Modelling of moisture content during baking of beetroot slices via Fick's law: A comparison of constant and variable effective diffusivity

Abstract

During baking of vegetables, water migration is governed by both internal and external diffusion mechanisms that define the baking kinetics. Accurately describing this process requires diffusion models capable of reflecting changes in effective diffusivity. The objective of this study was to model the mass transfer during the baking of beetroot slices with Fick's law of diffusion, using constant and variable effective diffusivity. Baking kinetics of beetroot slices were analysed at 110, 120, and 130 °C. The mass transfer coefficient, k_Y; critical and equilibrium moisture concentrations (C_c, C_∞) ranged from 1.91 to 2.10 kg water/m²sΔY, 4.22–5.36 kg water/kg d.s., and 0.10–0.11 kg water/kg d.s., respectively, indicating a faster water movement with temperature. Fick's law of diffusion was used to obtain the average moisture concentration, using the methods of slopes-by-subperiods (MSS) and successive approximations (MSA), considering a constant effective diffusivity, as well as a quadratic function of time (QFT) and Weibull distribution models, presuming a variable effective diffusivity. Diffusivity modelling showed that MSS is inadequate for accurately capturing moisture transfer during the falling-rate period. Its limited accuracy stems from the oversimplified assumption of constant diffusivity throughout the baking process of beetroot slices. In contrast, variable diffusivity models, including the QFT model and the Weibull distribution model, provided satisfactory fits to experimental data on average water concentration. These models contribute to a better understanding of water migration within the food, offering valuable insights into water mobility during food processing.