Homogenization of solute transport in double porosity materials
- Pietro Mascheroni,
- Laura Miller,
- Raimondo Penta
Pietro Mascheroni
Boehringer Ingelheim Pharma GmbH & Co KG Biberach
Author ProfileLaura Miller
University of Glasgow School of Mathematics and Statistics
Author ProfileAbstract
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.