Solute-mediated interactions between active droplets

Abstract

Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here, we uncover a regime in which solute gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, which scales with interparticle distance as F ∼ 1/r 2 . Our results show that the dissolution process is diffusion rather than reaction rate limited, and the theoretical model captures the dependence of the interactions on droplet size and solute concentration, using a single fit parameter, l = 16 ± 3 nm, which corresponds to the length scale of a swollen micelle. Our results shed light on the out-of-equilibrium behavior of particles with surface reactivity.

Nonlinear dynamics of a chemically-active drop: From steady to chaotic self-propulsion

“…We consider the dynamics of a force-free spherical droplet of radius R suspended in the bulk of a surfactant solution. In recent experiments, active droplets with R ∼ 1-10 µm were shown to spontaneously swim with velocities U ∼ 10-50 µm.s −1 [6,13,17], so that inertial forces in the fluid phases are negligible (i.e. the Reynolds number Re = U R/η o is exceedingly small, with η o the viscosity of the outer phase).…”

“…The physico-chemical activity of swimming droplets can involve several mechanisms, including micellar and molecular pathways to the droplet dissolution [6,13,14,17]. The former involves the dissolution of the droplet by micelles present in the surfactant-saturated outer phase [17], while in the latter, droplet dissolution is achieved through the formation of swollen micelles from the surfactant molecules present in the outer phase [13]. In the following, we specifically consider the molecular pathway, although the formalism presented here could easily be extended to account for other dissolution mechanisms.…”

“…At the collective level, and similarly to phoretic particles, active droplets can self-organize in complex clusters [10] in the presence of chemically-active species. Multiple active drops "feel" each other's presence and adjust their behavior: they may form ordered clusters [11,12], repel [13], or avoid crossing each other's trails [5]. * sebastien.michelin@ladhyx.polytechnique.fr Experimental observations of active drops typically employ relatively small droplets with radius ∼100 µm or less.…”

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

“…Recent modelling efforts have also uncovered several important features of individual self-propulsion [26][27][28][29]. In contrast, detailed modelling of the interaction of two or multiple droplets has so far been rather elusive, due to the non-linearity of the advective problem, and as a result, most of the existing models rely on far-field approximations for which superposition principles can be adapted [24,30]. 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.…”

Orientational instability and spontaneous rotation of active nematic droplets

“…We emphasize that active droplet mobility is typically attributed solely to the Marangoni effect [15,16]; Equation (2) thus represents an alternative approach to modeling of active drop mobility and the secondary goal of this paper is to demonstrate that such a model can successfully capture fundamental dynamical features of active drops, including the onset of chaos. In experiments, the energy required for self-propulsion of active drops is generated in a chemical reaction sustained at the droplet interface [8,[19][20][21]. Specifically, drops undergo gradual micellar dissolution and their dissolution time is orders of magnitude larger than the characteristic time scales associated with their propulsion.…”