Diffusion of finite-size particles and application to porous media

Dr Maria Bruna (University of Oxford)

G.205, Alan Turing Building,

We discuss nonlinear Fokker-Planck models describing diffusion processes with particle interactions. These models are motivated by the study of many particle systems in biology, and arise as the population-level description of a stochastic particle-based model. In particular, we consider a system of impenetrable diffusing spheres and use the method of matched asymptotic expansions to obtain a systematic model reduction. In the second part of the talk, we discuss how this method can be used to derive an effective transport equation for diffusion in a disordered porous medium. A nice feature of this approach is that it can easily account for macroscopic gradients in porosity.
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