Simulation of Osmotic Dehydration of a Spherical Material Using Parabolic and Power-Law Approximation Methods

Abstract

In this article, one-dimensional transient moisture and solute diffusions in the spherical geometry during osmotic dehydration were modeled by exact analytical method and two approximate models. Approximate models have been developed based on a parabolic and power-law profile approximation for moisture and solute concentrations in the spatial direction. The proposed models were validated by experimental water loss and solid gain data obtained from osmotic dehydration of spherical cherry tomatoes in NaCl salt solution. Experiments were conducted at six combinations of two temperatures (30°C and 40°C) and three solution concentrations (10%, 18%, and 25% w/w). A two-parameter model was used to predict moisture loss and solute gain at equilibrium condition, and moisture and solute diffusivities were estimated by fitting the experimental moisture loss and solute gain data to the Fick's second law of diffusion. The values of mean relative errors for exact analytical, parabolic, and power-law approximation methods respect to the experimental data were estimated between 6.58% and 9.20%, 13.28% and 16.57%, and 5.39% and 7.60%, respectively. Although the parabolic approximation leads to simpler relations, the power-law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time.

Keywords:

• Approximation
• Cherry tomato
• Mass transfer
• Osmotic dehydration
• Parabolic
• Power law