Self-propulsion near the onset of Marangoni instability of deformable active droplets

Abstract

Experimental observations indicate that chemically active droplets suspended in a surfactant-laden fluid can self-propel spontaneously. The onset of this motion is attributed to a symmetry-breaking Marangoni instability resulting from the nonlinear advective coupling of the distribution of surfactant to the hydrodynamic flow generated by Marangoni stresses at the droplet's surface. Here, we use weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet's deformability. We report that in vicinity of the threshold, deformability enhances self-propulsion of viscous droplets, but hinders propulsion of drops that are roughly less viscous than the surrounding fluid. Our asymptotics further reveals that droplet deformability may alter the type of bifurcation leading to symmetry breaking: for moderately deformable droplets the onset of self-propulsion is transcritical and a regime of steady self-propulsion is stable; while in the case of highly deformable drops, no steady flows can be found within the asymptotic limit considered in this paper suggesting that the bifurcation is subcritical.

arXiv commentAccepted for publication in Journal of Fluid Mechanics

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• Solute Induced Jittery Motion of Self-Propelled Droplets
• Bouncing, chasing or pausing: asymmetric collisions of active droplets
• Alignment and scattering of colliding active droplets
• Confined self-propulsion of an isotropic active colloid
• Two-dimensional diffusiophoretic colloidal banding: Optimizing the spatial and temporal design of solute sinks and sources
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• Active volatile drops on liquid baths
• Self-propulsion of active droplets without liquid-crystalline order
• Deformations of an active liquid droplet
• A Reduced Model for a Phoretic Swimmer
• Physicochemical Hydrodynamics of Droplets out of Equilibrium: A Perspective Review