Near-wall diffusion tensor of an axisymmetric colloidal particle

TL;DR

This paper derives explicit analytical formulas for the near-wall diffusion tensor of an axially symmetric colloidal particle, providing a simple approximation that improves upon previous numerical and theoretical models.

Contribution

The authors present new analytical expressions for the dominant correction to the bulk diffusion tensor of an axisymmetric colloid near a no-slip wall, including translation, rotation, and coupling effects.

Findings

Derived explicit formulas for diffusion corrections near a wall.

Provided simple polynomial-based angular dependence.

Validated approximation against previous numerical and theoretical results.

Abstract

Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple polynomials in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings.