Effective squirmer models for self-phoretic chemically active spherical colloids

TL;DR

This paper demonstrates how simple models of chemically active colloids can be effectively mapped onto hydrodynamic squirmers, highlighting the importance of chemical activity distribution and boundary effects on their collective behavior.

Contribution

It provides a detailed mapping of self-diffusiophoretic colloids onto squirmer models and shows the limitations of this analogy in multi-particle or confined scenarios.

Findings

Mapping of chemically active colloids onto squirmer models is effective in unbounded fluids.

Interactions with boundaries or other particles can qualitatively change colloid behavior.

Explicit consideration of chemical distribution is crucial for understanding collective dynamics.

Abstract

Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) -- as employed in many experimental studies -- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers [S. Michelin and E. Lauga, J. Fluid Mech. \textbf{747}, 572 (2014)]. Accordingly, intuitively appealing analogies of "pusher/puller/neutral" squirmers arise naturally. Within the framework of self-diffusiophoresis we illustrate the above mentioned mapping and the corresponding flows in an unbounded fluid for a number of choices of the activity function (i.e., the spatial distribution and the type of chemical reactions across the surface of the particle). We use the central collision of two active particles as a simple, paradigmatic case for demonstrating that in the presence of other particles or boundaries the behavior of chemically active colloids may be \textit{qualitatively} different, even in the far field, from the one exhibited by the corresponding "effective squirmer", obtained from the mapping in an unbounded fluid. This emphasizes that understanding the collective behavior and the dynamics under geometrical confinement of chemically active particles necessarily requires to explicitly account for the dependence of the hydrodynamic interactions on the distribution of chemical species resulting from the activity of the particles.