Drying viscoelastic materials: a non-Fickian approach

Abstract

In this paper, we study a system of partial differential equations defined in a moving domain. This system is defined by a heat equation and a diffusion equation for a concentration of non-Fickian type whose diffusion coefficient depends on the temperature, completed with suitable initial and boundary conditions. The non-Fickian mass flux is established considering the viscoelastic properties of the medium where the strain depends on the temperature and on the concentration. The initial boundary value problem (IBVP) analyzed can be used to describe the drying of viscoelastic materials where the internal structure offers a resistance to the movement of the moisture molecules and a consequent delay in the moisture removal. Due to heat transference into the materials and moisture removal, shrinkage of the medium occurs. The stability of the IBVP defined in a moving domain is analyzed and its qualitative behavior is numerically studied.

Generalized Diffusion–Relaxation Model for Solvent Sorption in Polymers

“…However, they neglected any relation between the flux and the gradient in chemical potential. This approach was further developed by Ferreira et al ,− with a series of marvelous works on the mathematical modeling for various application areas where anomalous sorption curves were observed like drying or drug release. ,, Different coefficients were required for describing the two fluxes, as the concentration gradient and stress gradient were superimposed to the total flux. The Fickian diffusion coefficient was used to relate the concentration gradient and flux, while a different proportionality constant was introduced for the stress gradient.…”

“…The first group of approaches comprises first-principles, thermodynamic-consistent models ,,,, developed to describe one particular anomalous-sorption behavior. A second group of approaches ,,, does model the coupled diffusion–relaxation behavior for particular anomalous-sorption behaviors. However, these approaches do not consider the interplay between polymer relaxation and gradients in solvent chemical potential.…”