Small Atwood number Rayleigh-Taylor experiments

Confinement-induced stabilization of the Rayleigh-Taylor instability and transition to the unconfined limit

The prevention of hydrodynamic instabilities can lead to important insights for understanding the instabilities' underlying dynamics. The Rayleigh-Taylor instability that arises when a dense fluid sinks into and displaces a lighter one is particularly difficult to arrest. By preparing a density inversion between two miscible fluids inside the thin gap separating two flat plates, we create a clean initial stationary interface. Under these conditions, we find that the instability is suppressed below a critical plate spacing. With increasing spacing, the system transitions from the limit of stability where mass diffusion dominates over buoyant forces, through a regime where the gap sets the wavelength of the instability, to the unconfined regime governed by the competition between buoyancy and momentum diffusion. Our study, including experiment, simulation, and linear stability analysis, characterizes all three regimes of confinement and opens new routes for controlling mixing processes.

Evaporation-induced Rayleigh-Taylor instabilities in polymer solutions

Understanding the mechanics of detrimental convective instabilities in drying polymer solutions is crucial in many applications such as the production of film coatings. It is well known that solvent evaporation in polymer solutions can lead to Rayleigh-Bénard or Marangoni-type instabilities. Here, we reveal another mechanism, namely that evaporation can cause the interface to display Rayleigh-Taylor instabilities due to the build-up of a dense layer at the air-liquid interface. We study experimentally the onset time (t_p) of the instability as a function of the macroscopic properties of aqueous polymer solutions, which we tune by varying the polymer concentration (c₀), molecular weight and polymer type. In dilute solutions, t_p shows two limiting behaviours depending on the polymer diffusivity. For high diffusivity polymers (low molecular weight), the pluming time scales as [Formula: see text]. This result agrees with previous studies on gravitational instabilities in miscible systems where diffusion stabilizes the system. On the other hand, in low diffusivity polymers the pluming time scales as [Formula: see text]. The stabilizing effect of an effective interfacial tension, similar to those in immiscible systems, explains this strong concentration dependence. Above a critical concentration, [Formula: see text], viscosity delays the growth of the instability, allowing time for diffusion to act as the dominant stabilizing mechanism. This results in t_p scaling as (ν/c₀)^2/3. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Convective instabilities derived from dissipation of chemical energy

Oxidation reactions of a series of organosulfur compounds by chlorite are excitable, autocatalytic, and exothermic and generate a lateral instability upon being triggered by the autocatalyst. This article reports on the convective instabilities derived from the reaction of chlorite and thiourea in a Hele-Shaw cell. Reagent concentrations used for the development of convective instabilities delivered a temperature jump at the wave front of 2.1 K. The reaction zone was 2 mm and due to normal cooling after the wave front, this induced a spike rather than the standard well-studied front propagation. Localized spatiotemporal patterns develop around the wave front. This exothermic autocatalytic reaction has solutal and thermal contributions to density changes that act in opposite directions due to the existence of a positive isothermal density change in the reaction. The competition between these effects generates thermal plumes. The fascinating feature of this system is the coexistence of plumes and fingering in the same solution as the front propagates through the Hele-Shaw cell. Wave velocities of descending and ascending fronts are oscillatory. Fingers and plumes are generated in alternating frequency as the front propagates. This generates hot and cold spots within the Hele-Shaw cell, and subsequently spatiotemporal inhomogeneities. The small ΔT at the wave front generated thermocapillary convection which competed effectively with thermogravitational forces at low Eötvös numbers. A simplified reaction-diffusion-convection model was derived for the system. Plume formation is heavily dependent on boundary effects from the cell dimensions.

Turbulent mixing and beyond

Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high- and low-energy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.