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Collisions and rebounds of chemically active droplets

Published online by Cambridge University Press:  14 January 2020

K. Lippera Open the ORCID record for K. Lippera [Opens in a new window] ,
M. Morozov Open the ORCID record for M. Morozov [Opens in a new window] ,
M. Benzaquen Open the ORCID record for M. Benzaquen [Opens in a new window]  and
S. Michelin Open the ORCID record for S. Michelin [Opens in a new window]
K. Lippera
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
M. Morozov
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
M. Benzaquen
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
S. Michelin*
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
*
†Email address for correspondence: sebastien.michelin@ladhyx.polytechnique.fr
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Abstract

Active droplets swim as a result of the nonlinear advective coupling of the distribution of chemical species they consume or release with the Marangoni flows created by their non-uniform surface distribution. Most existing models focus on the self-propulsion of a single droplet in an unbounded fluid, which arises when diffusion is slow enough (i.e. beyond a critical Péclet number, $Pe_{c}$). Despite its experimental relevance, the coupled dynamics of multiple droplets and/or collision with a wall remains mostly unexplored. Using a novel approach based on a moving fitted bi-spherical grid, the fully coupled nonlinear dynamics of the chemical solute and flow fields is solved here to characterise in detail the axisymmetric collision of an active droplet with a rigid wall (or with a second droplet). The dynamics is strikingly different depending on the convective-to-diffusive transport ratio, $Pe$: near the self-propulsion threshold (moderate $Pe$), the rebound dynamics is set by chemical interactions and is well captured by asymptotic analysis; in contrast, for larger $Pe$, a complex and nonlinear combination of hydrodynamic and chemical effects set the detailed dynamics, including a closer approach to the wall and a velocity plateau shortly after the rebound of the droplet. The rebound characteristics, i.e. minimum distance and duration, are finally fully characterised in terms of $Pe$.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Propulsion Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Lippera et al. supplementary movie 1

Collision dynamics of a droplet with a rigid wall with Pe=6. The evolution of the concentration field is also shown (colours)

Download Lippera et al. supplementary movie 1(Video)
Video 4.2 MB

Lippera et al. supplementary movie 2

Collision dynamics of a droplet with a rigid wall with Pe=20. The evolution of the concentration field is also shown (colours)

Download Lippera et al. supplementary movie 2(Video)
Video 3.1 MB