The boundary layer structure of laminar plug-to-Poiseuille transitions mediated by a porous medium

We derive the canonical boundary layer structure for 2D plug flow transitioning to Poiseuille flow in two parallel channels connected via a porous medium, using the method of matched asymptotic expansions and validated through numerical simulations. Plug flow enters through two long thin parallel 2D channels separated by a porous membrane wall, which we model using steady Navier-Stokes and Darcy flow equations, respectively. We investigate the flow behaviour in the boundary layer regions for all (laminar) Reynolds number regimes, providing insight into the laminar transition from plug to Poiseuille flow. We explore in detail the complex nested boundary layer structure that emerges in the high Reynolds number limit. We present generalised results for arbitrary Reynolds number and channel length, and systematically derive coupling conditions to match into the outer flow lubrication regions away from the channel inlets. Finally, we validate our asymptotic analysis with full numerical simulations using COMSOL Multiphysics.

Our asymptotic analysis is key to gaining a mechanistic understanding of the transitional behaviour and coupling of flow across a porous interface, and is applicable in a wide range of industrial applications including filtration and separation problems, tissue engineering and biofilm erosion.