Effect of operating parameters and membrane characteristics on the permeate rate and selectivity of ultra- and microfiltration membranes in the depth filtration model

The effect of transmembrane pressure, pore depth and initial radius, inlet concentration of suspended particles, and particle-collection efficiency of pore walls on the permeate rate and selectivity of ultraand microfiltration membranes with pores of the same radius operated under standard blocking conditions is studied using the previously developed depth filtration model, which takes into account the nonuniform capture of particles over the pore depth. It is shown that the variation of permeate rate and selectivity with time in standard blocking strongly depends on the studied parameters. Simple analytical formulas for calculating the membrane permeate rate and selectivity as well as the time at which the pore diameter reaches the cutoff value (time at which the transition to cake filtration takes place) are proposed. The formulas make it possible to find the values of the filter coefficient, which accounts for the particle-collection efficiency of membrane pore walls, and the cutoff pore diameter using the experimental curve of the membrane selectivity. It is demonstrated that the use of the classical Hermia standard blocking model for describing the experimental data on membrane permeate rate can lead to high errors, which are caused by its assumption on the uniform profile of the layer of particles caught inside the pore.