In the gravity field, density changes triggered by a kinetic scheme as simple as A þ B ! C can induce or affect buoyancy-driven instabilities at a horizontal interface between two solutions containing initially the scalars A and B. On the basis of a general reaction-diffusion-convection model, we analyze to what extent the reaction can destabilize otherwise buoyantly stable density stratifications. We furthermore show that, even if the underlying nonreactive system is buoyantly unstable, the reaction breaks the symmetry of the developing patterns. This is demonstrated both numerically and experimentally on the specific example of a simple acid-base neutralization reaction. DOI: 10.1103/PhysRevLett.104.044501 PACS numbers: 82.40.Ck, 47.20.Bp, 47.70.Fw, 82.33.Ln Convective motion due to hydrodynamic instabilities of an interface between two different fluids are known to impact the spatiotemporal distribution and dynamics of passive scalars in numerous applications. Much less studied is the active role that processes involving such scalars can have upon the flow dynamics if these scalars influence a physical property of the fluid such as its density for instance [1][2][3][4]. However, coupling between reactivetype processes and hydrodynamics is at the heart of applications in fields as diverse as earth mantle dynamics [5], geological formations [6], supernovae dynamics [7] or CO 2 sequestration [8], to name a few. Often, the specific active role of the scalars on the flow remains difficult to interpret due to difficulties of in situ experiments, as well as a lack of quantitative modeling and of simple benchmark experiments on which theories could be tested. In this respect, it is still unclear to what extent reactions involving these scalars can trigger hydrodynamic instabilities in a system that would otherwise remain stable and whether convective structures have the same symmetries in reactive and nonreactive situations.To gain insight into these issues, let us consider the generic case of a solution containing the scalar A put on top of a solution of B in the gravity field. For nonreactive systems, various hydrodynamic instabilities can impact such a stratification of miscible fluids. The RayleighTaylor instability occurs when the heavier fluid overlies the lighter fluid [9]. If the upper fluid is lighter, the system can also be destabilized either if B diffuses faster than A, because of double-diffusive fingering [10,11], or if a diffusive-layer convection (DLC) instability is triggered when A diffuses faster than B [12]. In all cases, these buoyancy-driven instabilities lead, in nonreactive miscible fluids, to convective motions which develop similarly above and below the initial contact line because of the symmetry of the underlying density gradient [9][10][11][12]. The situation can however be very different if a chemical reaction takes place between species A and B upon contact and mixing of the solutions.We demonstrate indeed both theoretically and experimentally that a reaction as simple as A þ B ! C ...

Buoyancy-driven flows induced by the hydrodynamic Rayleigh-Taylor or doublediffusive instabilities develop symmetrically around the initial contact line when two solutions of given solutes with different densities are put in contact in the gravitational field. If the solutes affecting the densities of these solutions are involved in chemical reactions, changes in composition due to the underlying reaction-diffusion processes can modify the density profile in space and time, and affect the hydrodynamic patterns. In particular, if the density difference between the two reactant solutions is not too large, the resulting chemo-hydrodynamic patterns are asymmetric with regard to the initial contact line. We quantify both experimentally and numerically this asymmetry showing that fingers here preferentially develop above the reaction zone and not across the mixing zone as in the non reactive situation. In some cases, the reaction can even lead to the onset of a secondary double-diffusive instability between the product of the reaction, dynamically generated in situ, and one of the reactants.

The structure of a shock wave propagating through a hard-sphere gas is obtained by the Direct Simulation Monte Carlo method (DSMC), in the limit of infinitely large Mach number. The shock profiles and the distribution function of molecular velocities f are compared with Grad’s and Mott–Smith approximations. It is shown that the “regular” part of f, exhibits a singularity in the velocity space at the location of the upstream bulk speed.

The validity of the principle of corresponding states is investigated for the case of a potential with more than one intrinsic length scale. The planar surface tension of coexisting liquid and vapor phases of a fluid of Lennard-Jones atoms is studied as a function of the range of the potential using both Monte Carlo simulations and density functional theory (DFT). The interaction range is varied from r(c)(*) = 2.5 to r(c)(*) = 6 and the surface tension is determined for temperatures ranging from T(*) = 0.7 up to the critical temperature in each case. The simulation results are consistent with previous studies and are shown to obey the law of corresponding states even though the potential has two intrinsic length scales. It is further shown that the corresponding states principle can also be used to enhance the accuracy of some, but not all, DFT calculations of the surface tension. The results show that most of the cutoff dependence of the surface tension can be explained as a result of changes in the cutoff-dependent phase diagram and that corresponding states can be a useful tool for explaining differences between theory and simulation.

The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.