Faxén's first law

For a sphere of radius $a$ in a slowly varying ambient Stokes flow ${\mathbf{u}}_{\infty }$, the translational force isevaluated at the sphere centre.

For two equal, well-separated spheres, the Rotne--Prager cross-mobility through order $a^3/R^3$ is proportional to

A passing forced sphere advects a distant force-free sphere along a curved trajectory. Its longitudinal displacement can diverge logarithmically even when its transverse displacement approaches a finite value.