Insights on the Physics of Stokes Flow

Abstract

Some key concepts on the physics of Stokes (i.e., low Reynolds number) flow are introduced. Stokes flow presents many paradoxes, in particular in its 2D formulation. For example, in 2D the drag on a moving particle will always strongly depend on the boundary conditions, even if very faraway. Ultimately this emerges by the fact that Stokes flow is the end member case of Navier Stokes for infinitively fast vorticity diffusion. Fundamental solutions of Stokes flow (Stokeslet, Stresslet, Rotlets) allow writing the solution of a sphere and any other body as a combination of them. Einstein viscosity can be shown to result from the average for the contribution for a large number of spheres. For high packing the viscosity increases until, jamming.