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Swimming dynamics of a self-propelled droplet

Published online by Cambridge University Press:  14 January 2022

Gaojin Li Open the ORCID record for Gaojin Li [Opens in a new window]
Gaojin Li*
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai 200240, PR China School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
†Email address for correspondence: gaojinli@sjtu.edu.cn
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Abstract

Chemically active droplets often show intriguing self-propulsion behaviour in a surfactant solution. The drop motion is controlled by the nonlinear coupling among chemical transport in the bulk fluid, consumption of surfactant at the drop surface, and the fluid flow driven by the self-generated Marangoni stress. To quantify the underlying hydrodynamics, this work investigates the swimming motion of a two-dimensional drop that is determined by two dimensionless parameters, the Péclet number ($Pe$) and Damköhler number ($Da$). The weakly nonlinear analysis shows that near the instability threshold, the drop undergoes a supercritical bifurcation with velocity $U\sim \sqrt {Pe-Pe_c}$, where $Pe_c$ is the critical Péclet number for the onset of dipole mode. In the highly nonlinear regime, the drop transits from steady translation of pusher swimming to unsteady motion of mixed pusher–puller swimming along zigzaging trajectories of quadrangle and/or triangle waves. Mode decomposition shows that the zigzag motion is directly related to the interaction between the secondary wake of low surfactant concentration and the primary wake.

JFM classification

Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A20
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Li Supplementary Movie 1

The concentration field and trajectory for a swimming drop at Pe=38 and Da=0.

Download Li Supplementary Movie 1(Video)
Video 61.2 MB

Li Supplementary Movie 2

The concentration field and trajectory for a swimming drop at Pe=40 and Da=0.

Download Li Supplementary Movie 2(Video)
Video 60.2 MB