Settling Flux as a Function of Suspension Concentration

When a batch of solids in suspension are allowed to settle, say in a measuring cylinder in the laboratory, there is no net flow through the vessel and so 

In hindered settling under gravity the relative velocity between the particles and the fluid (Up - Uf) is Ureix- Thus using the expression for Ureix found in Equation (3.7), we have 

Combining Equation (3.19) with Equation (3.18) gives the following expression for Up, the hindered settling velocity of particles relative to the vessel wall in batch settling  

Richardson and Zaki (1954) showed by experiment that for Rep 0.3 (under Stokes law conditions where drag is independent of fluid density). 

Khan and Richardson (1989) recommend the use of the following correlation for the value of exponent n over the entire range of Reynolds numbers  

---