(282a) The Effects of Brownian Motion On Particle Interactions with Patchy Surfaces Bearing Nanoscale Features

The effects of Brownian motion have been included in numerous computational studies of colloidal systems.  In particle deposition and particle tracking models, for example, stochastic Langevin equations have been used to compute particle trajectories and the deposition of particles on a collector.  Brownian motion is typically critical to the dynamics for homogeneous collectors, as it enables particle deposition even in the presence of an energy barrier.  In systems with charge heterogeneity, interesting dynamics can occur even with deterministic particle trajectories, and it is of interest to consider the significance of Brownian motion in these systems. 

For example, it was found in a recent study on the motion of blood platelets in the vicinity of a flat surface that the platelets’ motility and ability to reach the surface are only minimally affected by Brownian motion.  Furthermore, Brownian motion was found to have a weak influence on the bond-dissociation dynamics governing the receptor-ligand interactions between the platelets and surface.  For systems with low energy barriers, however, Brownian motion could significantly increase particle deposition rates. 

The focus of the present computational study is on the effect of Brownian motion on colloidal systems composed of particles of varying sizes (0.1 ≤ a ≤ 1, where a is the particle radius, in microns) translating over heterogeneous collectors comprised of cationic patches of O(10 nm) deposited on silica surfaces.  The patches are randomly arranged and are taken to be flat or to protrude slightly from the underlying surface to vary the influence of the repulsive background field.  The negatively-charged particles move under the influence of shear forces and torques, DLVO interactions with the patchy collector, and Brownian motion.   The heterogeneous collector is net repulsive, with the patches covering only about 10% of the surface, but local “hot-spots” created by a sufficiently high concentration of patches can adhere particles and induce dynamic adhesion behavior reminiscent of biological systems.

The computational results are obtained by implementing the grid-surface integration (GSI) technique to calculate the colloidal interactions between the particle and patchy collector. The GSI is coupled to a mobility tensor formulation of the hydrodynamics to yield the instantaneous translational and rotational velocities of the particle.  Two commonly-used models of Brownian interactions are compared: In one model, stochastic Brownian forces are included directly in the mobility tensor formulation.  In the second model, stochastic Brownian displacements are added to the particle trajectories.  The results of computations based on each model are compared to the case where Brownian motion is not included in the calculations, with an emphasis on adhesion thresholds determined by the average patch density on the collector required to adhere colloidal particles.  The relative importance of shear, colloidal, and Brownian effects is evaluated through the computation of appropriate Peclet numbers, some of which are unique for this heterogeneous system.