Diffusion-Sedimentation Equilibrium Problem

Consider a colloidal dispersion of uniform-sized (diameter 100 nm) polystyrene latex particles (density = 1.05 g/mL) in water at 298K in a vessel (of uniform cross-section normal to gravity) of depth 5 cm. Initially, the particle concentration in the vessel is uniform at 10¹⁰ particles/cm3. The dispersion is permitted to reach diffusion-sedimentation equilibrium. Compute the particle concentration at the top and bottom of the vessel.