Collisions and rebounds of chemically-active droplets

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, $\mbox{Pe}_c$). 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 bispherical grid, the fully-coupled nonlinear dynamics of the chemical solute and flow fields are 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, $\mbox{Pe}$: near the self-propulsion threshold (moderate $\mbox{Pe}$), the rebound dynamics are set by chemical interactions and are well captured by asymptotic analysis; in contrast, for larger $\mbox{Pe}$, 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 $\mbox{Pe}$.

27 pages, 12 figures, to appear in J. Fluid Mech

References in corpus (8)

• The hydrodynamics of swimming microorganisms
• Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion
• Dynamic clustering and chemotactic collapse of self-phoretic active particles
• Phoretic self-propulsion at finite Péclet numbers
• Autophoretic locomotion from geometric asymmetry
• Pulling and Pushing a Cargo With a Catalytically Active Carrier
• Modeling chemo-hydrodynamic interactions of phoretic particles: a unified framework
• Lattice Boltzmann study of chemically-driven self-propelled droplets

Cited by in corpus (3)

• Collective entrainment and confinement amplify transport by schooling micro-swimmers
• Local drag of a slender rod parallel to a plane wall in a viscous fluid
• Steady state propulsion of isotropic active colloids along a wall