Diffusiophoretic propulsion of an isotropic active colloidal particle near a finite-sized disk embedded in a planar fluid-fluid interface

TL;DR

This paper develops an analytical model to understand how isotropic active colloids move near a finite disk at a fluid interface, revealing conditions for attraction, repulsion, or stable hovering, aiding control of micro-scale swimmers.

Contribution

It introduces a far-field analytical approach to quantify phoretic velocities of isotropic colloids near finite disks at fluid interfaces, considering various physical parameters.

Findings

Particles can be attracted, repelled, or hover near the interface depending on parameters.

The model predicts stable hovering states for certain conditions.

Results can guide the manipulation of active colloids at interfaces.

Abstract

Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro-scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present manuscript, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circular shape resting on an interface separating two immiscible viscous incompressible Newtonian fluids. To this aim, the solution of the phoretic problem is formulated as a mixed-boundary-value problem which is subsequently transformed into a system of dual integral equations on the inner and outer domains. Depending on the ratio of different involved viscosities and solute solubilities, the sign of phoretic mobility and chemical activity, as well as the ratio of particle-interface distance to the radius of the disk, the isotropic active particle is found to be either repelled from the interface, attracted to it, or reach a stable hovering state and remains immobile near the interface. Our results may prove useful in controlling and guiding the motion of self-propelled phoretic active particles near aqueous interfaces.