Accumulating Particles at the Boundaries of a Laminar Flow

TL;DR

This paper analyzes how small particles accumulate at the boundaries of laminar flows in channels, considering forces, thermal fluctuations, and boundary conditions, revealing conditions for inhomogeneous particle distributions.

Contribution

It provides a detailed analysis of particle accumulation mechanisms in laminar flows, emphasizing the role of boundary conditions and forces for extended particles.

Findings

Uniform distribution for vanishing particle size

Conditions for particle accumulation and depletion

Boundary conditions critically influence particle distribution

Abstract

The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a Fokker-Planck equation for the particle density. It is shown that in the limit of vanishing particle size a uniform particle distribution is always approached in the long time limit. For extended spherical particles, conditions are specified that lead to inhomogeneous densities and consequently to particle accumulation and depletion. Hereby the boundary conditions for the particle density play a decisive role: The centers of spherical particles must keep the minimal distance of their radius from the fluid boundaries. The normal components of the forces acting on the sphere then may assume finite values which are diffusively transported into the bulk of the fluid.