Buoyancy-driven instabilities of a horizontal interface between two miscible solutions in the gravity field are theoretically studied in porous media and Hele-Shaw cells (two glass plates separated by a thin gap). Beyond the classical Rayleigh-Taylor (RT) and double diffusive (DD) instabilities that can affect such two-layer stratifications right at the initial time of contact, diffusive-layer convection (DLC) as well as delayed-double diffusive (DDD) instabilities can set in at a later time when differential diffusion effects act upon the evolving density profile starting from an initial step-function profile between the two miscible solutions. The conditions for these instabilities to occur can therefore be obtained only by considering time evolving base-state profiles. To do so, we perform a linear stability analysis based on a quasi-steady-state approximation (QSSA) as well as nonlinear simulations of a diffusion-convection model to classify and analyse all possible buoyancy-driven instabilities of a stratification of a solution of a given solute A on top of another miscible solution of a species B. Our theoretical model couples Darcy's law to evolution equations for the concentration of species A and B ruling the density of the miscible solutions. The parameters of the problem are a buoyancy ratio R quantifying the ratio of the relative contribution of B and A to the density as well as δ, the ratio of diffusion coefficients of these two species. We classify the region of RT, DD, DDD and DLC instabilities in the (R, δ) plane as a function of the elapsed time and show that, asymptotically, the unstable domain is much larger than the one captured on the basis of linear base-state profiles which can only obtain stability thresholds for the RT and DD instabilities. In addition the QSSA allows one to determine the critical time at which an initially stable stratification of A above B can become unstable with regard to a DDD or DLC mechanism when starting from initial step function profiles. Nonlinear dynamics are also analysed by a numerical integration of the full nonlinear model in order to understand the influence of R and δ on the dynamics. © 2011 Cambridge University Press.

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Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells

Buoyancy-driven instabilities of a horizontal interface between two miscible solutions in the gravity field are theoretically studied in porous media and Hele-Shaw cells (two glass plates separated by a thin gap). Beyond the classical Rayleigh–Taylor (RT) and double diffusive (DD) instabilities that can affect such two-layer stratifications right at the initial time of contact, diffusive-layer convection (DLC) as well as delayed-double diffusive (DDD) instabilities can set in at a later time when differential diffusion effects act upon the evolving density profile starting from an initial step-function profile between the two miscible solutions. The conditions for these instabilities to occur can therefore be obtained only by considering time evolving base-state profiles. To do so, we perform a linear stability analysis based on a quasi-steady-state approximation (QSSA) as well as nonlinear simulations of a diffusion–convection model to classify and analyse all possible buoyancy-driven instabilities of a stratification of a solution of a given solute A on top of another miscible solution of a species B. Our theoretical model couples Darcy's law to evolution equations for the concentration of species A and B ruling the density of the miscible solutions. The parameters of the problem are a buoyancy ratio R quantifying the ratio of the relative contribution of B and A to the density as well as δ, the ratio of diffusion coefficients of these two species. We classify the region of RT, DD, DDD and DLC instabilities in the (R, δ) plane as a function of the elapsed time and show that, asymptotically, the unstable domain is much larger than the one captured on the basis of linear base-state profiles which can only obtain stability thresholds for the RT and DD instabilities. In addition the QSSA allows one to determine the critical time at which an initially stable stratification of A above B can become unstable with regard to a DDD or DLC mechanism when starting from initial step function profiles. Nonlinear dynamics are also analysed by a numerical integration of the full nonlinear model in order to understand the influence of R and δ on the dynamics.

/pdf/buoyancy-driven-instabilities-of-miscible-two-layer-4l98iga9qn.pdf

Buoyancy-driven instabilities of miscible two-layer stratifications

We consider aspects of patternings that occur in a wide array of physical systems due to interacting combinations of dipolar, interfacial, charge exchange, entropic, and geometric influences. We review well-established phenomena as a basis for discussion of more recent developments. The materials of interest range from bulk inorganic solids and polymer organic melts to fluid colloids. Often, there are unifying principles behind the various modulated structures, such as the competition between surface or line tension and dipolar interaction in thermally reversible systems. Generally, their properties can be understood by free-energy minimization.

/pdf/modulated-phases-review-and-recent-results-4nsrn9xk9l.pdf

Modulated phases: review and recent results.

Patterns of convection in internally heated, self-gravitating rotating spherical fluid shells are investigated through numerical simulations. While turbulent states are of primary interest in planetary and stellar applications the present paper emphasizes more regular dynamical features at Rayleigh numbers not far above threshold which are similar to those which might be observed in laboratory or space experiments. Amplitude vacillations and spatial modulations of convection columns are common features at moderate and large Prandtl numbers. In the low Prandtl number regime equatorially attached convection evolves differently with increasing Rayleigh number and exhibits an early transition into a chaotic state. Relationships of the dynamical features to coherent structures in fully turbulent convection states are emphasized.

http://iopscience.iop.org/article/10.1088/1367-2630/5/1/397/pdf

Patterns of convection in rotating spherical shells

Editors' note: In the references cited we have used, as far as possible, the abbreviations for journals and reports used by Chemical Abstracts. A list of these abbrevi­ ations may be found in the List of Periodicals of the Chemical Abstracts Service published by the American Chemical Society. Transliteration of Russian names has essentially followed the system adopted by the Library of Congress, but with no distinction between e and e or between Η and fi, and with yu used for κ> and ya for H . In the case of books translated from Russian into English the transliterated author names are those appearing on the translation. Russian titles have been translated into English, but where a translation is indicated the title given is that appearing on the translated version. A source of an English translation for all cited Russian references has been given whenever known to the editors.

Cited References

A vertical stratification of a light and hot fluid over a heavy and cold one is expected to be stable with regard to buoyancy-driven convection. Here we show that chemical reactions can trigger convection around chemical fronts even in cases where concentration and heat both contribute to a stable density stratification. The balance between intrinsic thermal and solutal density gradients initiated by a spatially localized reaction zone and double diffusive mechanisms are at the origin of a new convective instability, the mechanism of which is explained by a displaced particle argument. Linear stability analysis of a reaction-diffusion-convection model confirmed by nonlinear simulations delimits the instability region in the parameter space spanned by the thermal and solutal Rayleigh numbers. Experimental systems in which to test our theoretical predictions are proposed.

/pdf/reaction-driven-convection-around-a-stably-stratified-58f1rs8ldc.pdf

Reaction driven convection around a stably stratified chemical front.

This work reports the first terrestrial laboratory study of thermal convection in a central body-force field. The force field is produced by gradients of magnetic field magnitude imposed on a spherical shell of heated, magnetizable fluid. Cells of thermal convection consistent with the notion of continental drift are detected using infrared imaging. Transitions of symmetry for the patterns of convection are observed in the range of Earth's Rayleigh number.

A. Zebib

Papers

Reaction driven convection around a stably stratified chemical front.

Laboratory Study of Spherical Convection in Simulated Central Gravity