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Shown is a sphere in Stokes flow, at very low Reynolds number. 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. . This is a typical situation in flows where the ...
Creeping flow past a falling sphere in a fluid (e.g., a droplet of fog falling through the air): streamlines, drag force F d and force by gravity F g. At terminal (or settling) velocity, the excess force F e due to the difference between the weight and buoyancy of the sphere (both caused by gravity [7]) is given by:
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.
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 ...
In the science of fluid flow, Stokes' paradox is the phenomenon that there can be no creeping flow of a fluid around a disk in two dimensions; or, equivalently, the fact there is no non-trivial steady-state solution for the Stokes equations around an infinitely long cylinder. This is opposed to the 3-dimensional case, where Stokes' method ...
The creeping flow results can be applied in order to study the settling of sediments near the ocean bottom and the fall of moisture drops in the atmosphere. The principle is also applied in the falling sphere viscometer, an experimental device used to measure the viscosity of highly viscous fluids, for example oil, paraffin, tar etc.
Streamlines around a sphere in axisymmetric Stokes flow.At terminal velocity the drag force F d balances the force F g propelling the object.. In fluid dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry.
Note there is no rate of strain on the sphere (no ) since the spheres are assumed to be rigid. Faxén's law is a correction to Stokes' law for the friction on spherical objects in a viscous fluid , valid where the object moves close to a wall of the container.