Statistically-based DLVO approach to the dynamic interaction of colloidal microparticles with topographically and chemically heterogeneous collectors.

Electrostatic surface heterogeneity on the order of a few nanometers is common in colloidal and bacterial systems, dominating adhesion and aggregation and inducing deviations from classical DLVO theory based on a uniform distribution of surface charge. Topographical heterogeneity and roughness also strongly influence adhesion. In this work, a model is introduced to quantify the spatial fluctuations in the interaction of microparticles in a flowing suspension with a wall aligned parallel to the flow. The wall contains nanoscale chemical and topographical heterogeneities ("patches") that are randomly distributed and produce localized attraction and repulsion. These attractive and repulsive regions induce fluctuations in the trajectories of the flowing particles that are critical to particle capture by the wall. The statistical distribution of patches is combined with mean-field DLVO calculations between a particle and two homogeneous surfaces: one with the surface potential of the patches and one with the potential of the underlying wall. These surface potentials could be obtained in experiments from zeta potential measurements for the bare wall and for one saturated with patches. This simple model reproduces the mean DLVO interaction force or energy vs. particle-wall separation distance, its variance, and particle adhesion thresholds from direct simulations of particle trajectories over patchy surfaces. The predictions of the model are consistent with experimental findings of significant microparticle deposition onto patchy, net-repulsive surfaces whose apparent zeta potential has the same sign as that of the particles. Deposition is significantly enhanced if the patches protrude even slightly from the surface. The model predictions are also in agreement with the observed variation of the adhesion threshold with the shear rate in published studies of dynamic microparticle adhesion on patchy surfaces.