For an immiscible oil drop immersed in a stably stratified ethanol–water mixture, a downwards solutal Marangoni flow is generated on the surface of the drop, owing to the concentration gradient, and the resulting propulsion competes against the downwards gravitational acceleration of the heavy drop. In prior work of Li et al. (Phys. Rev. Lett., vol. 126, issue 12, 2021, 124502), we found that for drops of low viscosity, an oscillatory instability of the Marangoni flow is triggered once the Marangoni advection is too strong for diffusion to restore the stratified concentration field around the drop. Here we experimentally explore the parameter space of the concentration gradient and drop radius for high oil viscosities and find a different and new mechanism for triggering the oscillatory instability in which diffusion is no longer the limiting factor. For such drops of higher viscosities, the instability is triggered when the gravitational effect is too strong so that the viscous stress cannot maintain a stable Marangoni flow. This leads to a critical drop radius above which the equilibrium is always unstable. Subsequently, a unifying scaling theory that includes both the mechanisms for low and for high viscosities of the oil drops is developed. The transition between the two mechanisms is found to be controlled by two length scales: the drop radius $R$ and the boundary layer thickness $\delta$ of the Marangoni flow around the drop. The instability is dominated by diffusion for $\delta < R$ and by viscosity for $R<\delta$ . The experimental results for various drops of different viscosities can well be described with this unifying scaling theory. Our theoretical description thus provides a unifying view of physicochemical hydrodynamic problems in which the Marangoni stress is competing with a stable stratification.
Freezing of dispersions is omnipresent in science and technology. While the passing of a freezing front over a solid particle is reasonably understood, this is not so for soft particles. Here, using an oil-in-water emulsion as a model system, we show that when engulfed into a growing ice front, a soft particle severely deforms. This deformation strongly depends on the engulfment velocity V, even forming pointy-tip shapes for low values of V. We find such singular deformations are mediated by interfacial flows in nanometric thin liquid films separating the nonsolidifying dispersed droplets and the solidifying bulk. We model the fluid flow in these intervening thin films using a lubrication approximation and then relate it to the deformation sustained by the dispersed droplet.
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When an immiscible oil drop is immersed in a stably stratified ethanol–water mixture, the Marangoni flow on the surface of the drop can experience an oscillatory instability, so that the drop undergoes a transition from levitating to bouncing. The onset of the instability and its mechanisms have been studied previously (Li et al., Phys. Rev. Lett., vol. 126, 2021, 124502; Li et al., J. Fluid Mech., vol. 932, 2022, A11), yet the bouncing motion of the drop itself, which is a completely different problem, has not yet been investigated. Here we study how the bouncing characteristics (jumping height, rising and sinking time) depend on the control parameters (drop radius, stratification strength, drop viscosity). We first record experimentally the bouncing trajectories of drops of different viscosities in different stratifications. Then a simplified dynamical analysis is performed to get the scaling relations of the jumping height and the rising and sinking times. The rising and sinking time scales are found to depend on the drag coefficient $C_D^S$ of the drop in the stratified liquid, which is determined empirically for the current parameter space (Zhang et al., J. Fluid Mech., vol. 875, 2019, 622–656). For low-viscosity (5 cSt) oil drops, the results on the drag coefficient match those from the literature (Yick et al., J. Fluid Mech., vol. 632, 2009, pp. 49–68; Candelier et al., J. Fluid Mech., vol. 749, 2014, pp. 184–200). For high-viscosity (100 cSt) oil drops, the parameter space had not been explored and the drag coefficients are not readily available. Numerical simulations are therefore performed to provide external verification for the drag coefficients, which well match with the experimental results.
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