 Gravitational Peclet number

For a sphere of radius $a$ and buoyant density difference $\Delta \rho$, define ${\mathrm{Pe}}_g=v_{s}a/D=m_{b}ga/(k_{B}T)$ using radius as the transport length. With Stokes law and Stokes–Einstein diffusion, ${\mathrm{Pe}}_g=4\pi \Delta \rho g{a}^4/(3k_{B}T)$. Replacing radius by diameter changes the convention by a factor of two. This local criterion does not guarantee a uniform suspension over a macroscopic vessel.