Calculation of particle deposition rate under unfavourable particle–surface interactions

When repulsive colloidal interactions are involved, calculating the rate of particle deposition becomes particularly difficult. To overcome the difficulty, a new (constant migration flux) boundary condition and a sophisticated numerical procedure are introduced. With these procedures, smooth solutions of the equation are obtained for the entire domain, including the region beyond the energy barrier adjacent to the collector surface. Numerical calculations demonstrate that the dependence of particle deposition rate on flow velocity is quite different from that reported previously. The difficulty of using the ‘perfect-sink’ boundary condition in numerical solutions and the inadequacy of previous numerical methods are discussed.