A study of the effect of boundary conditions and drag force on the diffusion of a Newtonian fluid through a non-linearly elastic solid

Abstract

In this work, we investigate the problem of diffusion of a Newtonian fluid through a non-linearly elastic solid undergoing large deformations, within the framework of mixture theory. The aim is to delineate the effect of various boundary conditions on the diffusion process while utilizing a suitable form for the drag force and the free energy of the mixture. Our investigation shows that the results are quite insensitive to the boundary conditions in that the predictions agree exceedingly well with the experiments (whether it is the saturation boundary condition used by Rajagopal, Wineman and Gandhi, the traction splitting boundary condition used by Rajagopal and Tao, the natural boundary condition used by Baek and Srinivasa, or the fact that the chemical potential is continuous across the boundary), provided that an appropriate choice is made for the drag.