 Solution

The ordinary physics is Stokes settling velocity. For a generic isolated rigid sphere of radius $a$, particle mass density ${\rho }_p$ and surrounding-fluid mass density ${\rho }_f$, balance the buoyancy-corrected body force against Stokes law:Here $\eta$ is the dynamic viscosity. If the effective acceleration is approximately constant over the displacement and the terminal regime has been reached, $s=Ut$. In an actual centrifuge $g_{\mathrm{eff}}={\Omega }^{2}r$, so a sufficiently large radial change requires integrating $dr/dt\propto r$ instead of assuming constant $U$. This generic relation does not resolve the deferred biological application.