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

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 paper, 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 that 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 repelled from the interface, be attracted to it, or reach a stable hovering state and remain immobile near the interface. Our results may prove useful in controlling and guiding the motion of self-propelled phoretic active particles near aqueous interfaces.

Self-propulsion of an elliptical phoretic disk emitting solute uniformly

“…2023) have been investigated. One specific point that we should mention is that an active droplet/particle near boundaries (Daddi-Moussa-Ider, Vilfan & Golestanian 2022), fluid interfaces (Malgaretti et al. 2018) or another droplet/particle (Michelin & Lauga 2015) generally exploits geometric asymmetry to propulsion, which is significantly distinct from an isolated droplet/particle.…”

Pair Interaction between Two Catalytically Active Colloids

“…We note that the far‐field approximation is a well‐established approach and has widely been used in the context of hydrodynamic interactions in confinement. [ 58–63 ]…”

“…We note that the far-field approximation is a wellestablished approach and has widely been used in the context of hydrodynamic interactions in confinement. [58][59][60][61][62][63] As shown in Methods, the present problem can be decomposed into three sub problems: (i) intrinsic self-propulsion without background phoretic or hydrodynamic fields, (ii) phoretic drift due to an external concentration field, that is, the phoretic motion of particle 2 due to the gradient in the chemical field induced by particle 1, and (iii) hydrodynamic drift due to an external flow field, that is, the swimming dynamics of particle 2 due to the hydrodynamic field induced by particle 1.…”

Hydrodynamic efficiency limit on a Marangoni surfer

“…Therefore, employing a guessed solution can often be advantageous in the given context. For instance, this approach has been applied to the flow generated by different types of force or source singularities near circular interfaces (Daddi-Moussa-Ider et al 2021b;Daddi-Moussa-Ider, Vilfan & Golestanian 2022;Daddi-Moussa-Ider et al 2023b). In our case, the dual integral equations are solved by…”

“…For instance, this approach has been applied to the flow generated by different types of force or source singularities near circular interfaces (Daddi-Moussa-Ider et al. 2021 b ; Daddi-Moussa-Ider, Vilfan & Golestanian 2022; Daddi-Moussa-Ider et al. 2023 b ).…”