Hindered settling
In hindered settling, the velocity gradients around each particle are affected by the presence of nearby particles. So the normal drag correlations do not apply. Also, the particles in settling displace liquid, which flows upward and make the particle velocity relative to the fluid greater than the absolute settling velocity. For uniform suspension, the settling velocity us can be estimated from the terminal velocity for an isolated particle using the empirical equation of Maude and Whitmore
us = ut(e )n
Exponent n changes from about 4.6 in the Stokes’ law range to about 2.5 in the Newton’s law region. For very small particles, the calculated ratio us/ut is 0.62 for e =0.9 and 0.095 for e =0.6. With large particles, the corresponding ratios are us/ut = 0.77 and 0.28; the hindered settling effect is not as profound because the boundary layer thickness is a smaller fraction of the particle size.
If particles of a given size are falling through a suspension of much finer solids, the terminal velocity of the larger particles should be calculated using the density and viscosity of the fine suspension. The Maude-Whitmore equation may then be used to estimate the settling velocity with e taken as the volume fraction of the fine suspension, not the total void fraction.
Suspensions of very fine sand in water is used in separating coal from heavy minerals and the density of the suspension is adjusted to a value slightly greater than that of coal to make the coal particles rise to the surface, while the mineral particles sink to the bottom.