Fabien Palencia

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.

Master singular behavior from correlation length measurements for seven one-component fluids near their gas-liquid critical point

We present the master (i.e., unique) behavior of the correlation length, as a function of the thermal field along the critical isochore, asymptotically close to the gas-liquid critical point of xenon, krypton, argon, helium-3, sulfur hexafluoride, carbon dioxide, and heavy water. It is remarkable that this unicity extends to the correction-to-scaling terms. The critical parameter set, which contains all the needed information to reveal the master behavior, is composed of four thermodynamic coordinates of the critical point and one adjustable parameter which accounts for quantum effects in the helium-3 case. We use a scale dilatation method applied to the relevant physical variables of the one-component fluid subclass, in analogy with the basic hypothesis of the renormalization theory. This master behavior for the correlation length satisfies hyperscaling. We finally estimate the thermal field extent where the critical crossover of the singular thermodynamic and correlation functions deviates from the theoretical crossover function obtained from field theory.

Granular gas in weightlessness: The limit case of very low densities of non interacting spheres

Experiments on non interacting balls in a vibrated box are reported. In a first experiment with an electromagnetic vibrator on earth or in board of Airbus A300 of CNES, the 1-ball dynamics exhibit little transverse motion and an intermittent quasi periodic motion along the direction parallel to the vibration. This behaviour proves a significant reduction of the phase space dimension of this billiard-like system from 11- d to 3- d or 1- d. It is caused by dissipation, which generates non ergodic dynamics. This experiment exemplifies the coupling between translation and rotation degrees of freedom during the collisions with the walls, due to solid friction at contacts. This eliminates ball rotation and freezes transverse velocity fluctuations. This trend is confirmed by 3d simulations with JJ Moreau discrete element code. A two-ball experiment performed under zero-g conditions in the Maxus 5 flight confirms the trend; the quasi-periodicity is found much greater, which is probably due to an improvement of experimental conditions. The two balls are not in perfect synchronisation showing the effect of small random noise; but the particles has never collided. This is then the normal dynamics of a gas of non-interacting dilute spherical grains in a vibrated container.

Master crossover behavior of parachor correlations for one-component fluids

The master asymptotic behavior of the usual parachor correlations, expressing surface tension sigma as a power law of the density difference rho(L)-rho(V) between coexisting liquid and vapor, is analyzed for a series of pure compounds close to their liquid-vapor critical point, using only four critical parameters (beta(c))-1 , alpha(c) , Z(c) , and Y(c) , for each fluid. This is accomplished by the scale dilatation method of the fluid variables where, in addition to the energy unit (beta(c))-1 and the length unit alpha(c) , the dimensionless numbers Z(c) and Y(c) are the characteristic scale factors of the ordering field along the critical isotherm and of the temperature field along the critical isochore, respectively. The scale dilatation method is then formally analogous to the basic system-dependent formulation of the renormalization theory. Accounting for the hyperscaling law delta-1/delta+1=eta-2/2d , we show that the Ising-like asymptotic value pi(a) of the parachor exponent is unequivocally linked to the critical exponents eta or delta by pi(a)/d-1=2/d-(2-eta)=delta+1/d (here d=3 is the space dimension). Such mixed hyperscaling laws combine either the exponent eta or the exponent delta , which characterizes bulk critical properties of d dimension along the critical isotherm or exactly at the critical point, with the parachor exponent pi(a) which characterizes interfacial properties of d-1 dimension in the nonhomogeneous domain. Then we show that the asymptotic (symmetric) power law [abstract; see text] is the two-dimensional critical equation of state of the liquid-gas interface between the two-phase system at constant total (critical) density rho(c) . This power law complements the asymptotic (antisymmetric) form [abstract; see text] of the three-dimensional critical equation of state for a fluid of density rho not equal to rho_(c) and pressure p not equal to p_(c) , maintained at constant (critical) temperature T=T_(c)} [mu_(rho)(mu_(rho,c)) is the specific (critical) chemical potential; p_(c) is the critical pressure; and T_(c) is the critical temperature]. We demonstrate the existence of the related universal amplitude combination [abstract; see text] = universal constant, constructed with the amplitudes D_(rho)(sigma) and D_(rho)(c) , separating then the respective contributions of each scale factor Y_(c) and Z_(c) , characteristic of each thermodynamic path, i.e., the critical isochore and the critical isotherm (or the critical point), respectively. The main consequences of these theoretical estimations are discussed in light of engineering applications and process simulations where parachor correlations constitute one of the most practical methods for estimating surface tension from density and capillary rise measurements.

Long range boundary effect of 2D intermediate number density vibro-fluidized granular media in micro-gravity

We present a micro-gravity experimental study of the statistical properties of intermediate number density vibro-fluidized inelastic spheres in a rectangular container. It is found that although when taking all the particles into account, the probability distributions of velocities both along and perpendicular to the vibration direction are exponential and symmetric, when dividing particles along the vibration direction into different bins, the local velocity distributions are found to deviate measurably from a symmetric distribution for the velocity component in the vibrating direction. The skewness analysis of the local distribution profiles for vx and vy shows that the local distribution of vx remains symmetric, however, the skewness of the distribution profile in vy changes nearly linear from positive to negative with skew = 0 near the center bin. This indicates a long range boundary effect of the asymmetry in vy. We further studied the hydrodynamic profiles granular pressure px and py, and temperature Tx and Ty in positive and negative components such as p+x and p−x, and Tx+ and Tx−, in accordance with the sign of velocity components. The profiles for the two components are found different along the y direction. Along vibration direction granular medium is found inhomogeneous and anisotropic not only in the particle number densities, but also in vy, py and Ty. This suggests new hydrodynamical modeling is needed for such vibro-fluidized granular systems.

An instrument for studying granular media in low-gravity environment

A new experimental facility has been designed and constructed to study driven granular media in a low-gravity environment. This versatile instrument, fully automatized, with a modular design based on several interchangeable experimental cells, allows us to investigate research topics ranging from dilute to dense regimes of granular media such as granular gas, segregation, convection, sound propagation, jamming, and rheology-all without the disturbance by gravitational stresses active on Earth. Here, we present the main parameters, protocols, and performance characteristics of the instrument. The current scientific objectives are then briefly described and, as a proof of concept, some first selected results obtained in low gravity during parabolic flight campaigns are presented.