Advection-diffusion past a strip. I: Normal incidence (Q2785748)

The authors investigate the concentration \(p(x,y)\) of particles driven by diffusion and drift. The motion is impeded by an impenetrable strip that is parallel to the \(z\)-axis. It is assumed that \(p\) satisfies the linear advection-diffusion equation with the condition of vanishing flux on the strip and \(p=1\) at infinity. By methods of asymptotic analysis the problem is solved for \(vL/D\gg 1\), \(v\) being the drift velocity, \(D\) the diffusion coefficient, and \(2L\) the strip width. It is found that \(p\) is large on the side of the strip facing the incident flow and small behind it, remaining nearly constant elsewhere.