Spontaneous onset of convection in a uniform phoretic channel

Sébastien Michelin (1) , Simon Game (2) , Eric Lauga (3) , Eric Keaveny (4) , Demetrios Papageorgiou (2)

1 LadHyX - Laboratoire d'hydrodynamique
2 Department of Mathematics [Imperial College London]
3 DAMTP - Department of Applied Mathematics and Theoretical Physics
4 Imperial College London

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 Bénard-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 Péclet 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.

Domains: Fluid mechanics [physics.class-ph]

Sébastien Michelin, Simon Game, Eric Lauga, Eric Keaveny, Demetrios Papageorgiou. Spontaneous onset of convection in a uniform phoretic channel. Soft Matter, 2020, 16 (5), pp.1259-1269. ⟨10.1039/C9SM02173F⟩. ⟨hal-02536802⟩