Analysis of Filtration Rate in Clarification Filtration of Power-Law Non-Newtonian Fluids–Solids Mixtures under Constant Pressure by Stochastic Model

Clarification filtration experiments are conducted under constant pressure, using a filter cloth and very dilute suspensions prepared by suspending diatomaceous earth in a power-law fluid comprising aqueous sodium polyacrylate. To analyze the clarification filtration process, a stochastic model that describes particle capture in a filtration process has been coupled with the conventional blocking filtration laws. Four types of blocking filtration equations are derived, including complete blocking, intermediate blocking, and standard blocking equations. The intermediate blocking law can be applied when the particle size is larger than the pore size or is almost the same as the pore size. In contrast, the standard blocking law can be applied when the particle size is considerably smaller than the pore size. In addition, the effects of the solid concentration in the feed suspension and of the applied filtration pressure on the clarification filtration characteristics are delineated.