Visual analysis of density and velocity profiles in dense 3D granular gases.

Granular multiparticle ensembles are of interest from fundamental statistical viewpoints as well as for the understanding of collective processes in industry and in nature. Extraction of physical data from optical observations of three-dimensional (3D) granular ensembles poses considerable problems. Particle-based tracking is possible only at low volume fractions, not in clusters. We apply shadow-based and feature-tracking methods to analyze the dynamics of granular gases in a container with vibrating side walls under microgravity. In order to validate the reliability of these optical analysis methods, we perform numerical simulations of ensembles similar to the experiment. The simulation output is graphically rendered to mimic the experimentally obtained images. We validate the output of the optical analysis methods on the basis of this ground truth information. This approach provides insight in two interconnected problems: the confirmation of the accuracy of the simulations and the test of the applicability of the visual analysis. The proposed approach can be used for further investigations of dynamical properties of such media, including the granular Leidenfrost effect, granular cooling, and gas-clustering transitions.

Measuring the Transition Rates of Coalescence Events during Double Phase Separation in Microgravity.

Phase transition is a ubiquitous phenomenon in nature, science and technology. In general, the phase separation from a homogeneous phase depends on the depth of the temperature quench into the two-phase region. Earth's gravity masks the details of phase separation phenomena, which is why experiments were performed under weightlessness. Under such conditions, the pure fluid sulphur hexafluoride (SF 6 ) near its critical point also benefits from the universality of phase separation behavior and critical slowing down of dynamics. Initially, the fluid was slightly below its critical temperature with the liquid matrix separated from the vapor phase. A 0.2 mK temperature quench further cooled down the fluid and produced a double phase separation with liquid droplets inside the vapor phase and vapor bubbles inside the liquid matrix, respectively. The liquid droplets and the vapor bubbles respective distributions were well fitted by a lognormal function. The evolution of discrete bins of different radii allowed the derivation of the transition rates for coalescence processes. Based on the largest transition rates, two main coalescence mechanisms were identified: (1) asymmetric coalescences between one small droplet of about 20 µ m and a wide range of larger droplets; and (2) symmetric coalescences between droplets of large and similar radii. Both mechanisms lead to a continuous decline of the fraction of small radii droplets and an increase in the fraction of the large radii droplets. Similar coalescence mechanisms were observed for vapor bubbles. However, the mean radii of liquid droplets exhibits a t 1 / 3 evolution, whereas the mean radii of the vapor bubbles exhibit a t 1 / 2 evolution.

Pattern Evolution during Double Liquid-Vapor Phase Transitions under Weightlessness.

Phase transition in fluids is ubiquitous in nature and has important applications in areas such as the food industry for volatile oils' extraction or in nuclear plants for heat transfer. Fundamentals are hampered by gravity effects on Earth. We used direct imaging to record snapshots of phase separation that takes place in sulfur hexafluoride, SF6, under weightlessness conditions on the International Space Station (ISS). The system was already at liquid-vapor equilibrium slightly below the critical temperature and further cooled down by a 0.2-mK temperature quench that produced a new phase separation. Both full view and microscopic views of the direct observation cell were analyzed to determine the evolution of the radii distributions. We found that radii distributions could be well approximated by a lognormal function. The fraction of small radii droplets declined while the fraction of large radii droplets increased over time. Phase separation at the center of the sample cell was visualized using a 12× microscope objective, which corresponds to a depth of focus of about 5 µ m. We found that the mean radii of liquid droplets exhibit a t 1 / 3 evolution, in agreement with growth driven by Brownian coalescence. It was also found that the mean radii of the vapor bubbles inside the liquid majority phase exhibit a t 1 / 2 evolution, which suggest a possible directional motion of vapor bubbles due to the influence of weak remaining gravitational field and/or a composition Marangoni force.

Direct imaging of long-range concentration fluctuations in a ternary mixture.

We used a direct imaging technique to investigate concentration fluctuations enhanced by thermal fluctuations in a ternary mixture of methanol (Me), cyclohexane (C), and partially deuterated cyclohexane (C*) within 1mK above its consolute critical point. The experimental setup used a low-coherence white-light source and a red filter to visualize fluctuation images. The red-filtered images were analyzed off-line using a differential dynamic microscopy algorithm that allowed us to determine the correlation time, τ, of concentration fluctuations. From τ, we determined the mutual mass diffusion coefficient, D, very near and above the critical point of Me-CC* mixtures. We also numerically estimated both the background and critical contributions to D and compared the results against our experimental values determined from τ. We found that the experimental value of D is close to the prediction based on Stokes-Einstein diffusion law with Kawasaki's correction.

Implementation of in situ SAXS/WAXS characterization into silicon/glass microreactors.

A successful implementation of in situ X-ray scattering analysis of synthetized particle materials in silicon/glass microreactors is reported. Calcium carbonate (CaCO3) as a model material was precipitated inside the microchannels through the counter-injection of two aqueous solutions, containing carbonate ions and calcium ions, respectively. The synthesized calcite particles were analyzed in situ in aqueous media by combining Small Angle X-ray Scattering (SAXS) and Wide Angle X-ray Scattering (WAXS) techniques at the ESRF ID02 beam line. At high wavevector transfer, WAXS patterns clearly exhibit different scattering features: broad scattering signals originating from the solvent and the glass lid of the chip, and narrow diffraction peaks coming from CaCO3 particles precipitated rapidly inside the microchannel. At low wavevector transfer, SAXS reveals the rhombohedral morphology of the calcite particles together with their micrometer size without any strong background, neither from the chip nor from the water. This study demonstrates that silicon/glass chips are potentially powerful tools for in situ SAXS/WAXS analysis and are promising for studying the structure and morphology of materials in non-conventional conditions like geological materials under high pressure and high temperature.

Dynamics of a wetting layer and Marangoni convection in microgravity.

Near the liquid-vapor critical point in pure fluids, material and thermal properties vary considerably with temperature. In a series of microgravity experiments, sulfur hexafluoride (SF6) was heated ∼1 K above its critical temperature, then quenched below the critical temperature in order to form gas and liquid domains. We found a power law exponent of 0.389 ± 0.010 for the growth of the wetting layer thickness during the intermediate stage of phase separation. Full and microscopic view images of the sample cell unit were analyzed to determine the changes in the size distribution of liquid droplets inside the gas phase over time. We found that the distribution of diameters for liquid droplets always contains a fraction of very small droplets, presumably due to a continuous nucleation process. At the same time, the size distribution flattens over time and rapidly includes large-size droplets, presumably generated through a coalescence mechanism. By following both a large gas bubble over two hours of video recordings, we found periodic and synchronous motion of the gas bubble along both the x and y directions. By following a large liquid droplet embedded into the large gas bubble, we found periodic, out of phase motions, which we related to Marangoni convection. The experimentally measured velocity of the liquid droplet is in good agreement with the theoretical predicted velocity of ∼0.386 µm/s obtained from Young's thermocapillary effect.

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 for the Sugden factor of one-component fluids near their gas-liquid critical point.

We present the master (i.e., unique) behavior of the squared capillary length-the so-called Sugden factor-as a function of the temperaturelike field along the critical isochore, asymptotically close to the gas-liquid critical point of about twenty (one-component) fluids. This master behavior is obtained using the scale dilatation of the relevant physical fields of the one-component fluids. The scale dilatation method introduces the fluid-dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the Ising-like universality class. The master behavior for the Sugden factor satisfies hyperscaling. It can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain, recently obtained from massive renormalization in field theory. In the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension, we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the Sugden factor, in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one-component fluid "subclass."

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.

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.