A moving boundary model for food isothermal drying and shrinkage. One-dimensional versus two-dimensional approaches

We investigate and quantify the error in the estimate of water diffusivity resulting from the adoption of one-dimensional (1-d) models to describe the drying process of thin discoidal or long-thin cylindrical samples. Numerical results obtained with the 1-d and the 2-d moving boundary models recently proposed by Adrover, Brasiello, and Ponso (2019a, 2019b) are compared for different sample aspect ratios. The overestimate error of 1-d model predictions of diffusivity falls below 5% for an aspect ratio radius-over-thickness R0/L0 > 10 for discoidal samples while, for cylindrical samples, the aspect ratio height-to-radius L0/R0 must be greater than 15 to get a similar level of accuracy. To overcome this issue we propose a modified 1-d model able to take into account water flux from lateral surfaces (usually neglected in a 1-d approach) thus reducing the overestimate error of water diffusivity below 2% even for low-intermediate values of the aspect ratio. The 1-d modified model is successfully applied to experimental data of convective drying of eggplant and chayote discoidal samples. Practical applications: End consumer is increasingly demanding for ever more standardized and high quality food products. To meet these requirements, food industries are challenged to refine process design and control tools in order to be able to take into account the variability of both food matrices and operating conditions. This objective cannot be reached without the help of mathematical models based on first principles as the one here discussed and applied to food drying. The comparison between one- and two–dimensional approaches and the resulting quantification of errors in the adoption of simpler one-dimensional models have a great practical interest for industrial applications as they provide reliable criteria to obtain good predictions even when the whole set of the needed experimental data are not available or too expensive. The developed method can be easily adopted to predict final food quality (moisture content, sample volume reduction, and deformation) and therefore to implement more refined control systems and to optimize process-operating conditions, thus saving experimental and processing costs.