Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations,including concentration effects

A theory for the rheological behavior and fluid flux in swelling tissues under small deformations is presented. Tissues are considered as bicomponent solid-fluid mixtures. Concentration effects are included. The driving forces (body, surface and interactive), are discussed and their constitutive relationships to the tissue’s deformation are specified. Mass and momentum balance equations are developed for each component and for the tissue as a whole. The concept of swelling stress emerges from the theory as an anisotropic generalization of the commonly used swelling pressure. It is shown to be a measure of the total chemical potential combining both mechanical and concentration effects. The theory shows that concentration effects modify the tissue’s bulk stiffness in a manner consistent with experimental observations.