Modeling Effective Moisture Diffusivity of Orange Slice (Thompson Cv.)

Abstract

The present study was conducted to compute effective moisture diffusivity and activation energy of orange slices during convection drying. The thin-layer drying experiments were carried out at five air temperatures of 40, 50, 60, 70, and 80^ºC, three air velocities of 0.5, 1.0, and 2.0 m/s and three orange slice thicknesses of 2, 4, and 6 mm. Results indicated that drying took place in the falling rate period. Moisture transfer from orange slices was described by applying the Fick's diffusion model. The effective diffusivity values were increased from 6.27 × 10⁻¹⁰ to 3.50 × 10⁻⁹ m²/s for the temperature range used in this study. An Arrhenius relation with an activation energy value of 16.47 to 40.90 kJ/mol and the diffusivity constant value of 7.74 × 10⁻⁷ to 3.93 × 10⁻³ m²/s were obtained. It was found that with increasing the temperature and air velocity the effective diffusivity increases while slice thickness showed no considerable changes on the effective diffusivity.

Keywords:

• Orange
• Activation energy
• Thin layer
• Page model

INTRODUCTION

Drying, as a complex process involving heat and mass transfer phenomena and frEq.uently used in food processing industries,[1] is probably the main and the most expensive step in postharvest treatment. It improves the product shelf life without the addition of any chemical preservative and reduces both the size of package and transport costs. Mathematical modeling and simulation of drying curves under different conditions is important to obtain a better control of this unit operation and an overall improvement of the quality of the final product. Models are often used to study the variables involved in the process, predict drying kinetics of the product and to optimize the operating parameters and conditions.[2] Drying process of food materials mostly occurs in the falling rate period.[3] To predict the moisture transfer during the falling rate drying period, several mathematical models have been proposed using Fickian's diffusion, as shown in Eq. (1), as a basis to describe the moisture transport process.[4–10] Moisture transfer during drying is controlled by internal diffusion:[8]

where D is effective moisture diffusivity in m²/s; t is time in second; and M is moisture content of the product in kg water/kg dry solid. The effective moisture diffusivity is representing the conductive term of all moisture transfer mechanisms. This parameter is usually determined from experimental drying curves.[4,10] The diffusion coefficient of a food product is a material property and its value depends upon the conditions within the material.[11,12] Effective moisture diffusivity describes all possible mechanisms of moisture movement within the product, such as liquid diffusion, vapor diffusion, surface diffusion, capillary flow and hydrodynamic flow.[13,14] Moisture transport which involves diffusion of moisture in solid foods is a complex process. Temperature dependence of the effective diffusivity has been shown to follow an Arrhenius relationship:[9–17]

where D₀ is The diffusion constant, and the pre-exponential factor of the Arrhenius Equation in m²/s; Ea is the activation energy in kJ/mol; R is the universal gas constant in values 8.3145 kJ/mol K; and Ta is the absolute air temperature in K. The activation energy can be determined from the slope of the Arrhenius plot of ln (D) versus 1/T. The temperature used in the Arrhenius analysis is the ambient temperature of drying, thus assuming that the temperature of the material being dried is also that of the surrounding drying environment. Therefore, the isothermal assumption has been applied in both determining the effective diffusivity and the activation energy. Potatoes and carrots have shown to develop negligible porosity during drying,[18] and thus will be representative hygroscopic, non-porous materials. No published literature is available on effective diffusivity data for orange slices during drying. A knowledge of effective moisture diffusivity is necessary for designing and modeling mass transfer processes such as dehydration, adsorption and desorption of moisture during storage. The aim of this work was to determine the effective moisture diffusivity and activation energy of orange (Thompson variety) slices during drying process and its dependence on factors such as air temperature, air velocity and thickness of orange that essentially influence the drying rate.

MATERIAL AND METHODS

Orange slices were considered as an infinite slab because the thickness of the slice (2, 4 and 6 mm) was much less than its diameter (about 85 mm). The moisture diffusivity for an infinite slab was therefore calculated by Eq. (3) proposed by Crank (1975)[19] considering assumptions mentioned hereunder:[15,20] a) Moisture is initially distributed uniformly throughout the mass of a sample; b) Mass transfer is symmetric with respect to the center; c) Surface moisture content of the sample instantaneously reaches Eq.uilibrium with the condition of surrounding air; d) Resistance to the mass transfer at the surface is negligible compared to internal resistance of the sample; e) Mass transfer is by diffusion only; f) Diffusion coefficient is constant and shrinkage is negligible; and g) M_e is omitted due to high initial moisture content of juicy fruits[27]:

where MR is the moisture ratio; L is the thickness of slice (m); and n is a positive integer. Only the first term of Eq. (3) is used for long drying times: [16]

The slope (k₀) is calculated by plotting ln (MR) versus time according to Eq. (5):

Sample Preparation

In this research, a thin layer laboratory dryer is used which has recently been designed and built in the Department of Agricultural Machinery at University of Tehran. Schematic diagram of the dryer system is shown in Fig. 1. A portable, 0–15 m/s range digital anemometer (TESTO, 405-V1) was used to occasionally measure air flow velocity of air passing through the system. The airflow was adjusted by means of a variable speed blower. The heating system was consisted of four heating elements placed inside the duct. A simple control algorithm was used to control and adjust the drying tunnel temperature. The opening side on the right was used to load or unload the tunnel and to measure drying air velocity. The trays were supported by lightweight steel rods placed under the digital balance.[21] Measured variables were air temperature, air velocity, relative humidity (RH), and loss of sample mass during drying. Specifications regarding the measurement instruments including their rated accuracy are summarized in Table 1. After turning on the computer, fan, scale, elements and data acquisition system, the essential velocity for the fan was set. A manual TESTO 405-V1 model sensor was used to measure the velocity. The control software was implemented and the rEq.uired temperature for the experiment was adjusted. Experiments were carried out 30 minutes after the system was turned on to reach to its steady state condition. Then, the tray holding the samples was carefully put in the dryer.

Figure 1 Schematic diagram of the drying system for measurement of the thin-layer parameters of orange slices. 1. PC; 2. microcontroller; 3. digital balance; 4. fan; 5. heating elements; 6. duct and tunnel; 7. trays; 8. temperature sensor; 9. relative humidity sensor.

Table 1 Specifications of measurement instruments including their rated accuracy

Instrument	Model	Accuracy	Make
Digital balance	GF3000	± 0.02 g	A&D, Japan
T-sensor	LM35	± 1° C	NSC, USA
RH-sensor	Capacitive	± 3%	PHILIPS, UK
V-sensor	405-V1	± 3%	TESTO, UK

At first, a foreign Thompson orange (Novel) cultivar was selected. Being seedless makes the sliced product suitable for drying. Oranges were washed and sliced perpendicular to the major diameter in thicknesses of 2, 4, and 6 mm using a slicing machine. The uniform thickness of t ± 0.01 mm was prepared by adjusting the opening of the slicer with a vernier caliper having a least count of 0.01 mm. About 150 g of orange slices were weighed and uniformly spread in a tray and kept inside the dryer. The orange moisture content of 5.5–7.1 kg water/kg dry solid was obtained by drying the sample in an oven at 105°C for 24 h.

RESULTS AND DISCUSSION

Drying rates were calculated from the drying data by estimating the change in moisture content, which occurred in each consecutive time interval and was expressed as kg water/(kg dry matter hr). The variations of the drying rates as against moisture content are shown in Fig. 2. As shown in Fig. 2, since at the start of drying period, moisture accumulates on the slice surface and the surface temperature becomes low, part of the drying air energy is used to warm up the product surface instead of moisture removal. Getting warmed up, the drying rate of orange slices increased up to a certain level. Then, due to advancement of drying front and the corresponding lower diffusivity, a barrier to moisture transfer of inside layers is created. Therefore, the drying rate slows down as the moisture content is reduced.

Figure 2 Influence of temperature on drying rate of orange slices at five temperatures of

, 40°C,

, 50°C,

, 60°C,

, 70°C,

_, 80°C and air velocity of 2 m/s and slice thickness of 6mm.

The accelerated drying rates may be attributed to internal heat generation. The absence of a constant drying rate period may be due to the thin layer of product that did not provide a constant supply of water in the specified period of time. Also, some resistance to water movement may exist due to shrinkage of the product on the surface, which reduces the drying rate considerably. The relationship between the drying rate and the moisture content was obtained by regression analysis. For temperature 40°C and 50°C the relationship was found to be linear while for 60°C, 70°C and 80°C it was of the second degree polynomial form.

Table 2 illustrates the linear and nonlinear relationships between drying rate and moisture content obtained from regression analysis. The values for the coefficient of determination R² were in the range of 0.9891–0.9935. Results show that the thin layer drying of orange slices occurs entirely in the falling rate period. However, the drying rate appears to be slow and gradually receding for the low level of temperature and was observed to increase at higher levels (Fig. 2). An increase in drying rates with an increase in temperature has been reported in earlier studies by Pathare and Sharma[3] for onion slice, Akpinar et al.[22] for red pepper slice, Mohapatra and Rao[23] for parboiled wheat, Doymaz[24] for green bean, Madamba et al.[25] for garlic slice.

Table 2 Values of constants and coefficients of linear and nonlinear model for different temperatures

Temperature (ºC)	a	b	c	R^2
80 ^1	−0.0903	1.0889	−0.0459	0.9891
70 ^1	−0.0537	0.7368	0.0103	0.9938
60 ^1	−0.0485	0.7472	−0.2900	0.9898
50 ^2	0.2783	−0.0156		0.9935
40 ^2	0.2408	−0.0589		0.9926
^1DR = aM^2 + bM + c.
^2DR = bM + c^2.

The effective moisture diffusivity D was calculated using Eq. (5) and is shown in Table 3. The effective diffusivity values of dried samples at 40–80ºC were varied in the range of 6.27 × 10⁻¹⁰ to 3.50 × 10⁻⁹ m²/s. It can be seen that D values increased greatly with increasing temperature. Drying at 80ºC gave the highest D values. Effective diffusivity values for orange skin was reported as 0.81 × 10⁻¹⁰ to 5.11 × 10⁻⁹ m²/s in the temperature range of 30 to 90ºC by Garau et al.[26] Based on the independent variables thickness (TK), drying air temperature and air velocity, using the multivariate regression technique, the effective diffusivity with R² of 0.815 was estimated. A multiple regression Equation as a function of temperature, air velocity and sample thickness was found to be:

Table 3 Effective diffusivity of orange slice in different drying conditions

		Effective diffusivity (×10^−10 m^2/s)
Slice thickness (mm)	Drying air velocity (m/s)	40 °C	50 °C	60 °C	70 °C	80 °C
2	0.5	6.57	7.83	12.7	16.3	20.1
2	1.0	8.26	10.4	17.2	23.5	31.5
2	2.0	9.87	11.2	18.6	23.8	32.1
4	0.5	7.52	8.48	14.7	23.4	35.0
4	1.0	8.76	17.2	22.0	24.0	26.8
4	2.0	10.4	18.0	23.3	24.9	26.5
6	0.5	6.27	7.72	12.4	14.8	19.8
6	1.0	6.83	8.42	13.3	17.1	22.4
6	2.0	7.90	8.97	14.4	18.3	23.9

The relationship of the effective moisture diffusivity and temperature follows the Arrhenius Equation as shown by Eq. (2). The activation energy (E_a) and diffusion constant were determined from the slope of the Arrhenius plot, ln (D) vs 1/T, and given in Table 4. The ln (D) as a function of reciprocal of absolute temperature (T) is plotted in different conditions of drying in Fig. 3. Results show linear relationships except for Fig. 3e and f corresponding to air velocity of 1 and 2 m/s in 4 mm thickness. The activation energy of all samples was less than 41.00 kJ/mol, ranging from 16.47–40.90 kJ/mol, similar to values reported by several authors for different fruits and vegetables. For example, 36.40 kJ/mol in orange skin;[26] 32.94 kJ/mol, for untreated tomato;[27] and 24.70–28.40 kJ/mol in green peas. [17] Activation energy of orange slice showed slightly higher compared to carrots (16.00 kJ/mol)[28] and lower than red chilli drying (41.95 kJ/mol)[29] and okra (51.26 kJ/mol).[24] Using the regression method, one can estimate ln(D) by knowing 1/T with high R² of 0.9741 to 0.9881. As can be seen from Fig. 3, for 4-mm thickness and air velocities of 1 and 2 m/s, the relationship is second degree polynomial while for the rest it is linear.

Table 4 Diffusivity constant and activation energy for orange slice (Thompson) for different slice thinness's and air velocities

Thickness (mm)	Velocity (m/s)	Diffusion constant, D0 ((×10^-5 m^2/s)	Activation energy, Ea (kJ/mol)
2	0.5	1.69 × 10^−5	26.46
	1.0	1.72 × 10^−4	32.00
	2.0	6.71 × 10^−5	29.20
4	0.5	3.93 × 10^−3	40.90
	1.0	1.82 × 10^−6	18.98
	2.0	7.74 × 10^−7	16.47
6	0.5	1.82 × 10^−5	26.78
	1.0	3.31 × 10^−5	28.17
	2.0	2.59 × 10^−5	27.26

Figure 3 Arrhenius type relationship between effective diffusivity and temperature.

CONCLUSIONS

Effective moisture diffusivity increased with increase in drying air temperature. The highest effective diffusion was found to be 3.50 × 10⁻⁹ m²/s in air temperature, air velocity and slice thickness of 80ºC, 0.5 m/s, and 4 mm, respectively. The lowest effective diffusion was 6.27 × 10⁻¹⁰ m²/s in air temperature, air velocity and slice thickness of 40ºC, 0.5 m/s, and 6 mm, respectively. The highest activation energy value of orange slice was determined as 40.90 kJ/mol at slice thickness of 4 mm and drying air velocity of 0.5 m/s, and the lowest value was 16.47 kJ/mol at slice thickness of 4 mm and drying air velocity of 2 m/s. The diffusion constant value of orange slice was attained as 3.93 × 10⁻³ m²/s at the slice thickness of 4 mm and drying air velocity of 0.5 m/s and the lowest value was 7.74 × 10⁻⁷ m²/s at the slice thickness of 4 mm and drying air velocity of 2 m/s.

ACKNOWLEDGMENTS

This research was supported by Bio-systems engineering faculty of University of Tehran.