Effective governing equations for dual porosity Darcy-Brinkman systems subjected to inhomogeneous body forces and their application to the lymph node

We derive the homogenized governing equations for a double porosity system where the fluid flow within the individual compartments is governed by the coupling between the Darcy and the Darcy-Brinkman equations at the microscale, and are subjected to inhomogeneous body forces. The homogenized macroscale results are obtained by means of the asymptotic homogenization technique and read as a double Darcy differential model with mass exchange between phases. The role of the microstructure is encoded in the effective hydraulic conductivities which are obtained by solving periodic cell problems whose properties are illustrated and compared. We conclude by solving the new model by means of a semi-analytical approach under the assumption of azimuthal axisymmetry to model the movement of fluid within a lymph node.