Abstract

We propose a novel model for the transport of solute in a vascularised poroelastic material. Our structure comprises a poroelastic matrix with an embedded connected fluid compartment and we consider a solute transported between the two subdomains. Due to the distinct scale separation between the scale where we can visibly see the connected fluid compartment separated from the poroelastic matrix and the overall material body. We apply the asymptotic homogenization technique to derive the new model. The latter consists of a macroscale system of PDEs involving the zero-th order contribution of pressures, velocities, solute concentration and elastic displacements. It effectively accounts for the fluid and solute transport between a poroelastic and fluid network compartments. The model coefficients are to be computed by solving the periodic cell differential problems arising from application of the asymptotic homogenization technique. This work paves the way in understanding mechanically-activated transport with a wide range of applications such as drug delivery in vascularised tumours.