Mathematical Modelling of a Nanoparticle Motion in a Membrane Pore under Action of Molecular Forces

A mathematical model is developed to describe microfiltration on membrane filters with plane-parallel and cylindrical pores. Consideration is given to two cases of motion of Brownian particles having a radius R comparable to the radius of the filter channel a. Relations are presented for the dependence of the efficiency of particle deposition on the channel walls on the parameter $${{ae }} = R{{a}^{{ - 1}}}$$ with different values of the molecular interaction constant and with allowance for the hydrodynamic factor. The results of modeling microfiltration on membrane filters with plane-parallel and cylindrical pores are compared. It is shown that there is a qualitative agreement between the main characteristics of the microfiltration process for these two types of membrane channel cross-section. It is established that the efficiency of purification on membrane filters with cylindrical pores is considerably more significant than the efficiency attained with plane-parallel pores.