Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

TL;DR

This paper develops a lubrication theory to analyze how small particles influence the near-wall dynamics of a large particle in a highly bidisperse colloidal suspension, revealing asymptotic behaviors of the resistance coefficient.

Contribution

The authors introduce a new lubrication theory that accounts for small particles' effects on a large particle near a wall, considering length-scale separation.

Findings

Resistance coefficient approaches that of a clear fluid at small gaps.

At very small gaps, the resistance coefficient matches the lubrication value with effective viscosity.

The theory captures the transition between different hydrodynamic regimes.

Abstract

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap $h_0$ between the large particle and the wall is assumed to be comparable to the diameter $2a$ of the smaller particles so there is a length-scale separation between the gap width $h_0$ and the radius of the large particle $b<<h_0$. We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations $h_0$, the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For $h_0<<a$, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.