Thin Layer Drying Kinetics of Solar-Dried Amaranthus hybridus and Xanthosoma sagittifolium Leaves

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Introduction
Leafy vegetables have gained commercial importance and form an essential part of the Ghanaian diet, providing vitamins and micronutrients. As a result of their high moisture and short shelf life, there is the need to process them into stabilized forms with controlled water activity [1] that can store for longer periods [2] so that they will be available all year round [3]. Drying presents one of the most effective methods of food preservation. The process broadly describes the thermal removal of moisture from a product to yield a solid product [4]. It is a dual process of heat transfer to the product from the heating source and the mass transfer of moisture from the interior of the product to its surface and from the surface to the surrounding environment [5] and therefore the rate at which drying proceeds depends primarily on the rate at which these two processes proceed [4].
Drying method and the physical and biochemical changes that occur during drying seem to affect the quality properties of the dehydrated product. The proper handling of these reactions ensures that the dried product has a high nutritional value as well as a significantly extended shelf life. It is, therefore, essential to model and study the drying characteristics of food products in order to predict the suitable drying conditions as part of process control [6] and in the design and manufacture of dryers.
The study aimed at observing the drying characteristics of solardried Amaranthus spp and Xanthosoma spp leaves in thin layers using five analytical models in order to ascertain the model which best describes these drying characteristics.

Drying experiments
Fresh fully mature and edible Amaranthus spp (months) and Xanthosoma spp leaves were obtained from the Centre for Biodiversity Utilisation and Development (CBUD) farms at the Amanfrom Prison Camp in Kumasi. The leaves were detached from their stalks and inedible parts removed. The leaves were washed and trimmed into thin strips of dimension (0.3×3 cm) spread evenly on drying trays and loaded into a solar cabinet dryer (made of wood with glass windows, schematic in Figure 1 at a density of 1.5 kg/m 2 , in a single layer of 5 mm. Moisture loss during drying was determined by measuring the loss in weight of samples at hourly interval and at the beginning and end of drying and the representative samples are then taken for moisture content determination [7]. The leaves, with initial moisture (wb) content 85.8% and 82.7%, were dried to a final moisture content of 8.5% and 8.9% for Amaranthus spp and Xanthosoma spp leaves respectively. Average drying temperatures over the period of drying in the dryers were 49.8°C (RH 31.3%) and 48.7°C (RH 32.8) (Thermo hygrometer, Hanna HI 91610) for Amaranthus spp and Xanthosoma spp respectively. In *Corresponding author: P.T. Akonor, Food Processing and Engineering Division, CSIR -Food Research Institute, P. O. Box M30, Accra, Ghana, E-mail: papatoah@gmail.com order to reduce the incidence of moisture reabsorption, drying was discontinued at sundown (30.1°C, RH 47.5% and 30.8°C RH 46.3% for Amaranthus spp and Xanthosoma spp respectively) and the products were sealed air-tight in polypropylene bags overnight and drying continued the next morning (ambient 24.9°C, RH 69.8%).

Model fitting of drying data
Drying data was fitted to the Newton's, Page's, Modified Page, Handerson and Pabis and Logarithmic models by Non-linear Regression Analysis (STATGRAPHICS Centurion, 15.1) and coefficient of correlation and goodness of fit of predicted to experimental data determined. The moisture ratio was simplified as M/M o because the relative humidity of the inlet air could not be controlled and M e is very small as compared to M o . (Table 1) The reduced chi square was calculated as:

Effective moisture diffusivity
During drying, a general diffusion transport mechanism in which the rate of moisture movement is described by an effective diffusivity value, D eff is often assumed, regardless of which mechanism is really involved in moisture movement. In this approach, Fick's diffusion equation is used to explain the effective diffusivity. Parameters required in this approach are only sample dimensions and the effective diffusion coefficient. This method is very practical and convenient in describing moisture content change during processing. In using Fick's equation, the leaves used were assumed as slabs and all assumptions for slabshaped objects were proposed by [8] observed. The effective diffusivity was calculated by a linearised version [9][10][11].
( ) Where, D eff is the effective diffusivity (m 2 /s); L is half the thickness of the slab (m).

Drying curves
The drying curves for the two leafy vegetables show a sample heatup period where there is little or no drying. This may probably have been due to low temperatures at the beginning of the drying process, and not actually a sample heat-up period that characterises most drying processes.
The drying curves ( Figure 2) show an "elbowing" along the curve, which indicates the period between the discontinuation and resumption of drying. The curves show a very short constant rate period as is observed in the drying of most food products [12] and a longer falling rate period, a phenomenon characteristic of food products with water activity less than 1 [13]. This occurrence demonstrates that diffusion is the dominant physical mechanism governing the removal of moisture from the samples. Similar observations were made by [14] for green beans, [15] for red chilli and [16] for okra.

Mathematical modelling
The r 2 , RMSE and reduced chi square values for Amaranthus and Xanthosoma leaves for the chosen models are shown ( Table 1). The appropriateness of a model for describing the drying characteristics of samples was based on its r 2 , RMSE and reduced chi-square. The higher the r 2 values and lower the reduced X 2 and RMSE values, the better the goodness of fit [17][18][19][20][21] (Table 2).
All five models showed very good fit with r 2 greater than 0.9 ( Table  2). For the two samples studied, the Page model resulted in the highest r 2 values and corresponding least values for RMSE and reduced chisquare whilst the Newton and Modified Page's models gave the lowest r 2 and highest RMSE and reduced chi-square. The high r 2 for the Page model is an indication that it best describes the thin layer solar drying characteristics of the two leafy vegetables and fitted curve for the model is shown in Figure 3. Similar findings were detailed by [22] for [23],     [24] for thin layer drying of diced cassava roots, and [25] for garlic slices.

Effective moisture diffusivity calculation
A plot of ln (MR) against time t, gives a line with slope: The slope, effective diffusivity values (D eff ), the corresponding values of coefficients of determination r 2 and the reduced chi square (X 2 ) for the two indigenous leafy vegetables are presented (Table 3) (Figures 4 and 5).

Conclusion
The results show that the change in moisture ratio over time for solar drying the two leafy vegetables can be best described by the Page's model. Under similar drying conditions, the model is appropriate for simulating the outcome of drying these vegetables during process control. Effective Moisture Diffusivity ranged between 1.9x10 -9 m 2 s -1 and 2.1 x 10 -9 m 2 s -1 for the two leafy vegetables.   Table 3: Effective diffusivity, slope, reduced X 2 and co-efficient of determination for the leafy vegetables.