Spontaneous onset of convection in a uniform phoretic channel

TL;DR

This paper theoretically demonstrates that chemical gradients can induce spontaneous, self-sustained flows in a uniform channel, significantly affecting solute transport without net pumping, through an instability similar to Bénard-Marangoni convection.

Contribution

It introduces a novel mechanism for spontaneous flow generation in uniform channels driven by phoretic effects, expanding understanding of active fluid systems.

Findings

Spontaneous flows occur above a critical Péclet number.

Flow patterns depend on perturbation wavenumbers.

Numerical simulations confirm long-term coupled dynamics.

Abstract

Phoretic mechanisms, whereby gradients of chemical solutes induce surface-driven flows, have recently been used to generate directed propulsion of patterned colloidal particles. When the chemical solutes diffuse slowly, an instability further provides active but isotropic particles with a route to self-propulsion by spontaneously breaking the symmetry of the solute distribution. Here we show theoretically that, in a mechanism analogous to B\'enard-Marangoni convection, phoretic phenomena can create spontaneous and self-sustained wall-driven mixing flows within a straight, chemically-uniform active channel. Such spontaneous flows do not result in any net pumping for a uniform channel but greatly modify the distribution of transport of the chemical solute. The instability is predicted to occur for a solute P\'eclet number above a critical value and for a band of finite perturbation wavenumbers. We solve the perturbation problem analytically to characterize the instability, and use both steady and unsteady numerical computations of the full nonlinear transport problem to capture the long-time coupled dynamics of the solute and flow within the channel.