It would be convenient to study the effects of changes in operating conditions on solid-solid separations within a free-settling-type device with a mathematical model that takes into account the changes in the physics of the separation process. One such model, the unsteady-state pulp-partition (USPP) model, based on a convection-diffusion equation, can be used to generate fractional recovery values. These values give the fraction of or probability that a given size feed material of known density will report to the product stream. Furthermore, curves generated from these values can be described by certain characteristic operating parameters — the density of separation and the mean probable error. By examining the variation of these characteristic parameters with systematic changes in the model variables such as the separation time, separation efficiency changes can be investigated.