Particle-Wall Hydronamic Coupling in Multi-Particle Ensembles

Hydrodynamic coupling of colloidal particles to bounding surfaces significantly influences particle motion and the resulting properties of suspensions near surfaces. Such interactions are ubiquitous in many systems, including complex fluids, proteins and polymer suspensions. This work investigates the multi-body interactions of small ensembles of colloidal particles near a surface, at varying distances from the wall and interparticle separations. We use holographic blinking optical tweezers to trap and position n particles, where n>2, in a variety of configurations. The two-dimensional experimental diffusivity tensors of the ensembles are calculated from particle positions, determined by standard particle tracking algorithms. The particle-particle interactions in the bulk away from surfaces can be well approximated by using the Oseen tensor to derive diffusivities along normal modes. Close to the wall (2 < h/a < 75), the cluster behavior can be represented by considering two-particle interactions close to surface, following Blake's method of images to satisfy the no-slip boundary condition [1]. For ensembles very close to the surface (h/a < 1.2), the two-body solutions are insufficient to describe system dynamics. A full n-body solution using method of images is required to successfully capture the hydrodynamic effects introduced by a bounding surface.

[1] Blake, J. R. Prog. Colloid Polymer Sci., 70 (1971) 303.