
after 4 h of dehydration averaged 2.18, 2.06, 1.87
and 1.70 g H2O g DM)1 for slabs dehydrated at
20, 30, 40 and 50 C, respectively. When calcula-ted on a fresh weight basis (wb), this corresponds
to 60.5, 58.0, 57.0 and 55.9% (wb) moisture.
Water loss in shark slabs calculated from
moisture data (eqn 7) was significantly affected
by immersion time and brine temperature
(P 0.001). This value represents the total
amount of moisture that has been lost by the
slabs from the beginning of the process up to the
sampling time. All slabs showed a noticeable
increase in WL during the first 4 h of dehydration,
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12 16 20 24
Time (h)
WR(ggDM1)
20C
30C
40C
50C
Figure 1 Effect of brine temperature on the weight reduc-
tion (WR) of shark slabs (10 5 1 cm) immersed in
100brine. SEM 0.0536.
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
0 4 8 12 16 20 24
Time (h)
MC(gH2OgDM1)
20C
30C
40C
50C
Figure 2 Effect of brine temperature on the moisture con-
tent (MC) changes of shark slabs (10 5 1 cm) immersed
in 100brine. SEM 0.093.
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after which WL became more gradual until
equilibrium was achieved (Fig. 3). The higher the
brine temperature, the greater the WL. Values
after 4 h of dehydration averaged 0.58, 0.71, 0.89
and 1.06 g H2O g DM)1 for slabs at 20, 30, 40 and
50 C, respectively. Beyond this time, WL gradu-
ally increased and levelled off, with values after
24 h averaging 0.69, 0.80, 0.95 and 1.22 g H2O g
DM)1 for slabs dehydrated at 20, 30, 40 and
50 C, respectively.
Salt content and salt gain
The SC of shark slabs was calculated on a dry
matter basis using eqn 8. SC was significantly
affected by immersion time (P 0.001) but not
by brine temperature. As shown in Fig. 4, all
slabs showed a similar rapid increase in SC
during the first 2 h of dehydration, after which
the increase became more gradual. The effect of
brine temperature was more apparent beyond the
first 2 h. Further increasing the temperature to
50 C resulted in a decline in salt uptake,
probably because of the cooking of the slabs.Values after 4 h of dehydration averaged 0.61,
0.64, 0.63 and 0.53 g NaCl g DM)1 for slabs
dehydrated at 20, 30, 40 and 50 C, respectively.
When calculated on a wet basis, this corresponds
to a SC of between 17% to 19% salt for all
slabs.
Salt gain in shark slabs was calculated using
the SC data and eqn 9. This value represents the
total amount of salt absorbed by the slabs from
the beginning of the process up to the sampling
time. As the initial SC of the slabs was found to
be zero, SG was equivalent to SC. Therefore, SG
was also affected by immersion time (P 0.001)
but not by brine temperature. SG values after 4 h
of dehydration averaged 0.61, 0.64, 0.63 and
0.53 g NaCl g DM)1 for slabs dehydrated at 20,
30, 40 and 50 C, respectively. At 20 C, SG
values were similar to WL values. As the immer-
sion temperature increased to 50 C, the slabs
showed an increase in WL, while SG values
remained stable.
An increase in WL rates with increasing tem-
perature without a concomittant rise in solute
uptake has been reported by many researchers
(Hawkes & Flink, 1978; Islam & Flink, 1982;
Raoult-Wack et al., 1989; Lazarides et al., 1995;
Lazarides & Mavroudis, 1996). Lazarides et al.
(1995) noted that at increased temperatures, high
rates of WL during the osmotic dehydration ofapples seem to prevent the development of pro-
portionally high rates of counter current sucrose
diffusion. They added that whenever it is desirable
to achieve higher water removal and lower solids
gain, a higher process temperature (within allow-
able limit) should be used.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 4 8 12 16 20 24
Time (h)
WL(gH2Og
DM1)
20C
30C
40C
50C
Figure 3 Effect of brine temperature on the water loss (WL)
of shark slabs (10 5 1 cm) immersed in 100brine.
SEM
0.043.
0.0
0.2
0.4
0.6
0.8
0 4 8 12 16 20 24
Time (h)
SC(gNaClgD
M1)
20C
30C
40C
50C
Figure 4 Effect of brine temperature on the salt content
(SC) changes of shark slabs (10 5 1 cm) immersed in
100brine. SEM 0.044.
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Salt:water ratio
For all osmotic trials, MC values were higher than
SC values, therefore throughout the osmotic trials
the S/W (eqn 10) was always less than 1.00. All
slabs showed an increase in S/W, but there was no
fixed pattern of change with increasing brinetemperature (Fig. 5). Equilibrium S/Ws for all
slabs averaged between 0.27 and 0.37. According
to Riley (1973), shark fillets can be oven dried
after a S/W exceeding 0.30 has been attained in the
fish flesh. Lazarides et al. (1997) also found that
the ratio of water to solids content of apple and
potato remained constant or decreased with
increasing temperature.
Water activity
Water activity (aw) reflects the active part of MC
or the part, which can be exchanged between the
product and the environment. It is a measure of
the free water in a food, which is available to react
chemically or to support the growth of micro-
organisms during spoilage. Most foods have an awlevel in the range of 0.2 for very dry foods to 0.99
for moist fresh foods. Water activity values of
slabs immersed in brines at all temperatures
were significantly affected by immersion time
(P 0.001). All slabs showed decline in water
activity (Fig. 6) from an approximate initial value
of 1.00, but there was no detectable pattern in the
change in aw with brine temperature. Values after
4 h of dehydration averaged 0.849, 0.802, 0.823
and 0.808 for slabs dehydrated at 20, 30, 40 and
50 C, respectively. Doe et al. (1982) noted that
the aw of fresh fish is above 0.95 and this can be
reduced during salting and drying. With the
exception of certain halophilic organisms, bacteria
do not generally grow in products with an aw of
less than about 0.88, and the growth of most
moulds is inhibited below 0.80 (FAO, 1981; Doe
et al., 1982).
Rate of change in MC and SC
According to Lazarides et al. (1995), the rate of
moisture removal is a characteristic of prime
importance to every dehydration process as it is
indicative of process effectiveness and suggests theproductive duration of the process. MC data for
shark slabs were used to calculate the rate of
change in moisture (RateMC). This was done by
calculating the difference in MC (g H2O g DM)1)
between consecutive sampling times (t, t + 1),
and dividing this value by the time interval (h):
0.0
0.1
0.2
0.3
0.4
0 4 8 12 16 20 24
Time (h)
S/Wr
atio
20C
30C
40C
50C
Figure 5 Effect of brine temperature on the salt/water ratio
(S/W) of shark slabs (10 5 1 cm) immersed in 100brine.
SEM 0.013.
0.75
0.80
0.85
0.90
0.95
1.00
0 4 8 12 16 20 24
Time (h)
aw
20C
30C
40C
50C
Figure 6Effect of brine temperature on the water activity(aw) of shark slabs (10 5 1 cm) immersed in 100brine.
SEM 0.0076.
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RateMC MCt MCt1t 1 t
: 11
Results of anova revealed that the rate of
change in MC (dM/dt) was significantly affected
by immersion time (P 0.001) but not by
immersion temperature. A plot of the rate ofchange in moisture (dM/dt) in shark slabs vs.
immersion time as shown in Fig. 7a revealed that
rate is highest at the beginning and declines
rapidly within the first hour of dehydration.
Generally, during the first hour, the higher the
brine temperature, the higher the drying rate.
Drying rates were highest for slabs at 50 C, and
lowest for slabs at 20 C. Initial rates of dehy-
dration averaged 0.56, 1.00, 1.74 and 2.83 g
H2O g DM)1 h)1 for dehydration at 20, 30, 40
and 50 C, respectively. Beyond 2 h of dehydra-
tion, rate changes were negligible regardless of
brine temperature and averaged below 0.10 g
H2O g DM)1 h)1.
The plot of rate of change in moisture (dM/dt)
vs. average moisture (M) is given in Fig. 7b. There
are no periods of constant water removal and
therefore no constant rate period. Rates declined
with declining MC (P 0.001). This means that
the drying rate of slabs was dependent on the
moisture concentration inside the fish muscle. It is
generally accepted that mass transfer during
osmotic dehydration of fruits is governed by
internal diffusion, that is, movement under the
influence of a concentration gradient. Where aconstant rate of drying does occur, the period is
brief and does not exceed tens of seconds (Magee
et al., 1983; Lenart, 1992). As also shown by
Lenart & Lewicki (1987) for the osmotic dehydra-
tion of fruit, the relationship between rate and MC
of shark during the falling rate period is firstly
exponential in character. However, when the MC
falls below a certain critical value, in this case
approximately 2.3 g H2O g DM)1, the plot was
linear.
Salt content data for shark slabs was used to
calculate the rate of change in salt (RateSC). This
was done by calculating the difference in SC
(g NaCl g DM)1) between consecutive sampling
times, and dividing this value by the time interval
(h):
RateSC SCt SCt1t 1 t
: 12
The rate of change in SC was significantly
affected by immersion time (P 0.001) but not by
temperature and was highest during the first 4 h of
dehydration. The rate of change in SC was
generally lower than the rate of change in MC,
averaging 0.60, 0.67, 0.52 and 0.61 g NaCl g
DM)1 h)1 for slabs dehydrated at 20, 30, 40 and
50 C, respectively.
High rates of WL and solids gain during the
initial stages of dehydration followed by drastic-
ally lower rates have been attributed (Lazarideset al., 1995) to the large initial osmotic driving
force between the sample and the surrounding
hypertonic solution, structural changes such as
shrinkage leading to the compaction of the surface
layers of the tissue and the decreasing availability
of free or loosely bound water leading to the
Rate vs. Time
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4
Time (h)
Rate(gH2OgDM1h1)
20C
30C
40C
50C
(b)
Rate(gH2O
gDM1h
1)
(a)
Rate vs. Moisture content
1.5 2.0 2.5 3.0
Moisture content (gH2O g DM1)
20C
30C
40C
50C
Figure 7 Effect of brine temperature on the rate of change in
moisture content (dM/dt) during the osmotic dehydration of
shark slabs (10 5 1 cm) immersed in 100brine.
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progressively slower moisture removal as the
process goes on.
Rate constants and diffusion coefficients
Model no. 1: Crank (1975)
When the solution given by Crank (1975) for a
well-stirred solution is applied to the WL and SG
by shark slabs, the t1/2 law given in eqn 1 can be
applied satisfactorily to the linear section of the
data which corresponds to the first 2 h of dehy-
dration (P 0.001). The slopes of these plots are
given in Table 1.
The higher the temperature of the osmotic
treatment, the steeper the slope of the graph and
the higher the constant (K). Increasing the brine
temperature from 20 to 50 C resulted in an
increase in the constant for moisture diffusion
from 0.3657 to 0.6561 h)0.5
, an almost twofoldincrease. Increasing the brine temperature from 20
to 50 C resulted in a small increase in the constant
for salt diffusion from 0.5254 to 0.6789 h)0.5.
Diffusion coefficients calculated using these rate
constants assuming a (thickness)2 relationship
between thickness and rate constant are also given
in Table 1. Moisture diffusion was found to
increase with increasing brine temperature from
7.29 10)6 to 2.35 10)5 cm2 s)1. Salt diffusion
showed a smaller increase from 1.50 to
2.51 10)5 cm2 s)1. The activation energy for
moisture diffusion, estimated using an Arrhenius
type equation, was calculated to be 31.7 kJ mol)1.
As expected, the data for salt diffusion did not fit
very well and the correlation coefficient was very
low (r2 0.68).
Model no. 2: Azuara et al. (1992)
Based on the approach of using Cranks solution
for a well-stirred solution, presented by Azuara
et al. (1992), the plot of t/WL vs. t based on the
straight line equation (eqn 3) was used to generate
S-values (intercept) and equilibrium values (slope)
that are given in Table 2. All r2-values were
>0.99. S-values, which are related to the rate of
WL, increased from 0.83 to 1.66 h)1
as brinetemperature was increased from 20 to 50 C. The
S-value is a measure of the rate of the diffusion
process, with 1/S being the time taken for half the
diffusible material to diffuse in or out. For
example, for WL at 20 C, this corresponds to
1.2 h, while for WL at 50 C, this corresponds to
0.6 h.
Table 1 Constants (K) and diffu-
sion coefficients (D) obtained using
water loss (WL) and salt gain (SG)
data and model no. 1 (Crank,1975) for shark slabs at different
temperatures
Temperature
Water loss (WL) Salt gain (SG)
K
(h)0.5) r2D
(10)5 cm2 s)1)K
(h)0.5) r2D
(10)5 cm2 s)1)
20 C 0.3657 0.9688 0.729 0.5254 0.9955 1.50
30 C 0.4350 0.9917 1.03 0.5991 0.9949 1.96
40 C 0.5649 0.9970 1.74 0.5615 0.9926 1.72
50 C 0.6567 0.9993 2.35 0.6789 0.9020 2.51
Constant slope of plot WL/WLeqm vs. t (for first hour of dehydration).
WLeqm equilibrium water loss.
D (slope)2 (pL2/4), where L 1/2 thickness of slab.
r2 determination coefficient.
Table 2 S-values (calculated from
intercept) and theoretical equilib-
rium values (calculated from slope)
obtained using model no. 2
(Azuara et al., 1992) for shark
slabs at different temperatures
Temperature
Water loss (WL) Salt gain (SG)
S-value
(h)1)WL model
(g H2O g DM)1)
S-value
(h)1)SG model
(g NaCl g DM)1)
20 C 0.83 0.7 1.44 0.7
30 C 1.05 0.8 1.74 0.7
40 C 1.92 1.0 1.54 0.7
50 C 1.66 1.3 2.22 0.7
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The diffusion coefficients for WL in shark slabs
were calculated at different times during the
osmotic process according to eqn 2 and are given
in Figs 8 and 9. Diffusivities were significantly
affected by immersion time (P 0.001) but not by
brine temperature. Generally values were highest
approximately after 1 h of dehydration, then
declined rapidly during the first 4 h, after which
the decline was more gradual. The diffusion
coefficients for WL increased as brine temperature
increased.
As shown in Fig. 8, water diffusivity values for
the first hour of dehydration averaged 0.90, 1.55,
2.25 and 2.31 10)5 cm2 s)1 for dehydration at 20,
30, 40 and 50 C, respectively. The results were
found to compare favourably with the results of
model no. 1, which was applicable only to the initial
stages of dehydration. The advantage of using this
approach is therefore the ability to calculatediffusivities for the entire duration of the osmotic
treatment and not just the initial stages. Values
after 24 h of dehydration were lower and averaged
0.17, 0.23, 0.23 and 0.24 10)5 cm2 s)1 at 20, 30,
40 and 50 C, respectively. Average diffusion
coefficients for WL for the 24 h of dehydration
were 0.54, 0.90, 1.34 and 1.35 10)5 cm2 s)1 at 20,
30, 40 and 50 C, respectively.
As shown in Fig. 9, there were no marked
changes in salt diffusion as brine temperature
increased from 20 to 40 C, but values increased as
the temperature was increased further to 50 C.
Salt diffusivity values for the first hour of dehy-
dration averaged 2.12, 2.07, 1.95 and
2.59 10)5 cm2 s)1 at 20, 30, 40 and 50 C,
respectively. Again, these results were found to
compare favourably with the results of model no.
1. Average diffusion coefficients for SG for the
entire process (24 h) were 1.23, 1.22, 1.13 and
1.29 10)5 cm2 s)1 for slabs at 20, 30, 40 and
50 C, respectively.
Azuara et al. (1992) modelled data of Favetto
et al. (1981) for the salting of beef and noted that
the diffusion coefficient was not constant for the
duration of the diffusion process. At 85 C, D-
values decreased from an initial value of 4.0
1.5 10)5 cm2 s)1 in 3 h. At 30 C, D-values
increased from an initial value of 0.5
1.0 10)5 cm2 s)1 in 3 h.
Conclusions
Brine temperature has a pronounced effect on theosmotic dehydration of small shark slabs
(10 5 1 cm). Salting can be successfully
achieved at 20 and 30 C. Dehydration at higher
temperatures (above 40 C) resulted in undesirable
changes such as shrinkage, discolouration and
cooking. For slabs at all temperatures, the greatest
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
Time (h)
D(105cm
2s
1)
20C
30C
40C
50C
Figure 8 Diffusion coefficients (D) for water loss in shark
slabs calculated using model no. 2 (Azuara et al., 1992).
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 2 4 6 8 10 12
Time (h)
D(105cm
2s1)
20C
30C
40C
50C
Figure 9 Diffusion coefficients (D) for salt gain in shark
slabs calculated using model no. 2 (Azuara et al., 1992).
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change in weight, MC, SC and water activity
occurred during the first 4 h of immersion. During
this time the higher the temperature, the greater
the reduction in weight and the decline in MC.
Mass transfer during osmotic dehydration of
shark slabs occurred in the falling rate period.
The expressions presented by Azuara et al.
(1992), based on the model presented by Crank
(1975), were successfully used to predict the
equilibrium point and to calculate diffusion co-
efficients during the osmotic process. This model
allows for the calculation of moisture and salt
diffusivities at intervals during the osmotic treat-
ment and not just the initial stages.
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