thin-layer models

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 8, Number 9 (2013) pp. 1053-1066 © Research India Publications http://www.ripublication.com/ijaer.htm

Thin Layer Drying Kinetics and Modelling of Spinacia oleracea Leaves

Prithvi Simha1 and Ashita Gugalia 1

1Mass Transfer Laboratory, Chemical Engineering Division,

School of Mechanical and Building Sciences (SMBS), VIT University, Vellore - 632014, Tamil Nadu, India.

[email protected] [email protected]

Abstract

In the present work, spinach samples were dried using three different drying techniques namely sun, conventional and microwave. Drying experiments were conducted using a constant air velocity and temperature but varying microwave output power. Drying rate enhanced in case of microwave compared to artificial and natural air with lower drying time. The experimental drying data of spinach were applied to seven moisture ratio models, given in literature. Nonlinear regression analysis was performed to relate the parameters of the models with the drying conditions. The performances of these models were evaluated by comparing the coefficient of determination (R2), standard error and residual sum of squares values. Among all the models, the Parabolic, Page and Midilli models were found to be the best for explaining the drying characteristics of spinach leaves with respect to sun, conventional and microwave treatment. The effective moisture diffusivity was in the range of 10-9- 10-10m2/sec in all the treatments studied. Keywords: Spinach, Effective Diffusivity, Modelling, Re-hydration, Nonlinear Regression

INTRODUCTION Spinach (Spinacia oleracea) is an edible flowering plant in the family of Amaranthaceae. It is native to central and south-western Asia. In India, it is cultivated in almost all the states. Spinach has a high nutritional value and is extremely rich in antioxidants, especially when fresh, steamed, or quickly boiled. It is a rich source of vitamin A, E, K, magnesium, iron, calcium, potassium, folic acid,

1054 Prithvi Simha and Ashita Gugalia

copper, protein, phosphorus, zinc and niacin. Spinach is low in calories and is a good source of ascorbic acid (vitamin C) [1]. Ascorbic acid is an important nutrient in vegetables. It is a hydro-soluble vitamin and more sensitive to heat, oxygen, light and considered to be highly sensitive to losses during processing [2].Spinach is a vegetable which rapidly perishes after harvest and which is consumed only in the product season. It is sold loose, bunched, packaged fresh in bags, canned, or frozen. Drying is the one of the storage methods, which has the capability of extending the consumption period of spinach while maintaining its vitamin content. Drying processes not only inhibit microbial growth but also several biological and chemical degradation reactions; nevertheless, they also affect nutritional characteristics leading to the collapse of vegetable tissues and the degradation of vitamins and antioxidants. Moreover, in the last 30 years the need of new technologies have lead to the development of several dehydration methods such as hot air dehydration, osmotic dehydration, microwave dehydration, infrared (IR) dehydration, ultrasonic dewatering, hybrid technologies, etc. The introduction of these technologies in food industry has increased the quality of dried vegetables leading to an exponential increase of the market of these products. During the drying processes, the major factor of all the stated techniques is the mass transfer of water from vegetable tissues to its surrounding and vice versa. This transfer occurs through several mechanisms such as capillary flow, diffusion of water due to concentration differences, surface diffusion, vapor diffusion in the pores due to pressure gradient and water vaporization-condensation [3], thus, making drying a very complex phenomenon. Fundamental research with aid of mathematical modeling and numerical simulation provides an extremely powerful tool for investigating the complicated physics that evolve during the drying of wet materials [4]. In this project, drying equations are developed for spinach leaves with respect to sun, convective air and microwave drying techniques. Experiments were performed by varying microwave output power and initial moisture content. The resulting moisture values were fitted to seven different empirical models. The model having highest correlation coefficient (R2) and lowest standard error and residual sum of squares value was determined to be the most relevant one. Thus, the present study was conducted with following objectives: (i) To study the drying rates, drying time and effective diffusivity of spinach for different techniques; (ii) To determine change in quality of spinach (iii) To select the best model to describe the behaviour of spinach in all the three cases and develop the respective drying equation. METHODS AND MATERIALS Fresh spinach leaves were procured from local market everyday prior to the experiment. They were washed with tap water and the moisture on the wet sample surface was removed with filter paper. They were weighed according to the need of the experiment. This step was followed by the treatment in different drying techniques. Furthermore, the moisture content was determined by placing the initially dried samples in a hot air oven set at 60ºC until bone dry, finally the weight of sample

Thin Layer Drying Kinetics and Modelling of Spinacia oleracea Leaves 1055

was noted. Another set of experiments were performed by increasing the initial moisture content by soaking it in 2 litres of water. The motive was to find the effect of initial moisture content on drying rate. A. Sun Drying 100 grams of spinach was weighed and taken to a place where exposure to sunlight was maximum. The leaves were at a considerable height from ground, thus, eliminating the possibility of mass transfer through ground. The leaves were spread on a thick stack of newspapers such that they were not touching each other. Experiments were carried out usually from 9 am to 5 pm when the sun’s light was substantial except on humid days. B. Conventional Drying The drying experiments were performed in tray dryer at constant air velocity and temperature (65 C). The dryer was started at about 30 min before the drying experiments to achieve steady-state conditions before each drying run.100 grams of spinach was weighed and was placed in the dryer. Initially, the weight on the scale was set such that it pointed the zero level on short scale. Each time the weight on the long scale was reduced by 9 grams and corresponding time taken was noted until case hardening occurred. C. Microwave Drying Drying treatment was performed in a domestic digital microwave oven (Samsung C-103F, Thailand) with technical features of 230 V and 50 Hz. The microwave oven has the capability of operating at five different microwave stages, being 100, 180, 300, 600 and 900W. The diameter of the plate was 250 mm and consisted of a rotating glass plate with 280 mm diameter at the base of the oven. Time adjustment is done with the aid of a digital clock located on the oven. Drying trials were carried out at two different microwave generation power being 180 and 300 W. These two powers are preferred for drying of fruits and vegetables taking into account the damage of leaves or fruits. The spinach leaves to be dried were 25 grams in weight. Rotating glass plate was removed from the oven periodically (every 5 or 10 s according to the need of experiment) during the drying period, and the moisture loss was determined by weighing the plate using digital balance with 0.01 g precision. During all experimentations, the loss of weight of the sample was continuously monitored with time and drying was continued until the samples achieve its final moisture content (equilibrium moisture content). ANALYSIS of DRYING DATA The analyses comprised of plotting the curves between moisture content, drying rate and moisture ratio versus time and comparing the results of all three types of drying techniques. Seven popular thin layer drying models were used to predict the relation between moisture ratio and drying time. DATAFIT 9.0(trial version) [5] was used for fitting the curves into the models.


The coefficient of determination (R2) [6] was used as the primary criteria to select the best equation to account for variation in the drying curves of the dried samples: ∑ (MRpre, i −MRexp,avg)態朝沈退怠∑ (MRexp, i −MRexp,avg)態朝沈退怠

The drying rate and moisture ratio of spinach leaves were calculated using the following equations:

X =歎辿貸歎但歎但 ; MR =

凧貸凧奪凧待貸凧奪 ; N =託坦代辰凧辰担

where , wi and wb are the wet weight at any time t , and bone dry weight of leaves, X is the moisture content at particular time (kg water/kg dry solid), MR denotes moisture ratio, X0 and Xe are the initial and equilibrium moisture contents (kg water/kg dry solid) respectively. N is the drying rate (kg dry solid/m2 hr), Ss and A are the bone dry weight and area of the tray or plate or newspaper respectively while t denotes the time of drying(hr). In general, drying of foods takes place in two periods, a constant rate and a falling rate period. The mode of moisture movement within a hygroscopic solid during the falling rate period could be represented by effective moisture diffusion phenomenon and represents an overall mass transport property of water in the material. During drying it can be assumed that diffusivity, as explained with Fick’s diffusion equation is the only physical mechanism to transfer the water to surface [7]. Effective moisture diffusivity which is affected by composition, moisture content, temperature and porosity of the material, is used due to the limited information on the mechanism of moisture movement during drying and complexity of the process [8]. For the solution of Fick’s diffusion equation, the leaves were assumed to be slabs of thickness 1 mm and the diffusivity was calculated using the simplification for longer drying times yielding a linear equation where diffusivity can be obtained from the slope of the plot [9].

ln(MR) = ln 磐 8講態卑 − (Deff.π態

4詣態 .建)

where, MR is the moisture ratio at specific time, Deff denotes effective diffusivity in m2/sec , L and t are the thickness of leaves(m) and time taken(hr) for drying respectively. Based on the criteria of highest R2, the best model describing the thin layer drying characteristics was chosen. RESULTS AND DISCUSSIONS A. Drying Curves The moisture ratio versus time curves for the sun and conventional drying treatments are shown in Fig.1. In general the curves show a decreasing trend as drying progresses. It is obvious that sun drying recorded the longest drying time as temperatures fluctuated according to the ambient which is very much lower than the


temperature used in artificial hot air drying (60–80C). This result in slower drying rates. It can be observed from Fig.1 that time taken for the moisture content to come down to 10% was 5 hrs in case of sun drying than that of 3 hrs in case of conventional, though same initial amount of spinach was taken.

Fig. 1: Comparing Sun and Conventional Drying- Moisture Ratio vs time The drying rate curves are presented in Fig. 2. In both the treatments constant rate periods were very small, most of the drying took place in falling rate period as indicated by the curves. It is true that there was only a small amount of free water present on the surface and drying mechanism was mainly controlled by diffusion of bound water. Drying rate is seen to be greater in the initial stages (1.8-1.6 kg dry solid/ m2 hr and 0.2-0.1 kg dry solid/ m2 hr for conventional and sun drying technique respectively until a moisture content of 2 kg water/kg dry solid. Beyond this moisture content, drying rates only deviated slightly from each other for both sun and conventional; this continued till the end. Moreover, it can be observed from plot that rate of drying in conventional dryer is more compared to that of sun drying, but the added value of the above statement is reduced by saying that drier will consume large amount of energy compared to sun drying because it is a natural source. Thus, depending upon the requirement of the product, either of the two drying techniques may be used.

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time (hrs)

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conventional


Fig. 2: Comparing Sun and Conventional Drying- Drying rate vs moisture content To investigate the effect of microwave output power on moisture content, moisture ratio, drying time, two microwave output powers 180 and 300W were used for drying of 25 grams spinach leaves as mentioned earlier. 180 and 300W were chosen to avoid spoilage of spinach leaves. The moisture content of the material was very high during the initial phase of the drying which resulted in a higher absorption of microwave power and higher drying rates due to the superior moisture diffusion. As the drying progressed, the loss of moisture in the product caused a decrease in the absorption of microwave power and resulted in a fall in the drying rate. The drying rates increased with the increase of microwave power levels (Fig 3). Thus, microwave power level had a positive effect on the drying rates. These results are in agreement with previous studies by Sharma and Prasad, 2001[10]. As the microwave output power was increased, the drying time of samples significantly decreased. By working at 300W instead of 180 W, the drying time was shortened by 16.7%. During the drying of 25 g spinach leaves at two different microwave powers, a total of 22 +0.06g of weight loss occurred from each drying sample. The quantities of moisture removed from the material in every 10 s time period of drying cycle at two different microwave power levels are given in Fig. 4.

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dr s

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/m2

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sun


Fig. 3: Microwave Treatment (180W and 300W) : Drying curves

Fig. 4: Microwave Treatment (180W and 300W): Variation of moisture lost in 10 sec(Y) vs Drying time (X)

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Maximum value of moisture removed from the material at 300W microwave power (2.8 g) was obtained between 20th and 25th sec of the drying period. The value of maximum evaporation between 170th and 200th seconds of the drying period at 180 W microwave powers was determined as 2 grams. Thus, the above observations validate the fact that increase in microwave power increases the rate of moisture removal though, energy consumption also increases. B. Modelling of Drying Kinetics Microwave drying kinetics of spinach leaves were described using the drying data. Seven different semi-empirical thin layer drying models as mentioned in Table 1 were used. Among these models examined, the moisture ratio followed parabolic model in case of sun drying, page model in tray drying while the Midilli model was observed to be the most appropriate one for microwave drying with the higher value for the coefficient of determination (R2) and lower standard error and RSS compared with those obtained for other models. Dwivedy [17], also reported that Midilli model is the best model describing the microwave drying behaviour of coriander and parsley leaves. The estimated parameters and statistical analysis of the models examined for the different drying conditions are illustrated in Table 2. TABLE I: MATHEMATICAL MODEL EQUATIONS FOR DRYING CHARACTERISTICS

Empirical Model Equation References Midilli MR = a.exp(-ktn) + bt [11] Page MR = exp(-kt)n [12]

Parabolic MR = c + bt + at2 [10] Logarithmic MR = a.exp(-kt) + b [13]

Wang and Singh MR = 1 + bt + at2 [14] Henderson and Pabis MR = a.exp(-kt) [15]

Lewis MR = exp(-kt) [16]


TABLE II: ANALYSIS OF MODEL FOR DIFFERENT DRYING TECHNIQUES

Type of Drying

Model Name

R2 Std. Error

RSS Coefficients

Midilli 0.99722 0.01925 0.00927 a = 0.983; b = -9.753; k = 0.523, n = 1.963

Page 0.99528 0.02416 0.01575 k = 0.163; n= 2.008 Parabolic 0.98882 0.03789 0.03733 a = 0.024; b = -0.358;

c = 1.129 Microwave

(180 W) Logarithmic 0.98707 0.04074 0.04316 a = 2.109; b = -0.983;

k = 0.172 Wang and

Singh 0.97477 0.05585 0.08421 a = 0.057;

b = -0.253 Henderson

& Pabis 0.93529 0.08945 0.21603 a = 1.265; k=0.519

Lewis 0.87704 0.12108 0.41047 k= -0.410 Midilli 0.99692 0.01759 0.00773 a = 0.998; b = 5.134;

k = 0.697;n = 1.697 Page 0.99498 0.0216 0.01261 k = 0.687; n= 1.64 Parabolic 0.98246 0.04115 0.04403 a = 8.768; b = -0.615; c = 1.044

Microwave (300W)

Logarithmic 0.98099 0.04205 0.04773 a = 1.279; b = -2.144; k = 0.986

Wang and Singh

0.97416 0.04995 0.06487 a = 8.158; b = -0.579

Henderson & Pabis

0.97197 0.05105 0.07036 a = 1.278; k=1.048

Lewis 0.9432 0.07136 0.14258 k= 0.841 Parabolic 0.97689 0.05502 0.02422 a = 1.682; b = -7.937;

c = 0.933 Wang and

Singh 0.96963 0.05946 0.03182 a = 1.904; b = -8.777

Sun Drying

Lewis 0.17238 0.29449 0.86726 a = 1

Henderson & Pabis

0.17238 0.31042 0.86726 a = 1; k = 1

Page 0.17238 0.31042 0.86726 k = 1; n = 1 Page 0.99495 0.02311 0.00534 k = 5.038; n = 0.802

Tray Dryer

Parabolic 0.95663 0.07135 0.04582 a = 3.871; b = -1.155; c = 0.843

Wang and Singh

0.87878 0.11316 0.12806 a = 5.567; b = -1.537


It was observed that the value of drying rate constant (k) increased with the increase in microwave output power. This implies that with the increase in microwave output power drying curve becomes steeper indicating faster drying rate. The fitness of the data is illustrated in Figures 5 and 6.

Fig. 5: Fitness of Midilli model for microwave drying.

Fig. 6: Fitness of Page model for microwave drying.

C. Moisture Diffusivity The effective moisture diffusivity was calculated by using the method of slopes. According to the experimental data obtained at various microwave output power levels, the logarithm of moisture ratio values, ln (MR), were plotted against drying time (t). The linearity of the relationship between ln (MR) and drying time is illustrated in Figure 7 and 8 for various techniques of drying (with R2 more than 0.90 for all the treatments).


Fig. 7: Plot of ln(MR) vs time to find effective diffusivity for Microwave Drying

Fig. 8: Plot of ln(MR) vs time to find effective diffusivity for Sun and Conventional Drying.

y = -0.024x + 0.665R² = 0.984

y = -0.015x + 0.877R² = 0.906

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Linear (180W)

y = -1.374x - 0.028R² = 0.984

y = -0.975x + 0.259R² = 0.931

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R)

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Linear (conventional)


The effective moisture diffusivity values (Deff) were calculated. The range of moisture diffusivities varied from 10-9 – 10-10 m2/sec which is similar as given by Ibrahim [18].Though similar trends were observed in all the techniques, effective diffusivity was found to be higher in case of microwave drying (6.085 x 10-9m2/sec and 9.736x 10-9 m2/sec for 180 and 300W respectively)compared to other techniques(1.099x10-10 and 1.5484x10-10 m2/sec for sun and conventional respectively). This may be due to lower drying time under microwave treatment. D. Comparison of all the three treatments Though all the treatments were found to be effective in removing moisture from spinach leaves, the rate of drying was higher for microwave irradiation. The drying time taken by microwave was 61% less compared to sun drying and 42.45% less with respect to conventional one for the same reduction of weight (90%). The product obtained by conventional drying became brittle at the end of the experiment, while the dried product obtained after irradiation and sun drying was very less brittle comparatively. This limitation of conventional drying became a hindrance for further moisture removal. The re-hydration properties were determined by immersion in distilled water [19].Four leaves of the dried sample obtained after each treatment, which were randomly chosen, were weighed and placed in a bucket with 400 mL distilled water at 30 C. After 4 hrs, the sample was removed from bucket; the surplus water was removed with tissue paper, and then weighed. The weights from all drying techniques followed the following pattern: microwave irradiated > conventional > sun. Microwaves caused violent evaporation of water in cells, followed by a collapse of cell structure and partial disconnection of cells which leads to increase in porosity followed by high absorption [20]. Though the treatment with irradiation is highly effective compared to sun and tray drying, but within seconds after the commencement of irradiation, blackening of leaves started and the product had a blackish green colour after 40 sec at microwave power of 300W. The leaves blackened after 3 hrs in tray drying while no such phenomenon was observed in case of sun dried samples. This may have occurred due to high absorption of microwave irradiation. This decline in quality makes microwave treatment less effective. Moving on to the mathematical modelling, it was surprising to note that all the three models followed different equations. Parabolic, Page and Midilli models were followed by sun, conventional and microwave moisture ratios respectively. The Midilli model showed that moisture ratio in third case, depended exponentially on nth power of time, indeed, this means the more amount of moisture gets removed in very less time which proves efficiency of microwave drying compared to others. Conventional drying was also efficient compared to sun drying, in which moisture ratio depended exponentially on time, compared to polynomial (t2) dependency of moisture ratio in latter case. Effective moisture diffusivity, calculated from slope of ln (MR) vs. time, was of the order 109 compared to other two techniques where it was of the order 10-10. This may be due to lower drying times and higher rate of evaporation as seen in microwave drying.


CONCLUSIONS The drying characteristics were investigated using three different techniques, namely sun, conventional and microwave. The parameters such as height from ground, artificial air velocity and temperature were kept constant while microwave output power was varied in the latter case. It was observed that the drying rate was maximum during the microwave treatment while the quality of dried sample was better after the first treatment. Drying Time was as short as 300 sec for microwave while it was as large as 5-6hrs for sun. The conventional drying proved to be optimum while evaluating each characteristic. The drying curve for sun and conventional drying showed almost similar trend with most of the drying taking place in falling period while it was very different from microwave one where the trend was found to be different. This is because the heat was mainly generated in the bulk of the sample and transported from the bulk to the environment. This type of temperature gradient can only be generated by microwave heating. Microwave drying is caused by water vapour pressure differences between interior and surface regions, which provide a driving force for moisture transfer. Experimental data were compared with predicted values of seven different models. Parabolic, Page and Midilli model was found to be best suited for the three techniques. The effective diffusivity values were obtained in the range of 10-9- 10-10 m2/sec. Acknowledgment The authors acknowledge the financial support provided by VIT University, Vellore, India under the VIT-SMBS research grant scheme (2040/VP-A-31082012) for conducting the initial experiments. The authors would like to thank Prof. G. S. Nirmala and Prof. Mahesh Ganesapillai for their guidance, support and valuable inputs during the project. REFERENCES

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[2] N. V. Yanishlieva-Maslarova, “Inhibiting oxidation,” In J. Pokorny, N. Yanishlieva, & M. Gordon (Eds.), Antioxidants in foods, Boca Raton, FL: CRC Press LLC, pp. 22–70, 2001.

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