Stokes flow around a circular cylindrical post confined between two parallel plates

Abstract

A slow viscous flow around a circular cylindrical post confined between two parallel flat plates is analyzed. The solution is given in the form of a series each term of which satisfies the equations of motion and continuity as well as the no-slip condition on the plates. A number of arbitrary constants left open in the series can then be determined according to the no-slip condition at the surface of the cylinder. Numerical results are presented. The series is found to be adequate when the ratio of the distance between the plates and the diameter of the post is not much larger than unity. The coefficient of resistance of the flow decreases rapidly as the sheet-thickness-to-post-diameter ratio increases. It is shown that the series converges rapidly when the thickness ratio is small, so that an approximate solution consisting of the two leading terms of the series, gives a reasonable representation of the velocity field and a good approximation to the flow resistance.