Can phoretic particles swim in two dimensions?

Abstract

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows and ultimately the swimming velocity, may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Peclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.

arXiv comment16 pages, 7 figures, RevTeX 4-1 style

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Cited by in corpus (6)

• Self-propulsion of chemically-active droplets
• Pairing, waltzing and scattering of chemotactic active colloids
• Active spheres induce Marangoni flows that drive collective dynamics
• Self-propulsion in 2D Confinement: Phoretic and Hydrodynamic Interactions
• Non-Brownian diffusion and chaotic rheology of autophoretic disks
• A numerical framework for phoretic particles