  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.
