Faxen Formula

Faxén's Law

In 1922 Faxén's introduced a relation for a sphere's velocity v to the forces and flows it experiences::$v\; =\; u(r)\; +\; b\_0\; F\; +\; frac\{a^2\}\{6\}\; abla^2\; u\; (r).$:where $b\_0$ is the mobility, $F$ is aforce acting on the sphere, $a$ the spheres radius and $r$ the spatial coordinate.In the case that the pressure gradient is small on the lengthscale of the sphere's diameter and where there is no externalforce, the last two terms may be neglected. In this casethe external fluid flow simply advects the sphere.

See also

* Immersed Boundary Method

References

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Kluwer, Dordrecht, 1991).