A numerical procedure is presented which allows one to predict the deposition rate of microparticles suspended in a liquid flow onto the confining walls. Particle transport: is nor only diffusive but also affected by hydrodynamically induced lift force and reduced particle mobility. An appropriate expression for the lift-induced migration is introduced into the numerical procedure. Its results agree quanititatively with previously published experimental data showing a significant effect of lift-induced particle transport. Based on the numerical results algebraic correlations are obtained, which enable to calculate the particle deposition rate in situations where lift forces and mobility reduction diminishes the particle deposition rate.