STRESS-RELAXATION BEHAVIOR OF DEFORMABLE POROUS SHELLS DURING PASSAGE OF POWER-LAW FLUIDS IN COMPRESSION

Abstract

Multiphasic deformation of the porous solids can be described using the low-viscosity fluid flow through the viscously deformable and permeable solid matrix. The purpose of the present paper is to develop a better understanding of the governing equations that have been derived for this purpose while considering two-phase flows. An insight into the stress-relaxation behavior of a deformable porous shell has been formulated during passage of power-law fluids, in compression. The fluid flow was considered outwardly directed during the act of loading at the deformable inner radius of the shell. The outer boundary was taken as a rigid mesh that offers negligible resistance during the passage of fluids. The governing dynamics were derived using the continuum mixture theory approach, whereas non-Newtonian flow behavior was incorporated in the governing equations using the power-law model. A coupled system of partial differential equations was derived for the porosity and solid deformation to consider the nonlinear interaction between the fluid and solid. In the case of transient problem, a numerical solution is computed along with an exact solution of a steady-state problem. The propagation of porosity of the shell is bounded by the viscosity; otherwise, fluid flow resists in the solid matrix. The viscous stresses cause more deformation in the radial geometry, when compared to the planer geometry. In this setting, an additional pressure gradient is required for the fluid flow around the obstacles. When viscous resistance is increased in the nonlinear governing models, porosity controls the solid matrix deformation.