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, Pec). 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, Pe: near the self-propulsion threshold (moderate Pe), the rebound dynamics are set by chemical interactions and are 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. * Electronic address: sebastien.michelin@ladhyx.polytechnique.fr arXiv:1912.04621v1 [physics.flu-dyn]

Bouncing, chasing, or pausing: Asymmetric collisions of active droplets

“…The smaller droplet being exposed to an increased chemical gradient is quickly repelled away, reducing the interaction time with the larger one. Additionally, the increased size (or Pe) of the larger droplet enhances the persistence of its chemical polarity and self-propulsion, as already observed for symmetric collisions [31].…”

“…Yet, most experiments report much denser situations; the present Letter thus focuses on such near-field interactions, which are likely critical to the emergence of collective behaviour. Exploiting the simplicity of a two-sphere geometry, we were recently able to fully-resolve the symmetric collision of two droplets [31], and provided a critical insight on how the nonlinear convective transport conditions the collision. To note, controlling experimentally the exact droplet radius, which slowly varies over time [6], is however impossible, giving rise to heterogeneous systems and non-symmetric in practice.…”

“…The full nonlinear coupling of the Stokes and chemical transport problems is solved numerically for arbitrary distance using an efficient scheme based on a time-dependent bispherical grid presented in detail in Ref. [31]. The problem is now re-scaled using R 2 , V 2 and AR 2 /D as reference length, velocity and concentration respectively,…”

“…As the smaller droplet swims away, the polarity of the larger droplet still allows it to accelerate and recover its original velocity, effectively chasing the smaller droplet. The absolute self-propulsion velocity of an isolated droplet increases with its radius (when rescaled by its radius it increases linearly with Pe i before reaching a plateau [6,31]). As a result, when far enough apart, the larger droplet will swim faster than and catch up with the smaller one.…”

“…Following Ref. [31], these arguments can be formulated quantitatively in the asymptotic limit of small supercriticality, i.e. when δ i = Pe i − Pe c are both small (which imposes ξ − 1 1).…”