Mass Transfer During Vacuum Frying of Eggplant Slices (Solanum melongena L.)

The objective of this research was to determinate the mass transfer and oil uptake parameters during vacuum frying of eggplant slices. The frying process was made in control and blanched samples at two temperatures (120 °C and 140 °C) and five frying times (0 s, 60 s, 120 s, 180 s, 240 s and 300 s). The calculation of moisture transfer coefficients was determined through mass diffusion differential equations. Moisture diffusion coefficients at 120 °C and 140 °C were 8.791 × 10 ms and 1.561 ×10 m s for control samples. Oil uptake kinetic parameters such as the specific absorption rate and equilibrium oil content were 0.080 s y 0.097 s for control samples at 120 °C and 0.0418 s y 0.048 s 1 at 140 °C. Keyword-Fick’s law, oil uptake, blanching, moisture, eggplant.

only when the steam output is reduced, the oil is transferred to the food, this depends on the permeability properties of the crust formed on the surface of the food [13], [14].
When the process ends, the food is removed from the oil and cooling begins, the vapour pressure decreases and a suction effect is produced, helping the oil deposited on the surface of the food to pass into the crust.Currently, the research that has been carried out in this vegetable, has been cooking [1], but it is important to note that in this food matrix has not been carried out research on the kinetic parameters of moisture and absorption of oil during the process of frying by vacuum immersion.In view of the above, the objective of this research was to determine the mass transfer coefficients of moisture and oil during vacuum frying of eggplant slices (S. melongena L.).

A. Raw Material
CriollaMorada variety eggplants (S. melongena L.)and palm oil were purchased at a local supermarket in the city of Cartagena de Indias. The eggplants were selected taking into account the size and not showing any damage by handling.The vegetable was washed and disinfected, then cut into flat leaf shape with dimensions of 0.025 × 0.003 × 0.05 m for further analysis.

B. Pretreatments
Once the vegetables were prepared, they were divided into two blocks; the first block was blanched in hot water for 2 min at 95°C in a 7 L capacity WNB (Germany) water bath, connected to a 220 V power supply and with dimensions of 240 × 210 × 140 mm, which had temperature control and digital time.Immediately afterwards the samples were cooled in water at room temperature for 20s to prevent softening. The second block was the control, which was not pre-treated.

C. Vacuum frying conditions
The eggplant slices were fried in a Gastrovac ® 167 (International Cooking Concepts, Barcelona, Spain) with the measures: 0.04×0.026×0.046 m, maximum capacity of 10.5 L and 220 V voltage [15].The maximum vacuum pressure applied to the equipment was 30 kPa. To define the temperature of the frying process, two deltas were used with respect to the boiling water temperature at 30 kPa: ΔT1 = 50°C and ΔT2 = 70°C. Therefore, the oil temperatures were 120°C and 140°C.The frying times were 0 s, 60 s, 120 s, 180 s, 240 s, and 300 s, established by preliminary tests. The ratio of the product/oil was 1:10 weight/volume. The oil was first heated to the desired temperature, samples of eggplant slices were placed in a stainless steel basket, the lid closed and the vacuum pump activated.When the equipment reached maximum pressure, the basket was immersed in hot oil. Once the set frying time had been achieved, the basket was raised and the pump was left on for one minute, then the vacuum broke and the equipment was turned off to remove the samples.The eggplant slices were placed in a wire mesh basket and placed at room temperature for five minutes and then analysed.

D. Moisture and oil analysis
The moisture content of the eggplant flakes was determined by drying at 105 ± 1 °C to constant weight [17], and the oil content was determined by Soxhlet extraction [16]. All trials were conducted in triplicate.

E. Determination of moisture transfer coefficients
Moisture content data based on frying time were used in a mathematical model to determine the moisture transfer coefficient.For this purpose, the equation of concentration as a function of time and position was used for an infinite 2L thick film, which is obtained by resolving the differential diffusion equation in transient state shown in equation (1), with the boundary and initial conditions expressed in Equation (2) as Yildizet al., [17] in potato frying, Alviset al., [18]in yam frying and Tirado et al., [5] in tilapia frying and breadfruit.
The following infinite series solution shows the concentration of moisture located at any point within the film as a function of time.
The reduced form of the Equation (3) can be used to obtain the solution for parallelepiped shaped sheets (finite in two dimensions), making use of the overlapping rule, according to which, the solution for the mass transfer of a 2-dimensional thin sheet is found by multiplying the solution for two infinite sheets, Equation (4), developed by Crank [19].
Where C (x, y, t) is the concentration of moisture at any point and at any time, (kg kg solids -1 ). Replacing in (4) for infinite plates of finite thickness in x and y, the Equation (5) and (6).
Taking only the first term of Equation (3) for calculations related to mass transfer, these equations were integrated across the entire volume, since mass transfer in general results were obtained experimentally across the entire volume rather than at a certain location and integrating it with respect to volume , , Equation (7). Where: Linearizing Equation (7), the Equation (9): By graphing ̅ , , vs.t, from the graph intercept the first root of the characteristic equation ( n ) was calculated using the Matlabfzero function. The coefficient of diffusion Da (m 2 s -1 ) was then determined from the slope of the linear section of this graph that equals 2 . Once found, Bi m was determined and then k c .
F. Oil uptake kinetics Empirical relationships are often used to describe the absorption of oil during frying. The relationship used in this study was described by Moyano and Pedreschi [11], using Equation (12).

(12)
Where O is the oil content in time t (free oil, on dry basis), O eq is the oil content in equilibrium (or maximum content) (free oil, on dry basis) at time t=∞, k represents the specific absorption rate for this model.The calculation of the activation energy was found to be dependent on the temperature dependency of moisture diffusivity using an Arrhenius equation.
Where D 0 represents the pre-exponential factor associated with the collision factor in terms of absolute reaction speed, E a is the activation energy (kJ mol -1 ), R is the constant of the perfect gases (8.31441 kJ kmol -1 K -1 ) and T is the temperature (K).

G. Statistical Analysis
A completely randomized 5 × 2 2 factorial design was performed, with three independent factors, including two levels (control and blanching), temperature (120°C and 140°C), and five time levels (0,60,120,180,240, and 300s).For data analysis, a variance analysis was performed using Statgraphics (Statgraphics Centurion Version 16.1.15, Chicago, EE. UU) [20]. The level of statistical significance used was 5%. All the experiments were conducted in triplicate. Fig. 1 and 2 show the dimensionless ratio of moisture concentration vs. time, obtained during vacuum eggplant frying. The slopes of the linear sections of these graphs were obtained by means of linear regression analysis. The rate of water loss was higher as the oil temperature increased.It is evident that the rate of moisture loss from the food increased with time and frying temperature. Once this was done, the number of biot used to determine the mass transfer coefficient was calculated.   Table 1 shows the diffusion coefficients, numbers of biot, mass transfer coefficients and activation energies. D a and k c increased with temperature for both treatments, as did activation energy.Soorgi et al., [21] reported effective diffusivity values for samples of chicken nuggets pre-treated with meticellulose immersion, ranging from 1.43 × 10-8 m 2 s -1 to 3.25 × 10 -8 m 2 s -1 . Adedejiet al., [22] reported values in the range of 6.39 × 10 -10 m 2 s -1 to 15.47 × 10 -10 m 2 s -1 for chicken nuggets, while Troncoso and Pedreschi [10] found values of 8.57 × 10 -9 m 2 s -1 to 2.95 × 10 -8 m 2 s -1 for fried potatoes. Also Amiryousefiet al., [23] reported effective diffusivity values ranging from 1.47 ×10 -8 to 4.17 × 10 -8 m 2 s -1 for frying meat plates.It is important to point out that vacuum frying could generate a significant hydrodynamic gradient that could affect the microstructure of the product, and consequently its physical-chemical and transport properties [10].Regarding activation energy, a range between 13.65 kJ mol -1 and 54.63 kJ mol -1 was presented by Adedejiet al., [22] for the diffusion of moisture in chicken nuggets. Troncoso and Pedreschi [10] reported this parameter between 23.5 kJ mol -1 and 29.3 kJ mol -1 for potato slices. Being close to those reported in this study.Amiryousefiet al., [23] found that the activation energy obtained by the Arrhenius equation for effective diffusivity against moisture ranged from 38.84 kJ mol -1 to 51.07 kJ mol -1 in fried ostrich meat.High activation energies are typically found in materials with low moisture content due to a strong substrate-water interaction [10]. In other words, as the activation energy increases, the more difficult it will be to remove water from the food.

III. RESULTS AND DISCUSSIONS
A. Oil transfer kinetics Table 2 shows the specific absorption rate and oil content in equilibrium. Certainly, the frying conditions, sample dimensions (especially thickness), product type, and pre-treatments are important parameters that determine the constant speed of oil absorption.In all the cases studied, the specific rate increased with frying temperature, but the O eq equilibrium oil content decreased. This behaviour can be explained by the fact that higher frying temperatures lead to higher oil absorption [24]. Adedeji et al., [22] reported velocity constant values in the range of 0.04-40.96 s-1 for coating fried chicken nugget empanadas at 170°C, 180°C and 190 °C. Amiryousefiet al., [23] reported values in the range of 0.024-19.708 s -1 for microwave fried pre-treated ostrich meat slices between 130°C and 160°C.Duran et al., [25] presented a range of values of 0.185-0.219 s -1 for potato chips between 120°C and 180°C, similar to those reported in this study. Fig. 3 shows the oil absorption kinetics of samples of control and blanched eggplants at different temperatures. It is illustrated that as the frying temperature increased independent of pretreatment and time, the oil gain was higher.However, with previous blanching the slices of eggplants showed a reduction in oil absorption of 23.21% and 14.51% with respect to the control at 120°C and 140°C, respectively. The oil absorption mechanism may be related to the capillary pressure difference and the interfacial tension between oil and water vapor within pores [24].Alvarez et al., [26] found that blanching at high temperatures and short times (e. g. 97 °C, 2 min) before frying potato strips resulted in a higher oil content than fresh strips, which is undesirable for consumer acceptance. However, some authors reported that low temperature blanching (e. g. between 55°C and 70°C) prior to frying activates the enzyme pectinesterase and the resulting reactions decrease porosity and therefore reduce oil absorption [7].On the other hand, at higher frying temperatures, oil absorption is generally reduced, as the process is shorter and the formation of the improved crust acts as a physical barrier to oil penetration [7]. The oil absorption rate constants depended on the main process variables such as oil temperature, product type, applied pre-treatment, type frying, product with and oil type [10], [23].

IV. CONCLUSIONS
The rate of moisture loss from the food was observed to have increased over time and at frying temperature. It was also illustrated that the diffusion and mass transfer coefficient increased as the temperature increased. On the other hand, regardless of the pre-treatment, oil absorption was increased at higher temperatures.Also for all cases studied, the specific absorption rate increased with frying temperature, however the Oeq equilibrium oil content decreased, and was lower in blanched samples.