Aleksandar Donev, Courant Institute of Mathematical Sciences, New York University

Abstract: I will describe numerical methods to study the dynamics of suspensions of colloids sedimented above a bottom wall and driven by externally-applied forces (sedimentation) or torques (microrollers). The proximity of the boundary controls the collective dynamics of these active suspensions.

Recently a new instability has been observed experimentally and numerically: the fingering of a front of suspended microrollers near a floor. A continuum model shows that this instability is linear and that the size scale selection arises only from hydrodynamic interactions between the particles and the wall. From these fingers, long-lived compact motile structures, called 'critters', can be formed just with hydrodynamic interactions.

The presence of a nearby no-slip boundary strongly affects the structures emerging in sedimenting colloidal suspensions. The suspensions first forms a monolayer with a dense traveling front, which can be described using a simple one dimensional nonlocal PDE. The front then transitions into finger-like structures whose width depends on the particle size and height from the floor.