First passage time approach to the kinetics of colloidal deposition onto permeable boundaries

Abstract The problem of colloidal deposition onto rigid membranes permeable to the suspending medium has been tackled, pursuing the first passage time approach. In the limit of complete permeability, the particle-membrane hydrodynamic interactions vanish, which considerably simplifies the problem. Unlike non-permeable surfaces where the particle transport from the bulk is mediated by a boundary layer, permeable surfaces cannot have such a layer in their vicinity. In treating the present problem, therefore, it is essential to take explicit account of the convective component of the particle flux in addition to the diffusive and the interactive components. We have been able to show that in situations where the convective potential, from which the flow field derives, is expressible as a simple function of distance normal to the absorbing boundary (i.e. the membrane), it is possible to solve the transport equation with all the three components of the flux present. Expressions for the first passage time corresponding to the deposition process have been derived in terms of a parameter, α, which specifies the relative significance of the diffusive and the convective contributions of particle motion to the deposition process. Three simple models have been considered: (a) particle confined between a pair of plane boundaries; (b) particle between cylindrical boundaries; and (c) particle between spherical boundaries. Numerical results are presented which elucidate the effect of the convective motion on the rate constant for particle deposition.