Effective interface laws for fluid flow and transport through reactive porous membranes

Abstract: We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is periodic in the tangential direction also with period $\varepsilon$. The fluid flow is described by an instationary Stokes system, properly scaled in the fluid part of the thin layer. The evolution of the solute concentrations is described by a reaction-diffusion-advection equation in the fluid part of the domain and a diffusion equation (allowing different scaling in the diffusion coefficients) in the solid part of the layer. At the microscopic fluid-solid interface inside the layer nonlinear reactions take place. This system is rigorously homogenized in the limit $\varepsilon \to 0$, based on weak and strong (two-scale) compactness results for the solutions. These are based on new embedding inequalities for thin perforated layers including coupling to bulk domains. In the limit, effective interface laws for flow and transport are derived at the interface separating the two bulk regions. These interface laws enable effective mass transport through the membrane, which is also an important feature from an application point of view. This is a joint work with Markus Gahn (Universität Heidelberg).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)