Faxén's first law
= Faxén's first law
{c}
= Faxén relation
{c}
{synonym}
= Faxén translation law
{c}
{synonym}
For a sphere of radius $a$ in a slowly varying ambient Stokes flow $\mathbf u_\infty$, the translational force is
$$
\mathbf F=6\pi\mu a
\left[\mathbf U-\left(1+\frac{a^2}{6}\nabla^2\right)\mathbf u_\infty\right]
$$
evaluated at the sphere centre.