Mechanistic Interpretation of Ethanol-Pretreatment-Enhanced Drying of Beetroot Through Coupled Diffusion–Shrinkage Modeling

Accurate prediction of moisture transfer during drying processes remains challenging. In the present study, a progressive numerical framework was developed to investigate moisture diffusion in ethanol-pretreated beetroot by systematically incorporating increasing levels of physical complexity into Fick’s second law of diffusion. Four one-dimensional formulations were examined, including constant moisture diffusivity, shrinkage under constant diffusivity, moisture-dependent effective diffusivity, and a fully coupled model combining moisture-dependent diffusivity with shrinkage. The methodology was further extended to two dimensions to evaluate the spatial evolution of moisture. The governing equations were solved using an implicit Crank–Nicolson finite difference scheme, while shrinkage was introduced through a time-dependent computational domain and moisture-dependent diffusivity was implemented as a variable transport property. The predicted moisture distributions demonstrated that incorporating shrinkage reduced the diffusion path length, whereas moisture-dependent diffusivity provided a more realistic representation of the transport resistance. The coupled formulation produced the most physically consistent description of moisture migration by simultaneously accounting for both mechanisms. Furthermore, the two-dimensional simulations provided additional insight into the spatial redistribution of moisture. The proposed framework establishes a physically based interpretation of the enhanced drying behavior observed after ethanol pretreatment and provides a flexible computational methodology for analyzing moisture transfer.