Lateral Velocity of a Small Sphere Sedimenting near a Cylindrical Wall

抄録

A simple formula is presented for the lateral velocity v 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 κ=r₀⁄l<<1, Re=Ul⁄ν<<1 and ε=l⁄r<<1. Here r is the radius of curvature at the nearest wall from the particle. We have v=U=(3⁄32)κRe(1+(1⁄4)ε+O(ε²)) for the normal velocity leaving off the wall, where ε should be negative if the wall is convex to the fluid.