Sedimentation length (${\ell }_g=k_{B}T/(m_{b}g)$)

For noninteracting particles with positive buoyant mass $m_b$ in a gravitational field, a dilute thermodynamic equilibrium profile is proportional to $e^{-z/{\ell }_g}$ with ${\ell }_g=k_{B}T/(m_{b}g)$. Uniformity over a vessel height $H$ requires $H\ll {\ell }_g$. Requiring only ${\ell }_g$ to exceed a particle radius is a weaker microscopic gravity-versus-diffusion condition.