Evaluation of some thin-layer drying models of persimmon slices (Diospyros kaki L.)

Energy Conversion and Management 56 (2012) 199–205

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Evaluation of some thin-layer drying models of persimmon slices (Diospyros kaki L.) _ Ibrahim Doymaz ⇑ Department of Chemical Engineering, Yildiz Technical University, 34210 Esenler, Istanbul, Turkey

a r t i c l e

i n f o

Article history: Received 22 September 2010 Received in revised form 28 November 2011 Accepted 30 November 2011 Available online 29 December 2011 Keywords: Persimmon Air drying Rehydration ratio Effective moisture diffusivity Activation energy

a b s t r a c t The effect of blanching and drying temperature (50, 60 and 70 °C) on drying kinetics and rehydration ratio of persimmons under hot-air drying was investigated. It was observed that both the drying temperature and blanching affected the drying time. The shortest drying times and highest rehydration ratios were obtained from blanched samples. Six thin-layer drying models were evaluated in the kinetics research. The fit quality of the proposed models was evaluated by using the determination of coefficient (R2), reduced chi-square (v2) and root means square error (RMSE). The Midilli et al., Page and Weibull models showed a better fit to experimental drying data as compared to other models. Effective moisture diffusivity (Deff) ranged from 7.05  1011 to 2.34  1010 m2/s calculated using the Fick’s second law. The activation energies of blanched and control samples determined from slope of the Arrhenius plot, ln(Deff) versus 1/(T + 273.15), was 30.64 and 43.26 kJ/mol, respectively. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Persimmon (Diospyros kaki L.) grows in subtropical and warm temperate climates. World-wide production of persimmon is 4.01 million tonnes in 2009 [1]. It is an important fruit in China, Japan and Korea and is also gaining popularity in the Mediterranean countries including Turkey [2]. Persimmon is relatively high content of dietary fibers, total and major phenolics, main minerals, and trace elements make persimmon preferable for healthy [3]. It is also a good source of fiber and vitamins, mainly A and C. It is mainly eaten fresh, but can be frozen, canned or dried and can be stored for up to 6 month in modified or controlled atmospheres [4]. The dried persimmon portions could be used as ingredient in products such as muesli, snacks and breakfast cereals [5]. Drying is probably the oldest and the most important method of food preservation practiced by humans. This process improves the food stability, since it reduces considerably the water and microbiological activity of the material and minimizes physical and chemical changes during its storage. Traditionally, fruits and vegetables are dried in open sunlight. However, sun drying is depending on weather, affecting the homogeneity and quality of the final product. Moreover, the products are prone to microbial and other contaminations [5]. To overcome these problems, the use of industrial dryers (solar or convective dryers) should be used [6,7]. Drying is a complex thermal process in which unsteady heat and moisture transfer occur simultaneously [8]. From an engineering point of view, it is important to develop a better understanding of the controlling parameters of this complex process. Mathematical models of the drying processes are used for designing new or ⇑ Tel.: +90 212 383 47 48; fax: +90 212 383 47 25. E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2011.11.027

improving existing drying systems or even for the control of the drying process. Many mathematical models have proposed to describe the drying process, of them, thin-layer drying models have been widely in use. These models can be categorized as theoretical, semi-theoretical, and empirical [9]. Many studies have emphasized drying kinetics and thin-layer drying models for fruits and vegetables – peach [6], apricot [10], apple [11–14], yam [15], berberis [16], mulberry [17], black grape [18] and carrot [19]. Some works have been published concerning processing attributes of persimmons. Cárcel et al. [5] studied the effect of high-intensity ultrasound on drying kinetics of persimmon slices. They reported that the high-intensity ultrasound increased the drying rate at the lowest air velocities. Nicoleti et al. [20] investigated the influence of drying conditions (temperature: 40–70 °C, air velocity: 0.8–1.2 m/s) on ascorbic acid during convective drying of whole persimmons. They reported that degradation rates of ascorbic acid were higher drying temperatures, independent of the necessary time to attain the desired moisture content. However, study on drying kinetics and activation energy of persimmon in thin-layer drying has not been reported yet. The objectives of this study were: (a) to study the effect of blanching on the drying time and rehydration ratio, (b) to fit the experimental data to six mathematical models, and (c) to compute effective moisture diffusivity and activation energy of persimmon slices.

2. Material and methods 2.1. Material Fresh persimmons (Diospyros kaki L.) were obtained from Iskenderun (Hatay, Turkey). The selected fruits showed uniform color

_ Doymaz / Energy Conversion and Management 56 (2012) 199–205 I.

200

and regular size. Samples were stored in a refrigerator at 4 °C until processing (2–3 days). The persimmons were washed with tap water, peeled and sliced manually by thickness of 5 mm and divided into two lots before use. One lot of samples was blanched in hot water at 70 °C for 2 min. The hot water treated slices were then immediately cooled down in tap water at room temperature to remove excess heat, and placed on tissue paper to absorb the excess surface water prior to drying (BLANCH). The other lot was unblanched (CONTROL). Moreover, some persimmons were washed with tap water, peeled and sliced manually by thickness of 3 and 8 mm. 2.2. Experimental apparatus The drying apparatus was a pilot-scale cabinet dryer that is described previously by Doymaz [10]. Cabinet dryer basically consists of a centrifugal fan to supply the air-flow, an electric heater, an air filter and an electronic proportional controller. The air temperature was controlled by means of a proportional controller. Air velocity was regulated by a centrifugal fan and fan speed control unit. The velocity was measured with TESTO 440 Vane Probe Anemometer (AM-4201, Lutron, Taipei, Taiwan), and flowed horizontally through the samples. The air passed from heating unit and heated to the desired temperature and then channelled to the drying basket. The samples were dried in the perforated square basket, which had a flow cross-section of 30 cm  30 cm. Weight loss of samples was recorded by using a digital balance (model BB3000, MettlerToledo AG, Grefensee, Switzerland) with a sensitivity of 0.1 g. 2.3. Experimental procedure Drying experiments (slice thickness: 5 mm) were performed at drying temperatures varying from 50 to 70 °C, with 10 °C increment, and a constant air velocity of 2 ± 0.1 m/s for all circumstances. In addition to this experiments, the persimmon slices (control; slice thickness: 3 and 8 mm) were dried at air temperature of 60 °C. The dryer was started about 30 min before drying experiments to achieve steady-state conditions. For each experiment, the 100 ± 2 g of persimmon slices was distributed uniformly into the perforated basket as a thin-layer. Sample weight was recorded at regular time intervals (15 min). Drying process was stopped when the moisture content of the samples was about 20 ± 0.5% (w.b.). The dried product was cooled and packed in low-density polyethylene bags that were heat-sealed. All the drying experiments were conducted in triplicate and the average of the moisture content at each value was used for the drawing of the drying curves. The average initial moisture content of persimmons was found to be 75.2 ± 0.2% (w.b.), as determined by using vacuum oven at 70 °C for 24 h following the Association of Official Analytical Chemists [21].

content of the samples were determined and used to calculate the moisture ratio. The drying rate (DR) of persimmon slices was calculated using Eq. (2):

DR ¼

M t  M tþDt Dt

ð2Þ

where Mt+Dt is moisture content at t + Dt (kg water/kg dm), t is the time (min) and Dt time difference (min). The drying data obtained were fitted to six thin-layer drying models that are detailed in Table 1 using the nonlinear least squares regression analysis. Statistical analyses of the experimental data were performed by using the software package (Statistica 6.0, Statsoft Inc., Tulsa, OK). The determination of coefficient (R2) is one of the primary criteria for selecting the best model to define the drying curves. In addition to R2, reduced chi-square (v2) and root mean square error (RMSE) are used to determine the quality of the fit. These parameters can be calculated by using the following equations: N P 2

v ¼

ðMRexp;i  MRpre;i Þ2

i¼1

" RMSE ¼

ð3Þ

Nz N 1X ðMRpre;i  MRexp;i Þ2 N i¼1

#1=2 ð4Þ

In these equations, MRexp and MRpre are the experimental and predicted dimensionless moisture ratios; N is the number of observations; z is the number of constants. The best model was selected to have the highest R2 and the lowest v2 and RMSE [11,14,17,32,33]. 2.5. Determination of effective moisture diffusivity The effective moisture diffusivity is an important transport property in food and other materials drying processes modeling, being a function of temperature and moisture content in material [24]. Fick’s second law of diffusion equation, symbolized as a mass-diffusion equation for drying agricultural products in a falling rate period, is shown in the following equation:

@M ¼ Deff r2 M @t

ð5Þ

The solution of diffusion equation Eq. (5) for slab geometry is solved by Crank [34], and supposed uniform initial moisture distribution, negligible external resistance, constant diffusivity and negligible shrinkage:

2

 2      3 p Deff t p2 Deff t p2 Deff t 1 1 þ þ þ exp  exp 9 exp 25 2 2 2 9 25 8 6 4L 4L 4L 7 MR ¼ 2 4   5 2D t p p eff 1 exp 49 4L2    49 ð6Þ

2.4. Mathematical modeling of drying curves 2

The moisture content of drying sample at time t can be transformed to be moisture ratio (MR):

MR ¼

Mt  Me M0  Me

ð1Þ

where Mt, M0 and Me are the moisture content at any time of drying, initial moisture content and equilibrium moisture content (kg water/kg dm), respectively. The equilibrium moisture contents of samples at different temperatures used in the drying runs were obtained by the dynamic model. About three grams of samples were exposed to 50, 60 and 70 °C air temperatures in the dryer until the weight loss of sample was ceased. Then, the equilibrium moisture

where Deff is the effective moisture diffusivity (m /s), t is the drying time (s), L is the half-thickness of samples (m) and n is a positive

Table 1 Thin-layer drying models applied to the persimmon slices drying curves. Model

Mathematical equation

Refs.

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

MR = exp(kt) MR = a exp(kt) MR ¼ a expðktÞ þ c MR = exp (ktn) n MR ¼ a expðkt Þ þ bt MR ¼ expððbt Þa Þ

[22] [23] [6,17,24] [25–27] [11,28–30] [31]

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integer. For long drying time, the Eq. (6) can be simplified as Eq. (7) by taking the first term of series solution and expressed in a logarithmic form [35]:



8



p2

 

p2 Deff t



4L2

ð7Þ

From Eq. (7), a plot of ln MR versus drying time gave a straight line with a slope (K) of:

K¼

p2 Deff

ð8Þ

4L2

2.6. Computation of activation energy

3.2 CONTROL; 50°C BLANCH; 50°C CONTROL; 60°C BLANCH; 60°C CONTROL; 70°C BLANCH; 70°C

2.8

Moisture content (kg water/kg dm)

ln MR ¼ ln

201

2.4 2.0 1.6 1.2 0.8 0.4

The dependence of the effective diffusivity on temperature is generally described by the Arrhenius equation Eq. (9) [26,36]:

Deff

 ¼ D0 exp 

 Ea RðT þ 273:15Þ

0.0 0

100

200

300

400

500

Drying time (kg water/kg dm)

ð9Þ

Fig. 1. Drying curves of persimmon slices at different temperatures.

Here D0 is the pre-exponential factor of Arrhenius equation in m2/s, Ea is the activation energy in kJ/mol, R is the universal gas constant in kJ/mol K, and T is the drying air temperature in °C.

0.032

CONTROL; 50°C BLANCH; 50°C CONTROL; 60°C BLANCH; 60°C CONTROL; 70°C BLANCH; 70°C

Rehydration of dried persimmon slices was performed in distilled water at 20 °C (±1 °C). About three grams of the dried product was added to 300 ml distilled water, in a 400 ml beaker. Weights of the samples were measured after 4 h. Subsequently, the samples were drained, blotted with tissue paper, and weighed. The rehydration ratio (RR) was calculated as follows:

RR ¼

Wr Wd

ð10Þ

where Wr is the weight rehydrated sample (kg), and Wd is the weight of dried sample (kg).

Drying rate (kg water/(kg dm*min)

0.028

2.7. Rehydration ratio

0.024 0.020 0.016 0.012 0.008 0.004 0.000 0.0

3. Results and discussions 3.1. Drying characteristics The characteristics of drying curves for control and blanched persimmon sliced to 5 mm thickness at 50, 60 and 70 °C are shown in Fig. 1. Fig. 2 shows the changes in drying rate as a function of moisture content at the same temperatures. It is clear that the moisture content and drying rate decrease continuously with drying time. The drying rate was rapid during the initial period but it became very slow at the last stages during the drying process. As shown in Fig. 2, there was no constant drying rate period, and the entire drying process occurred in the falling-rate period. This shows diffusion in dominant physical mechanism governing moisture movement in the samples. The results were generally in agreement with some of the literature on the drying of various food products [15,25,26,37,38]. According to the results in Fig. 1, the drying air temperature and blanching had a significant effect on the moisture content of the persimmon slices as expected. The results showed that drying time decreased greatly when drying temperature increased. The drying time required to reach the final moisture content of control samples were 450, 345 and 240 min at the drying air temperatures of 50, 60 and 70 °C, respectively. The decrease in drying time with an increase in the drying air temperature has been reported for many agricultural products such as orange slices [26], apple [35], strawberry [39], and carrot [40].

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

Moisture content (kg water/kg dm) Fig. 2. Variation of drying rate as a function of moisture content at various temperatures.

The blanching is very important parameter that affects the drying time. The blanched samples were found to have a shorter drying time compared to the control samples. The drying time required to reach final water content 20 ± 0.5% (w.b.) for blanched samples was 315, 285 and 180 min at 50, 60 and 70 °C, respectively. Corresponding values for control samples were 450, 345 and 240 min at the same respective temperatures. The drying time was reduced by about 21–42.8% for persimmon slices, as drying temperature was raised from 50 to 80 °C. Similar findings were reported in drying of various agricultural products [12,36,41]. Fig. 3 shows the effect of slice thickness on the moisture content variations at 60 °C. As expected, the total drying time increased with increasing slice thickness. For 60 °C, decreasing the slice thickness from 8 mm to 3 mm decreased the total drying time about 123.5%. Thinly products dried faster due to the reduced distance the moisture travels. The similar observation was found by Kaya et al. [19] for carrot slices and Lee and Hsieh [39] for strawberry leathers. 3.2. Fitting of drying curves The moisture content data obtained at different air temperatures were converted to dimensionless moisture ratio Eq. (1) and

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202

Table 3 Result of statistical analysis on the mathematical models for blanched samples.

3.5 d: 3 mm

Moisture content (kg water/kg dm)

3

d: 5 mm

T (°C)

Model

R2

v2

RMSE

d: 8 mm

50

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

0.9973 0.9986 0.9988 0.9993 0.9997 0.9993

0.00021 0.00011 0.00010 0.00006 0.00005 0.00006

0.04894 0.03535 0.03443 0.02716 0.01908 0.02716

60

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

0.9947 0.9971 0.9991 0.9991 0.9992 0.9991

0.00045 0.00025 0.00007 0.00001 0.00001 0.00001

0.07805 0.05369 0.02717 0.01004 0.01007 0.01004

70

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

0.9858 0.9902 0.9958 0.9993 0.9995 0.9994

0.00142 0.00106 0.00050 0.00007 0.00006 0.00007

0.11471 0.09673 0.06267 0.02267 0.02265 0.02270

2.5

2

1.5

1

0.5

0 0

100

200

300

400

500

600

Drying time (min) Fig. 3. Effect of slice thickness on moisture content of control samples during air drying at 60 °C.

3.3. Effective moisture diffusivity then fitted to six thin-layer drying models (Table 1). Non-linear regression analysis was used to estimate the parameters of those six models. The statistical results from models are summarized in Tables 2 and 3. The best model describing the thin-layer drying characteristics of persimmon slices was chosen as the one with the highest R2 values and the lowest v2 and RMSE values. The R2 values of Lewis, Henderson and Pabis, Logarithmic, Page, Midilli et al., and Weibull models were all above 0.98. The statistical parameter estimations showed that R2, v2 and RMSE values were ranged from 0.9823 to 0.9998, 0.00001 to 0.00158 and 0.01004 to 0.14242, respectively. Of all the models tested, the Midilli et al., Page and Weibull models give the highest values of R2 and the lowest values of v2 and RMSE. Generally R2, v2 and RMSE values of the selected models in all experiments were varied between 0.9983–0.9998, 0.00001–0.00013 and 0.01004–0.05519, respectively. Accordingly, the Midilli et al., Page and Weibull models were selected as the suitable models to represent the thin layer drying characteristics of persimmon slices. Figs. 4–6 compare experimental data with those predicted with the Midilli et al., Page and Weibull models for persimmon slices at 50, 60 and 70 °C. The prediction using the models showed MR values banded along a straight line, which showed the suitability of these models in describing the drying characteristics of persimmon slices.

The values of the effective moisture diffusivity were calculated using Eq. (8) and are shown in Fig. 7. The Deff values were varied in the range of 7.05  1011 m2/s to 2.34  1010 m2/s. It was noted that Deff values increased greatly with increasing drying temperature. When samples were dried at higher temperature, increased heating energy would increase the activity of water molecules leading to higher moisture diffusivity [36]. Furthermore, the values of effective moisture diffusivity of blanched samples were higher than those of control samples at all drying temperatures. This may be due to the fact that the blanching pretreatment considered in this study aids water movement to the persimmon surface for subsequent evaporation thus increasing the value of the effective moisture coefficients. The values of Deff obtained from this study lie within in general range 1012–108 m2/s for drying of food materials [42]. The values of Deff are comparable with the reported values of 2.27–4.97  1010 m2/s for the drying of apples in the temperature range of 40–60 °C [12], 3.32 to 90.0  1010 m2/s for berberis fruits at 50–70 °C [16], 6.27 to 35.0  1010 m2/s for orange slices at 40–80 °C [26], 2.40 to 12.1  109 m2/s for strawberry leathers at 50–80 °C [39], 1.19 to 4.27  109 m2/s for

1.0 50°C; CONTROL 50°C; BLANCH 60°C; CONTROL 60°C; BLANCH 70°C; CONTROL 70°C; BLANCH

Table 2 Result of statistical analysis on the mathematical models for control samples. Model

R2

v2

RMSE

50

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

0.9965 0.9972 0.9978 0.9983 0.9984 0.9983

0.00027 0.00022 0.00018 0.00013 0.00013 0.00013

0.07643 0.06856 0.06180 0.05519 0.05446 0.05519

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

0.9986 0.9993 0.9996 0.9997 0.9998 0.9997

0.00010 0.00005 0.00003 0.00002 0.00002 0.00002

0.03461 0.02160 0.01927 0.01829 0.01831 0.01829

Lewis Henderson and Pabis Logarithmic Page Midilli et al. Weibull

0.9823 0.9890 0.9960 0.9993 0.9994 0.9993

0.00158 0.00110 0.00040 0.00006 0.00006 0.00006

0.14242 0.11317 0.06615 0.02641 0.02593 0.02641

60

70

0.8

Predicted MR

T (°C)

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Experimental MR Fig. 4. Comparison of experimental and predicted moisture ratio by the Midilli et al. model.

_ Doymaz / Energy Conversion and Management 56 (2012) 199–205 I.

3.4. Activation energy

1.0 50°C; CONTROL 50°C; BLANCH 60°C; CONTROL 60°C; BLANCH 70°C; CONTROL 70°C; BLANCH

Predicted MR

0.8

The activation energy can be determined from the slope of Arrhenius plot, ln Deff versus 1/(T + 273.15) Eq. (9). The ln Deff as a function of the reciprocal of absolute temperature was plotted in Fig. 8. The slope of the line is (Ea/R) and the intercept equals to ln (D0). The results show a linear relationship due to Arrhenius type dependence. Eqs. (11) and (12) show the effect of temperature on Deff of samples with the following coefficients: For control samples:

0.6

0.4

 Deff ¼ 6:764  104 exp 

0.2

 5203:5 ðR2 : 0:9904Þ ðT þ 273:15Þ

ð11Þ

 3685:9 ðR2 : 0:9624Þ ðT þ 273:15Þ

ð12Þ

For blanched samples:

 Deff ¼ 1:042  105 exp 

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Experimental MR Fig. 5. Comparison of experimental and predicted moisture ratio by the Page model.

1.0 50°C; CONTROL 50°C; BLANCH 60°C; CONTROL 60°C; BLANCH 70°C; CONTROL 70°C; BLANCH

0.8

Predicted MR

203

3.5. Effect of blanching on rehydration ratio

0.6

0.4

0.2

0.0 0.0

0.2

The values of Deff for blanched and control samples found as 30.64 and 43.26 kJ/mol, respectively. These values are similar to those proposed in the literature by several authors for different fruits and vegetables such as 22.66–30.92 kJ/mol in apples [14], 25.26– 72.47 kJ/mol in yams [15], 67.29 kJ/mol in seedless grapes [36] and 30.46–35.57 kJ/mol in strawberry [39]. The values of activation energy were within the general range of 12.7 to 110 kJ/mol for various food materials [42].

0.4

0.6

0.8

1.0

Experimental MR

Rehydration is widely used as a parameter for dried sample quality. It indicates the physical and chemical changes during drying as influenced by processing conditions, sample pretreatment and composition [45]. Rehydration ratio values of persimmon slices at a constant rehydration temperature of 20 °C, calculated from Eq. (10), are shown in Fig. 9. Rehydration ratios of the blanched samples were higher than those of control samples at all drying temperatures, which means that structural damage and cell shrinkage occurred less during drying process. This factor adversely influenced the rehydration of blanched persimmons. The rehydration tests show that the rehydration ratios of dried blanched and control samples at 60 °C are higher than those of dried ones at other temperatures. An increase in temperature

Fig. 6. Comparison of experimental and predicted moisture ratio by the Weibull model.

-22 CONTROL BLANCH -22.4

2E-10 1.5E-10

2

R = 0.9624

ln (Deff )

D eff (m2 /s)

2.5E-10

1E-10 5E-11

-22.8

BLANCH

0 50

CONTROL

60 70

2

-23.2

R = 0.9904

-23.6 0.0029

0.0030

Air temperature (°C) Fig. 7. Variation of effective moisture diffusivity with air drying temperature.

pumpkin at 40–80 °C [43], and 2.60–5.40  1010 m2/s for persimmon slices at 50–80 °C [44]. These values are consistent with the present estimated Deff values for persimmon slices.

0.0031

1/(T+273.15) (1/K) Fig. 8. Arrhenius-type relationship between effective moisture diffusivity and reciprocal absolute temperature.

_ Doymaz / Energy Conversion and Management 56 (2012) 199–205 I.

204

4 CONTROL BLANCH

Rehydration ratio

3

2

1

0

50

60

70

Drying temperature (°C) Fig. 9. Rehydration curves for persimmon slices dried at 50, 60 and 70 °C.

above 60 °C had an adverse effect on the final rehydration ratio value, which decreased with increasing temperature. This may be indicative of a change in the product induced by temperature and perhaps a loss of solids during rehydration process. Similar results have been reported by Cunningham et al. [46]. 4. Conclusions Based on the experimental results reported herein, following conclusions can be made: a) Blanched samples had shorter drying times than the control samples. The drying time shortened with increasing drying temperature. b) Generally, the rehydration ratio of the blanched samples was higher than the control samples. c) Constant drying rate period was not observed, the drying process took place in the falling-rate period. d) The Midilli et al., Page and Weibull models gave the best representation of drying data under all experimental conditions. e) The effective moisture diffusivity was computed from Fick’s second law, the values of which varied between 7.05  1011 and 2.34  1010 m2/s, over the temperature range. f) The values of activation energy of blanched and control samples were found to be 30.64 kJ/mol and 43.26 kJ/mol, respectively.

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