Diffusion boundary layer theory

When we consider the flow of fluid over a surface, our boundary condition at the surface (no slip - surface velocity is zero) results in the formation of a thin layer of fluid in which the velocity increases rapidly from zero at the surface to a value comparable to the bulk velocity far from the surface. Drawing a parallel to this, when we consider diffusion between a flowing liquid and a surface, the effect of fixing a boundary condition at that surface is the creation of a thin boundary layer, where the concentration changes rapidly, so as to satisfy both the boundary condition at the surface, and match the bulk concentration far from the surface. Since diffusion is (generally) a much slower process than convection, the diffusion boundary layer is much thinner than the convective boundary layer. In this talk I will briefly discuss some of the history of diffusion boundary layer theory, and then show how we can use the theory to solve the convection-diffusion equation for some geometries of laminar flow. Finally, I will discuss how these solutions can lead to (perhaps unexpected) geometry-dependence in the particle flux to the boundaries.