Sedimentation of a Colloidal Monolayer Down an Inclined Plane

We study the driven collective dynamics of a colloidal monolayer sedimentating down an inclined plane. The action of the gravity force parallel to the bottom wall creates a flow around each colloid, and the hydrodynamic interactions among the colloids accelerate the sedimentation as the local density increases. This leads to the creation of a universal "triangular" inhomogeneous density profile, with a traveling density shock at the leading front moving in the downhill direction. Unlike density shocks in a colloidal monolayer driven by applied torques rather than forces [Phys. Rev. Fluids, 2(9):092301, 2017], the density front during sedimentation remains stable over long periods of time even though it develops a roughness on the order of tens of particle diameters. Through experimental measurements and particle-based computer simulations, we find that the Burgers equation can model the density profile along the sedimentation direction as a function of time remarkably well, with a modest improvement if the nonlinear conservation law accounts for the sub-linear dependence of the collective sedimentation velocity on density.