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

Abstract

Individual 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.

arXiv commentAccepted for publication in Journal of Chemical Physics

References in corpus (10)

• Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion
• Spontaneous autophoretic motion of isotropic particles
• Phoretic self-propulsion at finite Péclet numbers
• Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter
• Generic theory of colloidal transport
• Curling Liquid Crystal Microswimmers: a cascade of spontaneous symmetry breaking
• Phoretic Interactions Between Active Droplets
• Self-propulsion near the onset of Marangoni instability of deformable active droplets
• Unsteady feeding and optimal strokes of model ciliates
• Phoretic self-propulsion at large Peclet numbers

Cited by in corpus (26)

• Self-propulsion of chemically-active droplets
• Chemotactic self-caging in active emulsions
• Emergence of bimodal motility in active droplets
• We the Droplets: A Constitutional Approach to Active and Self-Propelled Emulsions
• Oscillatory rheotaxis of active droplets in microchannels
• Spontaneously rotating clusters of active droplets
• Tunable active rotational diffusion in swimming droplets
• Solute Induced Jittery Motion of Self-Propelled Droplets
• Instability and self-propulsion of active droplets along a wall
• Instabilities driven by diffusio-phoretic flow on catalytic surfaces
• Bouncing, chasing or pausing: asymmetric collisions of active droplets
• Alignment and scattering of colliding active droplets
• Confined self-propulsion of an isotropic active colloid
• Self-solidifying active droplets showing memory-induced chirality
• Dynamics of forced and unforced autophoretic particles
• Deforming Active Droplets in Viscoelastic Media
• Interfacial activity dynamics of confined active droplets
• Self-propulsion of active droplets without liquid-crystalline order
• Mode-Switching of Active Droplets in Macromolecular Solutions
• Non-Brownian diffusion and chaotic rheology of autophoretic disks
• A Reduced Model for a Phoretic Swimmer
• Steady state propulsion of isotropic active colloids along a wall
• Fluctuating hydrodynamics of an autophoretic particle near a permeable interface
• Physicochemical Hydrodynamics of Droplets out of Equilibrium: A Perspective Review
• Arrested on heating: controlling the motility of active droplets by temperature
• Instability and self-propulsion of flexible autophoretic filaments