An experimental study of small Atwood number Rayleigh-Taylor instability using the magnetic levitation of paramagnetic fluids

Abstract

Experiments that take advantage of the properties of paramagnetic liquids are used to study Rayleigh-Taylor (RT) instability. A gravitationally unstable, miscible combination of a paramagnetic salt solution and a nonmagnetic solution is initially stabilized by a magnetic field gradient that is produced by the contoured pole-caps of a large electromagnet. Rayleigh-Taylor instability originates from infinitesimal random background noise with the rapid removal of current from the electromagnet, which results in the heavy liquid falling into the light liquid due to gravity and, thus, mixing with it. The mixing zone is visualized by backlit photography and is recorded with a digital video camera. Several miscible, small Atwood number (A ⩽ 0.1) combinations of paramagnetic and nonmagnetic solutions are used. It is found that the RT flow is insensitive to the viscosities of the fluids composing the two-fluid system, and that the growth parameter α also does not show dependence on the Atwood number when the experiments are initialized under the same conditions. It is also observed that the turbulent mixing zone grows linearly with time following a period of self-similar quadratic growth. When the width of the mixing zone becomes comparable with the cross-sectional length scale of the experimental container, the bubble front characteristic velocity approaches a constant value, similar to that observed with a single bubble rising in the confined volume, with Froude number measured in the range Fr = 0.38÷0.45. However, flow visualization does not reveal any persistent large-scale perturbations, which would dominate the flow during this stage. We believe that this phenomenon is not an attribute of the given magnetic experiments and has been observed in many other experimental studies, which involve RT instability evolving in confined volumes.

Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification

“…In experimental procedures there is inevitably some memory of initial conditions, as large wavelength perturbations of the order of the dimensions of the container will be present (Youngs 1984;Dalziel 1993;Snider & Andrews 1994). Experiments of two-layer RTI with widely varying experimental procedures have found a value of α that is around 0.07 (Dalziel 1993;Tsiklashvili et al 2012), although other experimental studies have found values that are somewhat lower, e.g. 0.057 (Dimonte et al 2004).…”

“…Many authors now believe that this is due to differences in initial conditions (e.g. Dalziel et al 1999;Tsiklashvili et al 2012), although another suggested explanation for the variation in α is the difference in Schmidt number (Sc = ν/D, where ν is the kinematic viscosity and D is the mass diffusivity) between experiments and numerics (Glimm et al 2001). In experimental procedures there is inevitably some memory of initial conditions, as large wavelength perturbations of the order of the dimensions of the container will be present (Youngs 1984;Dalziel 1993;Snider & Andrews 1994).…”

“…Although there have been many experimental studies (see, among others, Read 1984;Dalziel 1993;Linden, Redondo & Youngs 1994;Snider & Andrews 1994;Dalziel, Linden & Youngs 1999;Mueschke et al 2009;Boffetta et al 2010;Lister et al 2011;Tsiklashvili et al 2012), few examine anything other than the classical case of two layers of constant density. Exceptions include Jacobs & Dalziel (2005), who examined the instability when both a stable and an unstable density interface were present in the system.…”

Dynamics of buoyancy-driven flows at moderately high Atwood numbers

“…White et al (2010) used a paramagnetic substance in a strong magnetic field to place the fluids in an unstable configuration. The same technique was used by Huang et al (2007) and Tsiklashvili et al (2012). RTI experiments were also conducted in a high-energy-density environment using the NOVA laser to test the applicability of available theories at these extreme conditions (Remington et al 1994;Budil et al 1997).…”

A wavelet based numerical simulation technique for two-phase flows using the phase field method

“…For small amplitude perturbations of an idealized gas-liquid interface, inviscid linear theory suggests an unbounded exponential growth, where different scales grow independently of one an- other. However, viscous effect may prevent from high wavenumber growth [3,14,58,60]; as a result, a 'most unstable' mode of solution is produced, which may be seen from the mechanical energy equation below. As the perturbations grow in a two-dimensional RTI, the gas-liquid interface deforms into counter-rotating rolls in the form of vorticity filaments.…”