We consider transport of neutral species interacting under a potential of mean force with randomly placed, rigid spherical obstacles. Generally, this kind of transport problems are studied as so-called perforated domain problems, where one imposes no-flux or reaction boundary conditions on the pore walls forming the interface between the pore and the solid phase. Here, we advocate a general framework that replaces the perforated domain formulation with interaction energies as well as with characteristic and scale-dependent randomness of materials. Our framework provides both well-posed effective macroscopic equations for highly heterogeneous situations and a full scale description for weakly heterogeneous materials for which we present first computational results.
- Hard-sphere potential
- Potential of mean force
- Random materials
- Smoluchowski equation
- Stochastic two-scale convergence in the mean