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Faxén's Law

The foundation for the analysis which follows is provided by Faxén's first law [58], introduced in 1922, which relates a sphere's velocity $ \vec v$ to the forces and flows it experiences:

$\displaystyle \vec v = \vec u(\vec r) + b_0 \vec F + \frac{a^2}{6} \, \nabla^2 \vec u (\vec r).$ (23)

If no external forces act on the sphere, and if pressure gradients are small over its diameter, then the last two terms on the right-hand side of Eq. (23) may be ignored. In this approximation, the sphere is simply advected by the external flow.

David G. Grier 2001-01-16