Homogenization of solute transport in double porosity materials

We propose a novel model for the transport of solute in a vascularized 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 sharp length scale separation that exists between the scale where we can visibly and distinctly identify the connected fluid compartment and the poroelastic matrix, and the scale of 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 zeroth order contribution of pressures, velocities, solute concentration, and elastic displacements. It effectively accounts for the fluid and solute transport between the poroelastic matrix and a fluid network compartment. 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 vascularized tumors.