Fractional Calculus Method Applied To the Candying Of Apple Rings in Osmotic Drying Process

Abstract

Water and solid effective diffusivities and shrinkage were correlated for finite hollow cylinder-shaped apple samples during the candying operation in the osmotic solution. Experiments were conducted in the sucrose solution as an osmotic agent at different temperatures (i.e., 40, 50, and 60 °C) and at a constant concentration of 55 °Brix. The effective diffusivities of water and solid were calculated by fitting the water loss and solid uptake experimental data to Fick's second law and fractional calculus method, considering the shrinkage of the samples during the candying process. The obtained results exhibited that the volume of the apples reduced linearly by increasing the water loss. For above conditions of the candying process, water effective diffusivities with Fick second law were determined in the range of 3.7×10⁻¹⁰ m²/s–8.73×10⁻¹⁰ m²/s, and those with fractional calculus method were in the range of 2.75×10⁻¹⁰ m²/s–6.98×10⁻¹⁰ m²/s. The results indicated that the coefficient of determination for the fractional calculus method was more than the coefficient of determination for the Fick model. The value of the empirical parameter α for the Non-Fickian diffusion model was always higher than unity, meaning that the dehydration process had a super-diffusive mechanism<strong>.</strong> <strong> </strong>