In fluid dynamics, Faxén's laws relate a sphere's velocity
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[1][2] where It can also be written in the form where
In the case that the pressure gradient is small compared with the length scale of the sphere's diameter, and when there is no external force, the last two terms of this form may be neglected.
In this case the external fluid flow simply advects the sphere.
Faxen's second law is given by[1][2] where Batchelor and Green[3] derived an equation for the stresslet, given by[1][2] where Note there is no rate of strain on the sphere (no