Marangoni flow at droplet interfaces: Three-dimensional solution and applications

Abstract

The Marangoni effect refers to fluid flow induced by a gradient in surface tension at a fluid-fluid interface. We determine the full three-dimensional Marangoni flow generated by a non-uniform surface tension profile at the interface of a self-propelled spherical emulsion droplet. For all flow fields inside, outside, and at the interface of the droplet, we give analytical formulas. We also calculate the droplet velocity vector ${\mathbf{v}}^D$, which describes the swimming kinematics of the droplet, and generalize the squirmer parameter $\beta$, which distinguishes between different swimmer types called neutral, pusher, or puller. In the second part of this paper, we present two illustrative examples, where the Marangoni effect is used in active emulsion droplets. First, we demonstrate how micelle adsorption can spontaneously break the isotropic symmetry of an initially surfactant-free emulsion droplet, which then performs directed motion. Second, we think about light-switchable surfactants and laser light to create a patch with a different surfactant type at the droplet interface. Depending on the setup such as the wavelength of the laser light and the surfactant type in the outer bulk fluid, one can either push droplets along unstable trajectories or pull them along straight or oscillatory trajectories regulated by specific parameters. We explore these cases for strongly absorbing and for transparent droplets.

20 pages, 15 figures

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Cited by in corpus (28)

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• Self-propulsion of chemically-active droplets
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• Collective Sedimentation of Squirmers under Gravity
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• Solute Induced Jittery Motion of Self-Propelled Droplets
• Hydrodynamics of chiral squirmers
• Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects
• Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion
• Numerical simulation of artificial microswimmers driven by Marangoni flow
• Rheotaxis of Active Droplets
• Gradients in solid surface tension drive Marangoni-like motions in cell aggregates
• Surfactant-loaded capsules as Marangoni microswimmers at the air-water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection
• Lattice Boltzmann study of chemically-driven self-propelled droplets
• From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats
• Steering droplets on substrates using moving steps in wettability
• Active volatile drops on liquid baths
• Phase separation dynamics in deformable droplets
• Feedback-Control of Photoresponsive Fluid Interfaces
• Self-propulsion of a light-powered microscopic crystalline flapper in water
• Self-propulsion of active droplets without liquid-crystalline order
• From active stresses and forces to self propulsion of droplets
• Brownian motion of droplets induced by thermal noise
• Marangoni droplets of dextran in PEG solution and its motile change due to coil-globule transition of coexisting DNA
• Deformations of an active liquid droplet
• Kinetic Monte Carlo Simulations for Birefringence Relaxation of Photo-Switchable Molecules on a Surface
• Hydrodynamic efficiency limit on a Marangoni surfer
• Theory of anomalous collective diffusion in colloidal monolayers on a spherical interface