Abstract
We study the hydrodynamics and shape changes of chemically active droplets. In non-spherical droplets, surface tension generates hydrodynamic flows that drive liquid droplets into a spherical shape. Here we show that spherical droplets that are maintained away from thermodynamic equilibrium by chemical reactions may not remain spherical but can undergo a shape instability which can lead to spontaneous droplet division. In this case chemical activity acts against surface tension and tension-induced hydrodynamic flows. By combining low Reynolds-number hydrodynamics with phase separation dynamics and chemical reaction kinetics we determine stability diagrams of spherical droplets as a function of dimensionless viscosity and reaction parameters. We determine concentration and flow fields inside and outside the droplets during shape changes and division. Our work shows that hydrodynamic flows tends to stabilize spherical shapes but that droplet division occurs for sufficiently strong chemical driving, sufficiently large droplet viscosity or sufficiently small surface tension. Active droplets could provide simple models for prebiotic protocells that are able to proliferate. Our work captures the key hydrodynamics of droplet division that could be observable in chemically active colloidal droplets.
Highlights
Living cells are compartmentalized in order to organize their biochemistry in space
We show that chemical reactions in active droplets can perform work against surface tension and flows, giving rise to a shape instability that can result in droplet division
We investigate the conditions for which droplets divide and determine hydrodynamic flow fields of dividing droplets
Summary
We discuss stationary solutions to equations (1-10) in the main text with spherical symmetry and without hydrodynamic flows v = 0, where the bar indicates a steady state value. In this case, the pressure is constant both inside and outside the droplet, with a pressure difference due to Laplace pressure between the inside and outside of the droplets, 2γ p− = p+ + R. The parameters A± are determined by the boundary condition at the droplet interface, Eq. Note that this equation typically has zero, one or two solutions for a given set of parameters
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