Periodic blocking in parallel shear or channel flow at low Reynolds number

Abstract

The two-dimensional creeping flow disturbance due to a periodic array of wall-attached barriers in either a parallel shear flow or a channel flow is determined by the use of a distribution of force singularities on each barrier. In each case, the Fredholm integral equation of the first kind, obtained by requiring no normal flow at a barrier, can be transformed into an infinite linear system of the second kind, whose coefficients involve, at most, infinite sums of elementary functions. The computed physical quantities include the displacement of the unbounded shear flow, the induced pressure gradient in the other flows, the maximum velocity in the symmetric flow through pairs of barriers, and the slip length derived by using the Maxwell slip-flow approximation to model the effect of barriers on a wall.