Numerical simulation of microchannel blockage by the random walk method

Abstract

The problem of blockage dynamics in the microchannel for small values of the initial solute concentration is investigated numerically using the random walk method. One of the most common reasons for clogged filters is the deposit of solute particles on the wall. To investigate this process theoretically we consider the drift of solid particles in the microchannel, which is filled with a viscous liquid. The model takes into account the random motion of the particles induced by diffusion. The attachment of the particles to the channel walls changes the form of the walls, which leads to a variation in the liquid flow. This complex flow generates the viscous stress on the curved channel walls and it may cause a particle detachment. The resulted evolution of the liquid flow, namely pressure field, stream function and vorticity, during blockage dynamics is obtained. To define the limits of validity for the most popular linear sorption model the dependences of the integral parameters (volume concentration of settled particles, flow rate, a width of channel gap) on the flow velocity and on initial particle concentration are analyzed. The validation of the linear sorption law is demonstrated for different initial concentrations.