Impact of large periodic deformations on solute transport in soft porous media

Soft biological tissues can be modelled as highly deformable porous media, characterised by a strong coupling between mechanical stimulation and fluid flow due to complex rearrangements of the pore space. In the context of living-tissue biomechanics or tissue engineering, the effects of large periodic deformations on solute transport and mixing can be of particular interest for predicting and/or controlling the motion of nutrients or waste substances. Here, we propose a 1D continuum model based on large-deformation poroelasticiy that links an applied periodic deformation to the resulting solute transport and mixing. Transport occurs through advection, molecular diffusion, and hydrodynamic dispersion, all of which are affected by the periodic deformation in specific ways. We explore the effects of several dimensionless parameters on the problem, focusing on the ones regulating the applied periodic load. We find that the amplitude and period of deformation influence the mechanical response of the material, which can belong to either a linear slow-loading or a nonlinear fast-loading regime. These mechanical regimes directly characterise the resultant movements of solutes.