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Register a new userMarangoni instability of a drop in a stably stratified liquid
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Marangoni instabilities can emerge when a liquid interface is subjected to a concentration or temperature gradient. It is generally believed that for these instabilities bulk effects like buoyancy are negligible as compared to interfacial forces, especially on small scales. Consequently, the effect of a stable stratification on the Marangoni instability has hitherto been ignored. Here we report, for an immiscible drop immersed in a stably stratified ethanol-water mixture, a new type of oscillatory solutal Marangoni instability which is triggered once the stratification has reached a critical value. We experimentally explore the parameter space spanned by the stratification strength and the drop size and theoretically explain the observed crossover from levitating to bouncing by balancing the advection and diffusion around the drop. Finally, the effect of the stable stratification on the Marangoni instability is surprisingly amplified in confined geometries, leading to an earlier onset.
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Interfacial stability is important for many processes involving heat and mass transfer across two immiscible phases. When this transfer takes place in the form of evaporation of a binary solution with one component being more volatile than the other, gradients in surface tension can arise. These gradients can ultimately destabilise the liquid-gas interface. In the present work, we study the evaporation of an ethanol-water solution, for which ethanol has a larger volatility. The solution is contained in a horizontal Hele-Shaw cell which is open from one end to allow for evaporation into air. A Marangoni instability is then triggered at the liquid-air interface. We study the temporal evolution of this instability by observing the effects that it has on the bulk of the liquid. More specifically, the growth of convective cells is visualized with confocal microscopy and the velocity field close to the interface is measured with micro-particle-image-velocimetry. The results of numerical simulations based on quasi 2D equations satisfactorily compare with the experimental observations, even without consideration of evaporative cooling, although this cooling can play an extra role in experiments. Furthermore, a linear stability analysis applied to a simplified version of the quasi 2D equations showed reasonably good agreement with the results from simulations at early times, when the instability has just been triggered and no coarsening has taken place. In particular, we find a critical Marangoni number below which a regime of stability is predicted.
This paper represents a theoretical and an experimental study of the spreading dynamics of a liquid droplet, generated by a needle free deposition system called the liquid needle droplet deposition technique. This technique utilizes a continuous liquid jet generated from a pressurized dosing system which generates a liquid drop on a substrate to be characterized by optical contact angle measurements. Although many studies have explored the theoretical modelling of the droplet spreading scenario, a theoretical model representing the spreading dynamics of a droplet, generated by the jet impact and continuous addition of liquid mass, is yet to be addressed. In this study, we developed a theoretical model based on the overall energy balance approach which enables us to study on the physics of variation of droplet spreading under surrounding medium of various viscosities. The numerical solution of the non-linear ordinary differential equation has provided us the opportunity to comment on the variation of droplet spreading, as a function of Weber number ($We$), Reynolds number ($Re$) and Bond number ($Bo$) ranging from 0.5-3, 75-150, and 0.001-0.3, respectively. We have also presented a liquid jet impact model in order to predict the initial droplet diameter as an initial condition for the proposed governing equation. The model has been verified further with the experimental measurements and reasonable agreement has been observed. Experimental observations and theoretical investigations also highlight the precision, repeatability and wide range of the applicability of liquid needle drop deposition technique.
We present an investigation of rapidly rotating (small Rossby number $Roll 1$) and stratified turbulence where the stratification strength is varied from weak (large Froude number $Frgg1$) to strong ($Frll1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that efficiently retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave-eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes characterized by the presence of well-formed, persistent and thin turbulent layers of locally-weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large a direct cascade of barotropic kinetic energy is observed, leading to total energy equilibration. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux and diagnose the horizontal scales active in these exchanges. We find that the baroclinic motions inject energy directly to the largest scales of the barotropic mode, implying that the large-scale barotropic dipole is not the end result of an inverse cascade within the barotropic mode.
Eutectic gallium-indium (EGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet can nonetheless undergo fingering instabilities. This effect arises because, under an applied voltage, oxides deposit on the surface of the metal, which leads to a lowering of the interfacial tension, allowing spreading under gravity. Understanding the spreading dynamics of room temperature liquid metals is important for developing soft electronics and understanding fluid dynamics of liquids with extreme surface tensions. When the applied voltage or the oxidation rate becomes too high, the EGaIn undergoes fingering instabilities, including tip-splitting, which occur due to a Marangoni stress on the interface. Our experiments are performed with EGaIn droplets placed in an electrolyte (sodium hydroxide); by placing the EGaIn on copper electrodes, which EGaIn readily wets, we are able to control the initial width of EGaIn fingers, setting the initial conditions of the spreading. Two transitions are observed: (1) a minimum current density at which all fingers become unstable to narrower fingers; (2) a current density at which the wider fingers undergo a single splitting event into two narrower fingers. We present a phase diagram as a function of current density and initial finger width, and identify the minimum width below which the single tip-splitting does not occur.
In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, provided a concentration gradient is maintained across the fluids. One long wave and two short wave Marangoni instability modes arise, in different regions of parameter space. A well-defined condition for the long wave instability is determined in terms of the viscosity and thickness ratios of the fluids, and the direction of mass transfer. Energy budget calculations show that the Marangoni stresses that drive long and short wave instabilities have distinct origins. The former is caused by interface deformation while the latter is associated with convection by the disturbance flow. Consequently, even when the interface is non-deforming (in the large interfacial tension limit), the flow can become unstable to short wave disturbances. On increasing $Re$, the viscosity-induced interfacial instability comes into play. This mode is shown to either suppress or enhance the Marangoni instability, depending on the viscosity and thickness ratios. This analysis is relevant to applications such as solvent extraction in microchannels, in which a surface-active solute is transferred between fluids in parallel stratified flow. It is also applicable to the thermocapillary problem of layered flow between heated plates.
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