Creeping flow

(fluid mechanics) Fluid flow in which the velocity of flow is very small.

Fluid at very low Reynolds number. In the flow of fluids, a Reynolds number (density · length · velocity/viscosity) describes the relative importance of inertia effects to viscous effects. In creeping flow the Reynolds number is very small (less than 1) such that the inertia effects can be ignored in comparison to the viscous resistance. Creeping flow at zero Reynolds number is called Stokes flow.

Mathematically, viscous fluid flow is governed by the Navier-Stokes equation. In creeping flow the nonlinear momentum terms are unimportant, and the Navier-Stokes equation can be linearized. See also Fluid flow; Fluid mechanics; Navier-Stokes equation; Reynolds number; Viscosity.

Examples of creeping flow include very small objects moving in a fluid, such as the settling of dust particles and the swimming of microorganisms. Other examples include the flow of fluid (ground water or oil) through small channels or cracks, such as in hydrodynamic lubrication or the seepage in sand or rock formations. The flow of high-viscosity fluids may also be described by creeping flow, such as the extrusion of melts or the transport of paints, heavy oils, or food-processing materials.