Sedimentation of a Colloidal Monolayer Down an Inclined Plane

TL;DR

This study investigates the collective sedimentation behavior of a colloidal monolayer on an inclined plane, revealing a universal density profile and stable shock fronts modeled effectively by the Burgers equation.

Contribution

It demonstrates the formation of a stable density shock in sedimenting colloids and validates a Burgers equation model incorporating nonlinear velocity dependence.

Findings

Universal triangular density profile observed

Stable density shock persists over time

Burgers equation accurately models density evolution

Abstract

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.