Collisions and rebounds of chemically-active droplets

TL;DR

This paper investigates the complex collision and rebound behaviors of chemically-active droplets near walls or other droplets, revealing how these dynamics depend on the ratio of convective to diffusive transport, using a novel numerical approach.

Contribution

It introduces a new numerical method based on a moving fitted bispherical grid to fully solve coupled nonlinear chemical and flow fields during droplet collisions.

Findings

Rebound dynamics are governed by chemical interactions near the self-propulsion threshold.

For higher Pe, hydrodynamic and chemical effects produce complex collision behaviors.

Rebound characteristics vary systematically with the Pe number.

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 P\'eclet 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 $\mbox{Pe}$.