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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

International Journal of Food Science and Technology 2006, 41, 405416 2006 Institute of Food Science and Technology Trust Fund


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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

2006 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2006, 41, 405416


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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




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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




10/12

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).




11/12

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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