Shape dependent phoretic propulsion of slender active particles

TL;DR

This paper provides a theoretical analysis of how the shape of slender active particles influences their self-propulsion velocity driven by surface chemical reactions, revealing shape-dependent propulsion efficiencies.

Contribution

It introduces a matched asymptotic expansion method to quantify how particle shape and surface properties affect self-phoretic propulsion at low Reynolds number.

Findings

Thin cylindrical swimmers with blunt ends are faster than prolate spheroids with the same aspect ratio.

Shape and surface curvature distribution significantly influence propulsion efficiency.

The analysis uncovers subtle effects of slenderness and slip layer width on swimmer behavior.

Abstract

We theoretically study the self-propulsion of a thin (slender) colloid driven by asymmetric chemical reactions on its surface at vanishing Reynolds number. Using the method of matched asymptotic expansions, we obtain the colloid self-propulsion velocity as a function of its shape and surface physico-chemical properties. The mechanics of self-phoresis for rod-like swimmers has a richer spectrum of behaviours than spherical swimmers due to the presence of two small length scales, the slenderness of the rod and the width of the slip layer. This leads to subtleties in taking the limit of vanishing slenderness. As a result, even for very thin rods, the distribution of curvature along the surface of the swimmer, namely its shape, plays a surprising role in determining the efficiency of propulsion. We find that thin cylindrical self-phoretic swimmers with blunt ends move faster than thin prolate spheroid shaped swimmers with the same aspect ratio.