Faxén's law

In fluid dynamics, Faxén's laws relate a sphere's velocity ${\displaystyle \mathbf {U} }$ and angular velocity ${\displaystyle \mathbf {\Omega } }$ to the forces, torque, stresslet and flow it experiences under low Reynolds number (creeping flow) conditions.

Faxen's first law was introduced in 1922 by Swedish physicist Hilding Faxén, who at the time was active at Uppsala University, and is given by

where

It can also be written in the form

where ${\displaystyle b_{0}=-{\frac {1}{6\pi \mu a}}}$ is the mobility.

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