Journal
JOURNAL OF FLUID MECHANICS
Volume 860, Issue -, Pages 711-738Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2018.853
Keywords
bifurcation; drops; low-Reynolds-number flows
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Funding
- European Research Council (ERC) under the European Union [714027]
- European Research Council (ERC) [714027] Funding Source: European Research Council (ERC)
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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 a weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet's deformability. We report that, in the 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.
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