Instability and self-propulsion of active droplets along a wall

Active droplets can swim spontaneously in viscous flows as a result of the nonlinear convective transport of a chemical solute produced at their surface by the Marangoni and/or phoretic flows generated by that solute's inhomogeneous distribution, provided the ratio of convective-to-diffusive solute transport, or Peclet number Pe, is large enough. As the result of their net buoyancy, active drops typically evolve at a small finite distance d from rigid boundaries. Yet, existing models systematically focus on unbounded flows, ignoring the effect of the wall proximity on the intrinsically nonlinear nature of their propulsion mechanism. In contrast, we obtain here a critical insight on the propulsion of active drops near walls by analyzing their stability against nonaxisymmetric perturbations and the resulting emergence of self-propulsion along the wall with no limiting assumption on the wall distance d. Dipolar or quadrupolar axisymmetric (levitating) base states are identified depending on d and Pe. Perhaps counterintuitively, a reduction in the drop-wall separation d is observed to destabilize these modes and to promote self-propulsion, as a result of the confinement-induced localization of the chemical gradients driving the motion. In addition, quadrupolar states are more unstable than their dipolar counterparts due to the redistribution of the chemical perturbation by the base flow, favoring the emergence of stronger slip forcing on the drop surface.

Automated summary

Active droplets can swim in viscous flows due to convective transport of a chemical solute produced at their surface, with stability against nonaxisymmetric perturbations and emergence of self-propulsion along the wall. Reduction in the drop-wall separation destabilizes modes and promotes self-propulsion due to confinement-induced localization of chemical gradients. Quadrupolar states are more unstable than dipolar counterparts favoring stronger slip forcing on the drop surface.