Adsorption inhibition by swollen micelles may cause multistability in active droplets

Experiments indicate that microdroplets undergoing micellar solubilization in the bulk of surfactant solution may excite Marangoni flows and self-propel spontaneously. Surprisingly, self-propulsion emerges even when the critical micelle concentration is exceeded and the Marangoni effect should be saturated. To explain this, we propose a novel model of a dissolving active droplet that is based on two fundamental assumptions: (a) products of the solubilization may inhibit surfactant adsorption; (b) solubilization prevents the formation of a monolayer of surfactant molecules at the droplet interface. We use numerical simulations and asymptotic methods to demonstrate that our model indeed features spontaneous droplet self-propulsion. Our key finding is that in the case of axisymmetric flow and concentration fields, two qualitatively different types of droplet behavior may be stable for the same values of the physical parameters: steady self-propulsion and steady symmetric pumping. Although stability of these steady regimes is not guaranteed in the absence of axial symmetry, we argue that they will retain their respective stable manifolds in the phase space of a fully 3D problem.Comment: This is the revised version of the manuscript accepted for publication in Soft Matte

Self-propulsion near the onset of Marangoni instability of deformable active droplets

International audienceExperimental observations indicate that chemically active droplets suspended in a surfactant-laden fluid can self-propel spontaneously. The onset of this motion is attributed to a symmetry-breaking Marangoni instability resulting from the nonlinear advective coupling of the distribution of surfactant to the hydrodynamic flow generated by Marangoni stresses at the droplet's surface. Here, we use weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet's deformability. We report that in vicinity of the threshold, deformability enhances self-propulsion of viscous droplets, but hinders propulsion of drops that are roughly less viscous than the surrounding fluid. Our asymptotics further reveals that droplet deformability may alter the type of bifurcation leading to symmetry breaking: for moderately deformable droplets the onset of self-propulsion is transcritical and a regime of steady self-propulsion is stable; while in the case of highly deformable drops, no steady flows can be found within the asymptotic limit considered in this paper suggesting that the bifurcation is subcritical

On the optimal rank-1 approximation of matrices in the Chebyshev norm

The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However, recent results reveal the potential of low rank approximations in Chebyshev norm, which naturally arises in many applications. In this paper we tackle the problem of building optimal rank-1 approximations in the Chebyshev norm. We investigate the properties of alternating minimization algorithm for building the low rank approximations and demonstrate how to use it to construct optimal rank-1 approximation. As a result we propose an algorithm that is capable of building optimal rank-1 approximations in Chebyshev norm for small matrices

Adsorption inhibition by swollen micelles may cause multistability in active droplets

Dissolving microdroplets that feature nonlinear surfactant adsorption and reaction kinetics may spontaneously excite two qualitatively different types of flow.info:eu-repo/semantics/publishe

Orientational instability and spontaneous rotation of active nematic droplets

International audienceIn experiments, an individual chemically active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's rotation. Within this reduced-order model, the coupling between the nematic ordering of the drop and the surfactant transport is represented by variations of the droplet's interfacial properties with nematic polarization. Our analysis reveals that a novel mode of orientational instability emerges from the competition of the two reorientation mechanisms and is characterized by a spontaneous rotation of the self-propelling drop responsible for helical self-propulsion trajectories. In turn, we also show that random trajectories in isotropic and nematic drops alike stem from the advection-driven transition to chaos. The succession of the different propulsion modes is consistent with experimentally-reported transitions in the shape of droplet trajectories as the drop size is varied

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

International audienceIndividual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. To elucidate how these drops can exhibit such strikingly different dynamics and "decide" what to do, we propose a minimal axisymmetric model of a spherical active drop, and show that simple and linear interface properties can lead to both steady self-propulsion of the droplet as well as chaotic behavior. The model includes two different mobility mechanisms, namely, diffusiophoresis and the Marangoni effect, that convert self-generated gradients of surfactant concentration into the flow at the droplet surface. In turn, surface-driven flow initiates surfactant advection that is the only nonlinear mechanism and, thus, the only source of dynamical complexity in our model. Numerical investigation of the fully-coupled hydrodynamic and advection diffusion problems reveals that strong advection (e.g., large droplet size) may destabilize a steadily self-propelling drop; once destabilized, the droplet spontaneously stops and a symmetric extensile flow emerges. If advection is strengthened even further in comparison with molecular diffusion, the droplet may perform chaotic oscillations. Our results indicate that the thresholds of these instabilities depend heavily on the balance between diffusiophoresis and the Marangoni effect. Using linear stability analysis, we demonstrate that diffusiophoresis promotes the onset of high-order modes of monotonic instability of the motionless drop. We argue that diffusiophoresis has a similar effect on the instabilities of a moving drop

nonlinear dynamics of chemically active microdrops grants an insight into interfacial chemistry

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Collisions and rebounds of chemically active droplets

International audienceActive 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 charac-terise 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