Gravitational Peclet number
= Gravitational Peclet number
{title2=$\mathrm{Pe}_g$}
For a sphere of radius $a$ and buoyant density difference $\Delta\rho$, define $\mathrm{Pe}_g=v_sa/D=m_bga/(k_BT)$ using radius as the transport length. With <Stokes law> and Stokes–Einstein <diffusion>, $\mathrm{Pe}_g=4\pi\Delta\rho ga^4/(3k_BT)$. 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.