LATERAL VELOCITY OF A SMALL SPHERE SEDIMENTING NEAR A CYLINDRICAL WALL

A simple formula is presented for the lateral velocity upsilon of a small sphere of radius r0 sedimenting with a velocity U in a viscous fluid at a distance l from a vertical cylindrical wall on the assumption that kappa = r0/l << 1, Re = Ul/upsilon << 1 and epsilon = l/r << 1. Here r is the radius of curvature at the nearest wall from the particle. We have upsilon = U = (3/32) kappa Re(1 + (1/4) epsilon + O (epsilon2)) for the normal velocity leaving off the wall, where epsilon should be negative if the wall is convex to the fluid.