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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. R e ≪ 1 {\displaystyle \mathrm {Re} \ll 1} .
Creeping flow past a falling sphere: streamlines, drag force F d and force by gravity F g. Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' law can be used to measure the viscosity of the fluid.
Laminar flow; No inertial effects (zero Reynolds number) Spherical particles; Homogeneous (uniform in composition) material; Smooth surfaces; Particles do not interfere with each other. Depending on desired accuracy, the failure to meet these assumptions may or may not require the use of a more complicated model.
If the Reynolds number is very small, much less than 1, then the fluid will exhibit Stokes, or creeping, flow, where the viscous forces of the fluid dominate the inertial forces. The specific calculation of the Reynolds number, and the values where laminar flow occurs, will depend on the geometry of the flow system and flow pattern.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
A reasonable assessment of whether the boundary layer will be laminar or turbulent can be made by calculating the Reynolds number of the local flow conditions. Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage, for example.
A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. [4]
The equation is only valid for creeping flow, i.e. in the slowest limit of laminar flow. The equation was derived by Kozeny (1927) [ 1 ] and Carman (1937, 1956) [ 2 ] [ 3 ] [ 4 ] from a starting point of (a) modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and (b ...