The Effects of Brownian Motion On Particle Interactions with Patchy Surfaces Bearing Nanoscale Features

The effects of Brownian motion on particle interactions with heterogeneous collectors are evaluated by adding stochastic Brownian displacements to the particle trajectories and comparing those trajectories to those where Brownian motion is not included. We define adhesion thresholds as the average patch density on the collector required to adhere colloidal particles and P\'{e}clet numbers that quantify the relative importance of colloidal, shear and Brownian effects. We show that Brownian motion has a negligible influence on particle trajectories over collectors patterned with nano-scale heterogeneity, the non-uniform distribution of which creates locally attractive and repulsive areas within the collector. High energy barriers in strong locally repulsive areas cannot be overcome by Brownian motion, such that particle deposition on patchy collectors is controlled by spatially varying DLVO interactions and not by Brownian motion. The overall adhesive behavior of the system remains unaffected by the introduction of Brownian motion effects in the simulations, and therefore, for particle sizes that are usually used in experiments of particle trajectories over nanoscale heterogeneous collectors, it is reasonable to neglect Brownian motion effects entirely.