A Class of Moving Boundary Problems Arising in Drying Processes

Abstract

Various representations of equilibrium drying processes are presented in a coherent framework as a class of moving boundary value problems involving the hysteresis phenomenon. The class splits into two subclasses of problems, called here implicit models and jump models; individual problems are categorized as sorption models, wet and dry models, and hysteresis-jump models. The mathematical model for the evolution of moisture, humidity, temperature, and pressure consists of a strongly coupled system of quasilinear partial differential equations, which is parabolic in the physical domain, together with the associated jump conditions of the Rankine–Hugoniot type. Whereas previous work on these models dealt with the numerical results, the present study addresses the mathematical wellposedness of the problems. The wet and dry jump model for a slab is stated, in both the classical and the weak formulations. Some results on local existence and uniqueness are obtained by using existing theory and the embedding tec...