Effect of a moving boundary on the deformation of a poro-elastic cylinder

The deformation of a poro-elastic cylinder due to radial fluid flow is considered. This has application to modelling arterial flow and certain filtration processes. A diffusion equation for the dilatation with unusual integral boundary conditions is derived for two typical boundary conditions. Asymptotic solutions, to the linearised equations for small times, are found using Maple and shown to be remarkably accurate even for relatively large times. Since the position of the boundaries changes with time, the fully nonlinear system is solved numerically as a moving boundary value problem. Solutions for the dilatation and displacement are found and comparisons made between the standard linearised and full moving boundary problems with a nonlinear, strain dependent permeability. It is shown that inclusion of the correct position of the moving boundaries has a comparable effect to inclusion of a nonlinear permeability on the deformation of the cylinder