Flow at Low Reynolds Numbers

Situations where the Reynolds number is very low form a class of incompressible flows that have common physical events. Low-Reynolds-number flows can occur as parts of larger flow fields. Flow in a tube of any cross-section shape that has parallel streamlines is a special Stokes flow that in principal is valid at any Reynolds number. Depending on whether the flow is two or three-dimensional, external flows about objects have quite different behavior. In both instances the problem is a singular perturbation with the nonuniform region at infinity. In a three-dimensional flow, this causes no trouble, as the first-order solution is uniformly valid. On the other hand, two-dimensional problems are essentially singular and the far flow will introduce a Reynolds number effect into any uniformly valid solution.