STOCHASTIC MODELING OF NON-LINEAR SIEVING KINETICS

The feed to a sieve is classified as oversize particles, undersize particles, and near mesh size particles. The sizes of the near mesh size particles vary around that of the sieve opening; the passage of these particles through the sieve effects the separation. A stochastic approach is employed for analyzing and modeling the sieving kinetics of the near mesh size particles, usually constituting the bulk of the material required to be separated. The master equation of the process is formulated based on probabilistic considerations, describing the passage of the particles in the presence of sieve blinding. However, an analytical solution cannot be obtained directly and hence a rational approximation technique, the system size expansion, is utilized to solve the master equation. This results in a system of non-linear, coupled, ordinary differential equations for the various statistical quantities characterizing the number of particles retained on the sieve and the number of blinded apertures. These equations are then solved numerically. From these general equations, specific cases as the first order kinetics law, applicable to the terminal stages of sieving, are easily obtained. In the absence of oversize particles, the process is described by a master equation which is solved directly, yielding an explicit analytical solution. The numerical solutions agree at least qualitatively with the available experimental observations