Stokes flow

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,^[1] is a type of fluid flow where advective inertial forces are small compared with viscous forces.^[2] The Reynolds number is low, i.e. ${\displaystyle \mathrm {Re} \ll 1}$. This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.^[3] In technology, it occurs in paint, MEMS devices, and in the flow of viscous polymers generally.

The equations of motion for Stokes flow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be solved by a number of well-known methods for linear differential equations.^[4] The primary Green's function of Stokes flow is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives, other fundamental solutions can be obtained.^[5] The Stokeslet was first derived by Oseen in 1927, although it was not named as such until 1953 by Hancock.^[6] The closed-form fundamental solutions for the generalized unsteady Stokes and Oseen flows associated with arbitrary time-dependent translational and rotational motions have been derived for the Newtonian^[7] and micropolar^[8] fluids.