Simple modelling of air drying curves of fresh and osmotically pre-dehydrated apple cubes

of Food En‘+7eering 33 (1997) 13% I so 0 1997 Elsevier Science Limited. All rights reserved. Printed in Great Britain 0260-8774197 $17.00 + 0.00

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P I I:

SO260-8774(97)00049-6

ELSEVIER

Simple Modelling of Air Drying Curves of Fresh and Osmotically Pre-dehydrated Apple Cubes S. Simal, E. Deyh, M. Frau & C. Rosselk* Department of Chemistry, University of Illes Balears, Ctra. Valldemossa km. 7.5. 07071 Palma de Mallorca, Spain (Received

16 December

1996; accepted

14 June 1997)

ABSTRACT Air drying curves simulation of fresh and pre-osmosed apple cubes was carried out through a diffusional mass transfer model solved by the separation of variables method. The influence of an osmotic pre-treatment of apple samples on air drying curves was evaluated. Drying curves of fresh apple cubes showed case-hardening when the air dtying temperature was higher than 60°C and the drying curves simulation was rendered inaccurate (%var = 92.9%). The effective diffusivity coeficient in the air drying process was considerably affected by the previous application of osmotic drying (7O”Bti sucrose at 50°C) between 30 and 180 min(D,tY decreased 38-6470). Howevel; the duration of this treatment did not show an important influence on this diffusivity. Simulation of the air dlying curves of osmotically pre-dtied samples was carried out satisfactorily when neglecting sample shrinkage in the proposed model (%var = 984%). 0 1997 Elsevier Science Limited. D ett

D,, E;, L

p,,,, p,,, R

s, S YX t

NOTATION Effective diffusivity (m’/s) Pre-exponential factor Arrhenius equation (m2/s) Activation energy (J/mol) Half-length of the cube (m) Initial dry matter (g) Final dry matter (g) Gas constant (8.3 J/mol K) Standard deviation (sample) [(g water/g dry matter)2] Standard deviation (estimation) [(g water/g dry matter)2] Time (s)

*To whom correspondence

should be addressed. 139

E-mail: [email protected].

140

T

W

WC W?_ W X Y z

Y %var

S. Simal et al.

Air temperature (“C) Average moisture content (kg water/kg dry matter) Critical moisture content (kg water/kg dry matter) Equilibrium moisture content (kg water/kg dry matter) Local moisture content (kg water/kg dry matter) x axis distance (m) y axis distance (m) z axis distance (m) Dimensionless moisture Percentage of explained variance

INTRODUCTION Fruits and vegetables are regarded as highly perishable food due to their high moisture content (Jayaraman and Das Gupta, 1992). Several technological processes have been employed on an industrial scale to preserve these types of food, with the majority being based on hot air dehydration. Simultaneous mass and heat transfer takes place during dehydration. From an engineering point of view, it is important to develop a better understanding of the controlling parameters of this complex process. Mathematical models have proved to be very useful in the design and analysis of these transfer processes during dehydration (Wang and Brennan, 1995). In some of the models, the assumptions of negligible shrinkage and an isothermal process are made for mathematical convenience (Balaban, 1989). Several methodologies of pre-treatment are commonly used in order to obtain high quality dehydrated food. Osmotic dehydration of fruits and vegetables by immersion in liquids with a water activity lower than that of food has received considerable attention in recent years as a pre-drying treatment so as to reduce energy consumption and to improve food quality (Jayaraman and Das Gupta, 1992; Torreggiani, 1993; Karathanos et al., 1995). This method of dehydration in which simultaneous movement of water and solutes from and into the material takes place (Yao and Le Maguer, 1994), can be used as a pretreatment before air drying in order to reduce the water content of the food by between 30 and 70% of the original amount (Lenart and Lewicki, 1988). However, osmotic dehydration will usually not give rise to a sufficiently low moisture content for the product to be considered shelf-stable (Rahman and Lamb, 1991). Osmotic dehydration preceding air drying preserves fruits and vegetables from some colour changes and increases the retention of flavour during the drying process (Lenart and Lewicki, 1988). Moreover, the resulting product is generally of good quality and an attractive food than can be consumed without prior rehydration. In this study, the applicability of the separation of variables method for solving the equations of a diffusional mass transfer model for the simulation of apple cube air drying will be evaluated, neglecting sample shrinkage during the drying process. Moreover, the influence of an osmotic pre-treatment of apple samples on both the air drying process and air drying curves will be evaluated.

Model&

qf air drying curves of apple cubes

141

Mathematical model In order to establish the equations of mass transfer during air drying, the following considerations were taken into account: the process was isothermal (Coonce et tzf., 1993; Rovedo et al., 1995), the main mass transfer mechanism is of diffusional nature and sample deformations and shrinkage during drying were negligible. According to the literature, if the diffusivity coefficient (D& is an effective parameter (Fusco et al., 1991), constant and uniform, and assuming isotropic behaviour of the solid with regard to water diffusion, mass transport can be then described by considering Fick’s law in an unsteady state mass balance, which for a parallelepipedic shape can be written as follows (Welty et al., 1993):

awl

-

at

=Drf,

a2W, -+-+6x2

(

zw,

a’w,

i?y

a?

(1)

>

The initial moisture content was considered uniform throughout the solid (Karathanos et al., 1990). The boundary conditions considered in this study were those related to both the thermodynamic equilibrium and the symmetry of the solid. As an initial condition it was assumed that the critical moisture content (W,) corresponds to the moisture content of the solid at the beginning of the air hot drying process (Karathanos et al., 1990). Eqn (1) can be solved analytically using the method of separation of variables when the sample volume is considered constant throughout the drying process (Jayas et al., 1991) and expressing the moisture concentration in the solid in a dimensionless way (eqn (2)): ‘Y(t) =

w-w,

(2)

w,-w,

The solution in series obtained for water transport in a cubic solid (eqn (3)) (Zogzas to the product of three perpendicular infinite slab solutions.

et al., 1994) corresponds

-(21)+1)2

3n=D& 4L2

I

(3)

Eqn (3) was solved by using the Microsoft Excel 5.0’” spreadsheet (Microsoft Corporation, 1992) in order to identify the diffusivity coefficient at different air drying temperatures. For this purpose, from the spreadsheet containing the experimental data of average dimensionless moisture content vs drying time, the diffusivity coefficient (D& was determined using SOLVER, a tool included in EXCEL that uses the Newton’s method to identify one unknown variable. Identified Deff values from the proposed method were fitted to the Arrhenius equation (eqn (4)) (Banga and Singh, 1994), from which D, and E, parameters were calculated.

142

S. Simal et al.

In order to mathematically evaluate the accuracy of the simulation obtained using the proposed method, the percentage of explained variance (%var) (eqn (5)) was computed. The calculation was performed by using the standard deviation of the sample (S,) and the corresponding estimation (S,,).

1 II2

l_$

%var = [

MATERIALS

.lOO

?

(5)

AND METHODS

In all experiments, apples were previously washed, peeled, cored, cut into 1 cm edge cubes and dipped in 0.2% ascorbic acid and 1% citric acid solution for 10 min, surfaced dried with filter paper and preserved at 4°C for 20 h before air or osmotic drying (Simal et al., 1997). Osmotic dehydration of apples was carried out in 70”Brix sucrose solution (commercial sugar). Samples were osmosed in dynamic conditions provided by agitation (50 oscillations/min). The product/solution ratio was 1:6 (weight basis). Osmotic solution was periodically re-concentrated, being f 3”Brix deviation allowed. The maximum dehydration time was 3 h (Lerici et al., 1988; Raoult et al., 1989; Simal et al., 1997). The osmotic set-up, described in a previous work (Simal et al., 1997) basically consisted of a Unitronic 320 OR thermostatic bath which operates within a temperature range 5--lOO”C, and provides agitation by oscillation from 10 to 100 oscillations/min. For the osmotic treatment, plastic jars filled with the osmotic solution were heated in the thermostatic bath until the solution reached the temperature chosen for the experiment. Next, samples were placed inside the jars to initiate the process. When jars were removed, the apple cubes were quickly rinsed and blotted with tissue paper in order to remove surface water. After osmotic treatment, final moisture content and final sample weight were measured. Drying experiments with hot air were carried out in a laboratory scale drier, operating at an air mass flux of 3 kg/m2 s, a figure high enough to ensure that mass transfer was controlled by the internal resistance, and temperatures between 30” and 90°C. The drier used for sample dehydration, described in a previous work (Simal et al., 1996) was equipped with an automatic temperature controller (kO.l“C). The air flowed perpendicular to the bed. A monolayer loading was used. Water losses were measured by weighing the basket and its content automatically. The average ambient air characteristics during hot air dehydration were: 29*2”C temperature and 36 + 6% humidity. Moisture content of dehydrated products was obtained by the AOAC method No. 934.06 (AOAC, 1990). Volume changes were calculated by sudden immersion of dried samples with different moisture contents in distilled water, and measurement of water displacement. Air drying experiments with fresh apple cubes Apple cubes of side length 1 cm were dehydrated from an initial moisture content of 9 kg water/kg dry matter to 1 kg water/kg dry matter with hot air at different air

143

Model&g of air drying curves of apple cubes

drying temperatures, tion.

30, 40, 50, 60, 70, 80 and 90°C without prior osmotic dehydra-

Air drying experiments with osmotically pre-dehydrated apple cubes Apple cubes of side length 1 cm were osmotically dehydrated at 50°C with a 7O”Brix sucrose solution for 30, 60, 90, 120 or 180 min, and then dehydrated with hot air at 60°C to a final moisture content of 0.2 kg water/kg dry matter. In addition, apple samples osmotically dehydrated for 90 min at 50°C with a 70”Brix sucrose solution were dried with hot air at different temperatures, 30, 40, 50, 60, 70, 80 and 90°C until a final moisture content of O-2 kg water/kg dry matter was obtained.

RESULTS

AND DISCUSSION

Drying experiments with fresh apple cubes by using hot air Drying curves corresponding to apple cubes of 1 cm side length at different air temperatures (30, 40, 50, 60, 70, 80 and 90°C), from 9.0 to 1.0 kg water/kg dry matter, are shown in Fig. 1. A constant drying rate period was not detected in these drying experiments, and only one diffusional period was observed.

n

T= 30°C

q

T= 40°C

l

T= 50°C

o T= 60°C A T= 70°C

n

n

n

qQ l

0

2000

n

QQ l

4000

n n q

6000

I 0

m 0

8000

n

A

T= 80°C

l

T= 90°C

n

loo00

n

12000

Time (s) Fig. 1. Influence

of air-drying

temperature

on drying curves of 1 cm fresh apple cubes

S. Simal et al.

144

As it can be seen in this figure, drying rate clearly increased when temperature increased between 30 and 60°C. Nevertheless, the influence of air temperature was less important from 60 to 90°C. Apple cubes dehydrated at 60, 70, 80 and 90°C showed similar drying rates. The explanation of this observation lies in the fact that at temperatures higher than 60°C case-hardening took place (Ratti, 1994; Khraisheh et al., 1995; Simal et al., 1996). Drying curves showed low drying rates when the average moisture content approached 2 to 1 kg water/kg dry matter. Drying time from 2 to 1 kg water/kg dry matter accounted for 30-40% of total drying time. Therefore, a considerably long drying period would be necessary to achieve a final moisture content lower than 1 kg water/kg dry matter. The separation of variables method was used to identify the effective diffusivity coefficient at different air temperatures (30, 40, 50 and 60°C) (Table 1). Experimental data obtained at air drying temperatures higher than 60°C were not used in modelling due to the case-hardening effect observed. The identified Deff values (Table 1) were fitted to the Arrhenius equation (eqn (4)). Results are shown in eqn

Identified

TABLE 1 Effective Diffusivity Coefficients and Percentages in Air Drying Simulation Time of osmotic treatment (min)

Fresh applecubes

Air drying temperature (“C)

AVERAGE

Osmotically pre-dehydrated apple cubes

Osmotically pre-dehydrated apple cubes

of Explained

Variance

Identified D&m214

30 3.21x10-” 40 5.31x10-‘O 50 9.67x10- lo 60 12+67x10- lo %var = 92.9 k 6.0

30 60 90 120 180

60 60 60 60 60

5.40x10- ‘O 5.65 x lo-” 4.58 x lo- ‘O 5.13 x lo-“’ 5.43 x low”’

90 z’:

30 50 40

1.98 x lo- lo 3.55 2.71 x 1ow’O lo-‘”

90 90 90 90

60 4.55 70 5.86 80 7.60 90 9.79 %var = 98-4 + 1.2

AVERAGE

x x x x

lo- ‘O lo-” lo-” lo- ‘O

Obtained %var

84.0 95.4 96.7 96.9

99.8 99.6 99.2 98.9 97.5 96.8 97.1

Model@

of air drying curves of apple cubes

(6). From these results, the activation energy determined process of fresh samples was 39.7 kJ/mol. Dcff= 2.29 x

3O”C<6O”C

lOV”exp

145

for the air dehydration

r2=0.985

(6)

Comparison of diffusivities and activation energies reported in the literature is difficult because of the different estimation methods and models employed together with the variation in food composition and physical structure. Mulet et al. (1989) proposed the following values for diffusivity and activation energy in carrot determined by the separation of variables method: D,rf = 1.93 x lo- m2/s at 60°C and E, = 24.6 kJ/mol. Gekas and Lamberg (1991) measured 2.3 x lo-“’ m2/s at 60°C for D,rr in potato. Plots of calculated versus experimental average dimensionless moisture content are shown in Fig. 2. As can be observed in this figure, the simulation of drying curves was not accurate. Percentages of explained variance in the simulation of drying curves at 30, 40, 50 and 60°C using eqn (6) were low (Table 1). The average %var was 92.9*6-O%. Therefore, the separation of variables method seems to be inadequate in establishing a diffusional model to simulate air drying experiments of fresh apple cubes of 1 cm side. Sample shrinkage during drying of apple cubes of 1 cm side was experimentally measured. The percentage volume reduction of apple cubes during drying from 9.0

1

n

T= 30°C

q

T= 40°C

l

T= 50°C

o T= 60°C 0 0

0.2

0.4

0.6

0.8

1

experimental dimensionless moisture Fig. 2. Computed versus experimental average dimensionless moisture content. carried out at 30, 40, 50 and 60°C with 1 cm fresh apple cubes.

Experiments

146

S. Simal et al.

to 1-Okg water/kg dry matter was approximately 62%. This result indicates the importance of taking into account sample shrinkage when modelling air drying curves of fresh apple cubes. When sample shrinkage is considered, mass transfer is a moving boundary problem which cannot be solved using a simple method such as separation of variables. In this case, either a finite element or finite difference methods may be appropriate.

Air drying experiments with apple cubes osmotically pre-dehydrated Apple samples were osmotically dehydrated at 50°C and 7O”Brix for 30, 60, 90, 120 and 180 min, and then dehydrated with hot air at 60°C until a final moisture content of 0.2 kg water/kg dry matter was obtained. The osmotic dehydration of apple cubes was accompanied by the penetration of sucrose into the dehydrated tissue. Moisture content (dry matter) and weight gain during osmotic dehydration are shown in Fig. 3. As it can be seen in this figure, the most important water losses took place during the first 90 min of osmotic treatment, from 9 to 1.5 kg water/kg dry matter After this period of time, small variations in water content were detected, from 1.5 to 1 kg water/kg dry matter. Nevertheless, apple samples gained sugar regularly from 30 to 180 min of treatment. After osmotic dehydration, the samples were dehydrated with hot air at 60°C. The time required to achieve a final moisture content of O-2 kg water/kg dry matter was different in each experiment, ranged from 135 to 160 min. Samples treated osmot-

+

0

moisture content

30

60

90

120

1.50

180

Time (min) Fig. 3. Average

moisture

content

and weight gain of samples 70”Brix sucrose at 50°C.

during

osmotic treatment

in

147

Modelling qf‘uir dying curves of apple cubes

ically for 30 min needed more time to be dehydrated. Using the separation of variables method the effective diffusivity coefficients of these air drying curves were identified. These five identified values of Deff were similar (Table l), with an average D,ff figure of (5.24 kO.41) x lo- “’ m*/s. In Table 1, it can be observed that the D,rr value calculated for samples dehydrated with air at 60°C without osmotic pre-treatment was higher, 12.7 x 10P “’ m*,‘s. A similar result was found by Lenart and Lewicki (1988). From these results, it could be concluded that although the effective diffusivity coefficient in air drying process is considerably affected by the previous application of osmotic drying, the duration of this treatment, from 30 to 180 min, has not an important influence on the former parameter. This may be due to small solid gain after 30 min. In the third set of experiments, apple cube samples were osmotically dehydrated at 50°C for 90 min and then, dehydrated with hot air at different temperatures, 30, 40, SO, 60, 70, 80 and 90°C until a final moisture content of approximately 0.2 kg water/kg dry matter was achieved. The corresponding air drying curves are shown in Fig. 4. A constant rate drying period was not detected and only one diffusional period could be observed. In this case, an important influence of air drying temperature on the drying rate was observed from 30 to 90°C. The proposed model was developed to simulate the drying curves of these experiments. The effective diffusivity coefficient at different air drying temperatures was

l

T= 30°C

o T= 40°C n

T= 50°C

q

T= 60°C

A T= 70°C

4

4

0

0.0

I 0

4

0

m

0

1 ,

I t

10000

$

4

4

n

2oooo

A

T= 80°C

l

T= 90°C

4

4 *

I I

3oooo

r

4oooo

Time (s) Fig. 4. Influence

of air-drying

temperature

on drying curves of 1 cm pre-osmosed cubes.

apple

S.Simal et al.

148

identified using the separation of variables method. The experimental data of moisture variation versus drying time used for this purpose were those between the moisture content achieved after the osmotic treatment (l-52 kO.06 kg water/kg dry matter) and O-2 kg water/kg dry matter. In Table 1, it can be observed that Deff identified through air drying experiments carried out with pre-osmosed apple cubes, ranged from 2-O x loat 30°C to 9.8 x lo-” m2/s at 90°C. These values are lower than those corresponding to the experiments carried out with fresh apple cubes (from 3.2 x lo-” m’/s at 30°C to 12.7 x 10-lo m2/s at 60°C). Similar results were found by different authors. Rahman and Iamb (1991) found important differences between air drying rates in pineapple slices osmosed in 60” Brix sucrose solution at 20°C and non-osmosed samples. According to these authors, the sucrose infused during the osmotic process increased the internal resistance to moisture movement. Karathanos et al. (1995) found that Deff (considered as a moisture dependent parameter) was 16 x 10-‘” m’/s at 1 kg water/kg dry matter in apples air dried at 55°C while this parameter decreased to 5 x lo- lo m’/s when samples were osmotically pre-treated in 45”Brix sucrose solution for 12 h. Identified Deff values (Table 1) were fitted to the Arrhenius equation (eqn (4)). The results yielded in eqn (7). The activation energy determined for the air dehydration process of samples osmotically pre-treated was 24.0 kJ/mol. This value is considerately lower than that calculated for drying curves of fresh samples (39.7 kJ/ mol).

1

o T= 40°C H T= 50°C q

T= 60°C

A T= 70°C A T= 80°C

F’

0

l

0.2

0.4

0.6

T= 90°C

0.8

1

experimental dimensionless moisture Fig. 5. Computed versus experimental average dimensionless moisture content. Experiments carried out at 30, 40, 50, 60, 70, 80 and 90°C with 1 cm pre-osmosed apple cubes.

149

Modelling of air drying curves of apple cubes

Dcff= 2.74 x

lo-‘exp

30°C < 90°C

r2 = 0.999

(3

Using eqn (7) in addition to the proposed model, air drying curves of experiments performed with pre-osmosed apple cubes were simulated. In Fig. 5, calculated versus experimental dimensionless moisture contents were represented. As it can be observed in this figure, the accuracy provided by the proposed model was adequate. The %var explained in the simulation of drying curves at different temperatures (Table 1) were high, mainly in experiments performed at lower temperatures. Higher deviation observed in simulation at higher temperatures could be due to a slight case-hardening effect in osmosed apple samples during air drying. The average %var obtained in the simulation of air drying curves of samples osmotically pre-dehydrated was 98.4 + 1.2%. Sample volume variation during air drying processes was experimentally measured. Apple cubes treated osmotically using 70”Brix osmotic solution at 50°C for 90 min shrank almost 35% during the subsequent air drying, figure considerably lower than that measured in samples dehydrated without previous osmotic treatment, which shrank approximately 62%. These results indicate the suitability of the assumption of constant volume during air drying included in the modelling. Therefore, the simulation provided by the proposed model solved by the separation of variables method was more accurate when apple samples were osmotically predehydrated.

ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support of CICYT (ALI940565-C03) and M. For&n for her suggestions on the English of the manuscript.

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