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

Published online by Cambridge University Press:  11 December 2018

Matvey Morozov Open the ORCID record for Matvey Morozov [Opens in a new window]  and
Sébastien Michelin Open the ORCID record for Sébastien Michelin [Opens in a new window]
Matvey Morozov
Affiliation:
LadHyX – Département de Mécanique, École Polytechnique – CNRS, 91128 Palaiseau CEDEX, France
Sébastien Michelin*
Affiliation:
LadHyX – Département de Mécanique, École Polytechnique – CNRS, 91128 Palaiseau CEDEX, France
*
†Email address for correspondence: sebastien.michelin@ladhyx.polytechnique.fr
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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 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.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Drops and Bubbles: Drops Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 711 - 738
Copyright
© 2018 Cambridge University Press 

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