Miscible Fluids Research Articles

Miscible Fluids in Microgravity (MFMG): A zero-upmass investigation on the International Space Station

Miscible Fluids in Microgravity (MFMG) was a zero-upmass investigation performed on the International Space Station. The goal of MFMG was to determine if interfacial phenomena seen with immiscible fluids could be seen with miscible fluids. The experiments had to be performed with existing materials on the ISS. Honey and water were chosen as the fluids, and urine collection syringes were used as the vessels in which the experiments were performed. In March 2004 (Increment 8) Dr. Michael Foale performed four experiments under isothermal conditions to determine: If a stream of honey injected into water would exhibit the Rayleigh-Tomotika instability and break into small drops. If an aspherical drop of water in honey would spontaneously assume a spherical shape. The experiments were performed successfully. During Increment 9, Mike Fincke performed two runs in which a stream of honey was injected into water while the syringe was attached to the surface of the Commercial Generic Bioprocessing Apparatus (CGBA) at approximately 31° C. No change in the stream shape was observed. Two more runs were performed on Increments 10 and 11 but no additional phenomena were observed. No behavior beyond simple diffusion was observed. We performed simulations with the Navier-Stokes equations plus a Korteweg stress term. We estimated that the maximum possible value of the square gradient parameter was 10−12 N for the honey-water system.

Experimental study of the single-mode three-dimensional Rayleigh-Taylor instability

The three-dimensional Rayleigh-Taylor instability is studied in a low Atwood number (A≈0.15) miscible fluid system. The two fluids are contained within a Plexiglas tank that is mounted on vertical rails and accelerated downward by a weight and pulley system. A net acceleration between 13 and 23m∕s2 can be maintained, resulting in an effective body force equivalent to 0.33–1.35 times Earth’s gravity. A single-mode, three-dimensional perturbation is produced by oscillating the tank, which has a square cross section, along its diagonal. Early time measured growth rates are shown to have good agreement with linear stability theory. At late time, the instability exhibits a nonconstant vertical interfacial velocity in agreement with the recent numerical computations of Ramaprabhu et al. [Phys. Rev. E 74, 066308 (2006)]. Both the late-time bubble and spike velocities have values greater than those predicted by both the simple buoyancy-drag model developed by Oron et al. [Phys. Plasmas 8, 2883 (2001)] and the potential flow model of Goncharov [Phys. Rev. Lett. 88, 134502 (2002)]. The disagreement with the models can be attributed to the formation of vortices, in this case vortex rings, observed in the experiments but not accounted for by the models.

Advances in Diffusivity Measurement of Solvents in Oil Sands

Abstract This work deals with the prediction of mass transfer of solvents in bitumen in the presence and absence of sand through a unified model that uses magnetic resonance response information. Experiments were performed with pairs of solvents and bitumen in the presence of sand and without sand. Low field NMR was used to acquire spectra of the migrating solvent in bitumen or oil sand as a function of time. The experimental results of this work, along with data collected previously on similar systems in the Tomographic Imaging and Porous Media Laboratory, were fit together in a one-dimensional Fickian model. The novelty of the presented approach is not only that the new model matches all the experiments to date, but also that this matching can be done independently and without external input parameters. In previous work, matching could only be achieved if the depth of solvent penetration was provided through external measurements. The present model predicts diffusivities of solvents in bitumen in the presence of sand to be in the same order of magnitude and a bit lower than diffusivities of solvent in bulk bitumen. It is anticipated that this method would be of value when estimates of mass transfer in solvent-based heavy oil processes are attempted in the field. Introduction In solvent-based recovery processes for heavy oil and bitumen, mass transfer phenomena compete with viscous forces, gravity and capillary forces as the predominant means for oil recovery or trapping. In order to understand the relative merit of such forces, one must be able to measure mass transfer at reservoir conditions and potentially verify such measurements in the field. There is considerable literature on the measurement of recovery mechanisms and recovery efficiency through solvent-based processes for heavy oil and bitumen. The bulk of the work presented in the recent literature focuses around the VAPEX (Vapour Extraction) process, but the fundamental work presented can easily apply to any solvent displacement process. If we were to measure mass transfer phenomena in the field, it appears that a possible logging tool with significant potential is magnetic resonance. Thus, the TIPM group has embarked in a project whereby magnetic resonance is used for the determination of bitumen (or heavy oil) solvent interactions. As two miscible fluids are in contact, they will slowly diffuse into each other. This molecular transport of one substance relative to another is known as diffusion. With time, the interface between the fluids will appear as a diffused mixed zone grading from one pure fluid to the other. The mechanism of diffusion happens due to the random motion of molecules(1,2). The diffusion flux between solvent and heavy oil can be defined as the flow due to concentration gradient between solvent and heavy oil. The diffusion phenomena take place when there is no mixing in the system and the only driving force is the concentration gradient, unlike dispersion that is caused due to convective fluid mixing in the porous medium. It was observed that as solvent and heavy oil diffuse into each other, the mobility of hydrogen bearing molecules of both oil and solvent change(3).

Buoyancy-driven variable-density turbulence

Buoyancy-generated motions in an unstably stratified medium composed of two incompressible miscible fluids with different densities, as occurs in the variable-density Rayleigh–Taylor instability, are examined using direct numerical simulations. The non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study: (i) the nature of variable density turbulence, (ii) the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy; (iii) the role of non-Boussinesq effects; and (iv) a parameterization of the initial conditions by a static Reynolds number. Simulations are performed for Atwood numbers up to 0.5 with root mean square density up to 50% of the mean density and Schmidt numbers, 0.1 ≤ Sc ≤ 2. The benchmark problem has been designed to have the largest mass flux possible and is, in this configuration, the maximally unstable non-equilibrium flow possible. It is found that the mass flux, owing to its central role in the conversion of potential to kinetic energy, is probably the single most important dynamical quantity to predict in lower-dimensional models. Other primary findings include the evolution of the mean pressure gradient: during the non-Boussinesq portions of the flow, the evolution of the mean pressure gradient is non-hydrostatic (as opposed to a Boussinesq fluid) and is set by the evolution of the specific volume pressure gradient correlation. To obtain the numerical solution, a new pressure projection algorithm which treats the pressure step exactly, useful for simulations of non-solenoidal velocity flows, has been constructed.

Coiled flow inverter as an inline mixer

Helical coils are widely used in the process industries to improve the mixing efficiency under laminar flow conditions. It was further observed that in the regular helical coils, there exists a confined region in the tube cross-section where fluids are entrapped and can escape only by diffusion. In the present work, an attempt has been made to further enhance the mixing in the coiled tube at low Dean number using the phenomenon of flow inversion. The study is performed in coiled flow inverter (CFI) [Saxena, A.K., Nigam, K.D.P., 1984. Coiled configuration for flow inversion and its effect on residence time distribution. A.I.Ch.E. Journal 30, 363–368] which was developed using the concept of inverting the direction of fluid by 90 ∘ . It comprises coils with equidistant 90 ∘ bends. The scalar mixing of two miscible fluids has been quantified for different process conditions (Dean number, Schmidt number and number of bends) by using scalar transport technique. There was a significant increase in mixing performance of CFI as compared to regular helical coils at low Dean number. The mixing efficiency increased with the increase in Dean number and number of bends. It was also observed that the mixing performance was enhanced with increase in Schmidt number. A new correlation has been proposed for unmixedness coefficient of CFI as a function of Dean number, Schmidt number and number of bends. The proposed correlation has maximum error of ± 20 % with the numerical predictions.

Convergence analysis of an approximation to miscible fluid flows in porous media by combining mixed finite element and finite volume methods

AbstractThis article deals with development and analysis of a numerical method for a coupled system describing miscible displacement of one incompressible fluid by another through heterogeneous porous media. A mixed finite element (MFE) method is employed to discretize the Darcy flow equation combined with a conservative finite volume (FV) method on unstructured grids for the concentration equation. It is shown that the FV scheme satisfies a discrete maximum principle. We derive L∞ and BV estimates under an appropriate CFL condition. Then we prove convergence of the approximate solutions to a weak solution of the coupled system. Numerical results are presented to see the performance of the method in two space dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008

Fragmentation instabilities of a drop as it falls in a miscible fluid

We review here a series of experiments on the fragmentation instabili- ties that a liquid drop undergoes as it falls inside a fluid with which it is miscible, so called the solvent. Motivated by the original experiments initiated by Thomson and Newall in 1885, we started to investigate this subject more than one decade ago, encountering up to date a number of challenging problems in hydrodynam- ical instabilities, complicated by the presence of transient interfaces between the drop and the solvent. In particular, we have shown that when a drop of liquid is deposited over the surface of the same liquid, it falls down inside the solvent because the energy associated to its surface tension against air is instantaneously converted into kinetic energy. As a consequence, a very fast fluid injection takes place as the drop touches the free surface of the solvent and the drop enters inside the solvent. Due to the hydrodynamical instabilities related to the large velocity gradients, it develops into a ring that expands radially. The ring continues to go downwards inside the solvent until it stops at a certain height due to viscous dissipation. In the first stages of the ring expansion, a fluid membrane remains attached to the ring, so-called "turban" for its shape, which is concave or con- vex depending on the sign of the density difference between the drop and the solvent. When a small density difference is introduced between the drop and the solvent, the ring becomes unstable because of density gradients and it fragments into smaller droplets. On their turn, the secondary droplets may undergo the same instability and may fragment again, so that a cascade of fragmentation takes place. If the density difference is positive, that is, the drop is heavier than the solvent, the secondary droplets continue to go down deeper inside the solvent, until the whole process is washed out by the slow diffusion of the concentration gradients. When the density difference between the drop and the solvent is negative, then the secondary droplets rise up to the free surface of the solvent, where they are distorted by the equivalent of an impact with a rigid wall. Universal scaling laws for the cascade of fragmentation and for the dynamical behavior of the drop have been derived and accompany the experimental observations.

Miscible viscous fingering with linear adsorption on the porous matrix

Viscous fingering between miscible fluids of different viscosities can affect the dispersion of finite samples in porous media. In some applications, as typically in chromatographic separations or pollutant dispersion in underground aquifers, adsorption onto the porous matrix of solutes (the concentration of which rules the viscosity of the solution) can affect the fingering dynamics. Here, we investigate theoretically the influence of such an adsorption on the stability and nonlinear properties of viscous samples displaced in a two-dimensional system by a less viscous and miscible carrying fluid. The model is based on Darcy’s law for the evolution of the fluid velocity coupled to a diffusion-convection equation for the concentration of a solute in the mobile phase inside the porous medium. The adsorption-desorption dynamics of the solute onto the stationary phase is assumed to be at equilibrium, to follow a linear isotherm and is characterized by a retention parameter κ′ equal to the adsorption-desorption equilibrium constant K multiplied by the phase ratio F. In practice, retention on the porous matrix renormalizes the log-mobility ratio by a factor (1+κ′). Correspondingly, a linear stability analysis and nonlinear simulations of the model show that an increase of κ′ leads to a stabilization of viscous fingering with fingers appearing on a dimensional time scale multiplied by (1+κ′)3 and with a dimensional wavelength multiplied by (1+κ′).

Fluid Fluid Interactions in the Earth's Lithosphere

Fluids rich in water, carbon and sulfur species and a variety of dissolved salts are a ubiquitous transport medium for heat and matter in the Earth’s interior. Fluid transport through the upper mantle and crust controls the origin of magmatism above subduction zones and results in natural risks of explosive volcanism. Fluids passing through rocks affect the chemical and heat budget of the global oceans, and can be utilized as a source of geothermal energy on land. Fluid transport is a key to the formation and the practical utilization of natural resources, from the origin of hydrothermal mineral deposits, through the exploitation of gaseous and liquid hydrocarbons as sources of energy and essential raw materials, to the subsurface storage of waste materials such as CO2. Different sources of fluids and variable paths of recycling volatile components from the hydrosphere and atmosphere through the solid interior of the Earth lead to a broad range of fluid compositions, from aqueous liquids and gases through water-rich silicate or salt melts to carbon-rich endmember compositions. Different rock regimes in the crust and mantle generate characteristic ranges of fluid composition, which depending on pressure, temperature and composition are miscible to greatly variable degrees. For example, aqueous liquids and vapors are increasingly miscible at elevated pressure and temperature. The degree of this miscibility is, however, greatly influenced by the presence of additional carbonic or salt components. A wide range of fluid–fluid interactions results from this partial miscibility of crustal fluids. Vastly different chemical and physical properties of variably miscible fluids, combined with fluid flow from one pressure – temperature regime to another, therefore have major consequences for the chemical and physical evolution of the crust and mantle. Several recent textbooks (e.g., Walther and Wood 1986; Carrol and Holloway 1994; Shmulovich et al. 1995 …

The effects of gravity modulation on fluid mixing. Part 2. Stochastic modulation

We study numerically the effects of zero-mean stochastic gravity modulation on the mixing characteristics of two interdiffusing miscible Boussinesq fluids initially separated by a thin diffusion layer. The gravity modulation has a Gaussian probability distribution and is characterized by an exponentially damped cosine autocorrelation function, i.e. $\langle g(t) g(t+\tau)\rangle/\langle g^{2}(t)\rangle\,{=}\,{\rm e}^{-\lambda \tau} \cos (\omega \tau)$. The associated power spectrum is a Lorentzian with peak at ω and width λ. The flow is found to depend on the following parameters: the Grashof number, Gr, based on the viscous length scale, $l_{\nu}\,{=}\,\sqrt{{\nu}/{\omega}}$; the Schmidt number, Sc; the correlation exponent, λ; and other geometric parameters. Even for extremely small Gr, we observe the propagation of gravity currents, Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instabilities. This is in contrast to the case of harmonic modulation considered in Part 1 (Siddavaram & Homsy J. Fluid Mech. vol. 562, 2006, p. 445) wherein these phenomena occur sequentially as Gr increases. The mixed volume is found to vary non-monotonically with the correlation exponent, λ, with narrow-band modulation having the largest mixed volume followed by harmonic modulation and then broadband modulation. This non-monotonicity of the mixed volume with λ is explained on the basis of the competition between the effects of excitation of lower frequencies, which lead to higher mixing, and the effects of the reduction in the energy content at the dominant frequency, which leads to reduced mixing. The value of the correlation coefficient, λ, at which the mixed volume is the largest is found to be independent of Gr. To understand the finer details of the mechanisms, we consider two- and three-frequency modulations. We find that increasing the amplitude of the secondary component when its frequency is smaller than that of the primary component leads to the occurrence of KH and RT instabilities at smaller Gr than that for the case of single-frequency modulation. We have understood the non-monotonic variation in the mixed volume by considering a three-frequency modulation, where one of the frequencies is smaller than the characteristic frequency and the other larger.

Emulsification of Partially Miscible Liquids Using Colloidal Particles: Nonspherical and Extended Domain Structures

We present microscopy studies of particle-stabilized emulsions with unconventional morphologies. The emulsions comprise pairs of partially miscible fluids and are stabilized by colloids. Alcohol-oil mixtures are employed; silica colloids are chemically modified so that they have partial wettability. We create our morphologies by two distinct routes: starting with a conventional colloid-stabilized emulsion or starting in the single-fluid phase with the colloids dispersed. In the first case temperature cycling leads to the creation of extended fluid domains built around some of the initial fluid droplets. In the second case quenching into the demixed region leads to the formation of domains which reflect the demixing kinetics. The structures are stable due to a jammed, semisolid, multilayer of colloids on the liquid-liquid interface. The differing morphologies reflect the roles in formation of the arrested state of heterogeneous and homogeneous nucleation and spinodal decomposition. The latter results in metastable, bicontinuous emulsions with frozen interfaces, at least for the thin-slab samples, investigated here.

Evidence for the Existence of an Effective Interfacial Tension between Miscible Fluids. 2. Dodecyl Acrylate−Poly(dodecyl acrylate) in a Spinning Drop Tensiometer

We studied drops of dodecyl acrylate in poly(dodecyl acrylate) (molecular weight of 25,000) in a spinning drop tensiometer to determine whether an effective interfacial tension (EIT) existed between these two miscible fluids. We found convincing evidence. We estimated the mechanical relaxation time from an immiscible analogue (1-propanol and poly(dodecyl acrylate)) and showed that the dodecyl acrylate drops maintained quasi-steady diameters long after this relaxation period. Drops continuously grew in length and became more diffuse, but the width of the transition zone did not grow with t(1/2) as expected from Fick's law although this system had been shown to follow Fick's law in a static configuration (Antrim, D.; Bunton, P.; Lewis, L. L.; Zoltowski, B. D.; Pojman, J. A. J. Phys. Chem. B 2005, 109, 11842-11849). The EIT was determined from Vonnegut's equation, EIT = (Deltarho)omega(2)r(3)/4; both the inner and outer diameters were measured, yielding values of 0.002 and 0.02 mN m(-1), respectively. The EIT was found to be independent of the rotation rate above 6000 rpm and independent of the initial drop volume. The EIT was found to decrease with temperature and increase with the difference in concentration between the monomer drop and polymer-monomer fluid. The square gradient parameter, k, was determined from EIT = k(Deltac(2)/delta), where Deltac is the difference in mole fraction and delta is the width of the transition zone. The square gradient parameter was on the order of 10(-9) N. The square gradient parameter was found to decrease with temperature, to be independent of concentration, and to increase with the molecular weight of the polymer.

Mathematical and numerical study of a system of conservation laws

The system of equations (f (u)) t − (a(u)v + b(u)) x = 0 and u t − (c(u)v + d(u)) x = 0, where the unknowns u and v are functions depending on $${(x, t) \, \in \, \mathbb{R} \times \mathbb{R}_+}$$ , arises within the study of some physical model of the flow of miscible fluids in a porous medium. We give a definition for a weak entropy solution (u, v), inspired by the Liu condition for admissible shocks and by Krushkov entropy pairs. We then prove, in the case of a natural generalization of the Riemann problem, the existence of a weak entropy solution only depending on x/t. This property results from the proof of the existence, by passing to the limit on some approximations, of a function g such that u is the classical entropy solution of u t − ((cg + d)(u)) x = 0 and simultaneously w = f (u) is the entropy solution of w t − ((ag + b)(f(−1)(w))) x = 0. We then take v = g(u), and the proof that (u, v) is a weak entropy solution of the coupled problem follows from a linear combination of the weak entropy inequalities satisfied by u and f (u). We then show the existence of an entropy weak solution for a general class of data, thanks to the convergence proof of a coupled finite volume scheme. The principle of this scheme is to compute the Godunov numerical flux with some interface functions ensuring the symmetry of the finite volume scheme with respect to both conservation equations.

Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media

We study a finite volume discretization of a strongly coupled elliptic-parabolic PDE system describing miscible displacement in a porous medium. We discretize each equation by a finite volume scheme which allows a wide variety of unstructured grids (in any space dimension) and gives strong enough convergence for handling the nonlinear coupling of the equations. We prove the convergence of the scheme as the time and space steps go to $0$. Finally, we provide numerical results to demonstrate the efficiency of the proposed numerical scheme.

Hydrodynamically tunable optofluidic cylindrical microlens

In this work, we report the design, fabrication, and characterization of a tunable optofluidic microlens that focuses light within a microfluidic device. The microlens is generated by the interface of two co-injected miscible fluids of different refractive indices, a 5 M CaCl(2) solution (n(D) = 1.445) and deionized (DI) water (n(D) = 1.335). When the liquids flow through a 90-degree curve in a microchannel, a centrifugal effect causes the fluidic interface to be distorted and the CaCl(2) solution bows outwards into the DI water portion. The bowed fluidic interface, coupled with the refractive index contrast between the two fluids, yields a reliable cylindrical microlens. The optical characteristics of the microlens are governed by the shape of the fluidic interface, which can be altered by simply changing the flow rate. Higher flow rates generate a microlens with larger curvature and hence shorter focal length. The changing of microlens profile is studied using both computational fluid dynamics (CFD) and confocal microscopy. The focusing effect is experimentally characterized through intensity measurements and image analysis of the focused light beam, and the experimental data are further confirmed by the results from a ray-tracing optical simulation. Our investigation reveals a simple, robust, and effective mechanism for integrating optofluidic tunable microlenses in lab-on-a-chip systems.

Mass Transfer Analysis of Calcium in Concrete Using the Lattice Kinetic Scheme for a Binary Miscible Fluid Mixture

The lattice kinetic scheme (LKS) for a binary miscible fluid mixture is a applied to mass transfer analysis of Calcium in concrete. In general, cement paste that is a major component of concrete is a porous medium with three-dimensional complicated geometries. The present concrete structure is determined on the basis of experimental data previously obtained by high-intensity X-Ray Computed Tomography (X-Ray-CT). As for the numerical method, the LKS, which is an improved scheme of the original lattice Boltzmann method (LBM), is employed to save computation memory and to maintain numerical stability. First, an unsteady convection-diffusion problem is calculated and the accuracy of the method and error norms with different lattice resolutions are investigated. Next, the mass transfer problem of Calcium in concrete is simulated. Pressure drops in the concrete are calculated for different Reynolds numbers and compared with the empirical equation based on experimental data. Also, velocity fields and concentration profiles are obtained at a pore scale in the structure with heterogeneous mass diffusivity. These simulations indicate that the present method can be useful for prediction of Calcium leaching in concrete from the microscopic point of view.

Continuous-velocity lattice gas cellular automata for miscible binary fluid and its application to simulation of interface instability

Continuous-velocity lattice gas cellular automata (CVLGA) is extended to miscible binary fluid systems. A new parameter is introduced in order to control the diffusivity of the fluids. The correlation between the diffusivity and the new parameter proves that there exists the maximum value of the diffusivity. Quantitative verifications of the model are carried out with numerical simulations of the diffusion phenomena across a falling fluid film. The model is then applied to the simulations of Rayleigh–Taylor instability during the gravitational mixing phenomena. The qualitative tendency of the growth of the interface instability is the same as that obtained in conventional numerical methods.

General continuum boundary conditions for miscible binary fluids from molecular dynamics simulations

Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated.

Fluid flow and mixing in rough‐walled fracture intersections

Fracture intersections play a basic role in contaminant transport through fracture networks because they allow different fluids to mix and disperse along the flow paths. We use experimental and numerical methods to understand and improve predictions of these phenomena. Laboratory experiments of mixing between two miscible fluids were performed within an artificial, rough‐walled fracture intersection made of textured glass. We also develop a numerical model of mixing based on local application of streamline routing within the irregular aperture distribution of the intersection. This model shows good agreement with the laboratory experiments, both in the amount of average mixing and in the spatial distribution of dye streamlines. The numerical model is used to generalize our results based on aperture statistics, and shows that mixing is significantly affected by how well apertures correlate across the intersection, especially as fractures are closed. We conclude that flow channelization through rough‐walled intersecting fractures significantly enhances physical mixing compared to intersecting parallel plates. Relative to transport through parallel plate aperture networks, surface roughness may reduce solute dilution and increase solute dispersion.

Stability diagram and effect of initial density stratification for a two-layer system in a supercritical fluid

A numerical study of the stability in a two-layer system filled with a single pure supercritical fluid subjected to an initial temperature difference is performed. The very large compressibility and the very low heat diffusivity of near-critical fluids lead to a Rayleigh-Taylor-like gravitational instability of the heat diffusion layer. This instability is similar to the one of two miscible fluids where molecular species diffusion coefficient is replaced by the heat diffusion coefficient. Our numerical results are consistent with respect to the dispersion relation derived by Duff et al. [Phys. Fluids 5, 417 (1962)] for a system of two incompressible miscible fluids (argon-bromine mixture falling into helium or air). It has also been shown that when the thickness of the lower layer becomes smaller than the heat diffusion length based on the maximum growth rate, the system is stable [Phys. Fluids 17, 054102 (2005)]. A linear stability diagram has been established as a function of three parameters: the thickness of the lower layer, the density difference between the two layers and the distance to the critical point. When the critical point is approached, the high initial stratification (due to the high compressibility) of this Rayleigh-Taylor-like configuration has seen the effect of stabilizing the system.