Shear induced redistribution of fluid within a uniformly swollen nonlinear elastic cylinder

Abstract

The theory of mixtures is applied to the determination of equilibrium states of a solid-fluid mixture which is isolated from contact with a fluid bath. In the particular problem considered, a hollow rubber cylinder first undergoes unconstrained swelling in a fluid bath. The solid is homogeneously deformed to a larger cylindrical shape, the fluid is uniformly dispersed and the mixture is in a saturated equilibrium state. The mixture is then bonded to rigid impermeable membranes at its inner and outer surfaces. Rigid impermeable flat plates restrain motion at its ends. While the swollen length is held fixed, relative rotation of the membranes induces shear distortion in the rubber-fluid mixture. The resulting normal stresses cause a change in the mixture from its initial equilibrium state in which the system is homogeneously swollen but unsheared to a new equilibrium state in which there is radial variation of both the solid deformation and fluid density. A numerical example, using properties for a particular rubber-fluid mixture, shows that the volume of the mixture and the fluid density decrease near the inner wall of the cylinder and increase near the outer wall.