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.

Turbidity data obtained from image analysis in near critical hydrogen.

Video images are being used with increased frequency in science, supplanting current methods such as light scattering by statistical evaluation of the images. In this study we use light turbidity data due to density-induced refractive index fluctuations to obtain critical amplitudes from image analysis. In order to bring hydrogen (H_{2}) very close to its critical point, we place the sample cell under weightlessness using a magnetic levitation device. Images of an H_{2}-filled cell are taken near its critical temperature of 33 K by illuminating the cell with three different filters. We fit the turbidity data to a theoretical expression that allows us to estimate the critical amplitudes of isothermal compressibility and fluctuation correlation length. The values of isothermal compressibility and correlation length obtained from turbidity fitting are compared against literature values. Our data analysis shows a large sensitivity of the fitting parameters to the refractive index value and to even minute density deviations from criticality.

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.

Dimple coalescence and liquid droplets distributions during phase separation in a pure fluid under microgravity.

Phase separation has important implications for the mechanical, thermal, and electrical properties of materials. Weightless conditions prevent buoyancy and sedimentation from affecting the dynamics of phase separation and the morphology of the domains. In our experiments, sulfur hexafluoride (SF6) was initially heated about 1K above its critical temperature under microgravity conditions and then repeatedly quenched using temperature steps, the last one being of 3.6 mK, until it crossed its critical temperature and phase-separated into gas and liquid domains. Both full view (macroscopic) and microscopic view images of the sample cell unit were analyzed to determine the changes in the distribution of liquid droplet diameters during phase separation. Previously, dimple coalescences were only observed in density-matched binary liquid mixture near its critical point of miscibility. Here we present experimental evidences in support of dimple coalescence between phase-separated liquid droplets in pure, supercritical, fluids under microgravity conditions. Although both liquid mixtures and pure fluids belong to the same universality class, both the mass transport mechanisms and their thermophysical properties are significantly different. In supercritical pure fluids the transport of heat and mass are strongly coupled by the enthalpy of condensation, whereas in liquid mixtures mass transport processes are purely diffusive. The viscosity is also much smaller in pure fluids than in liquid mixtures. For these reasons, there are large differences in the fluctuation relaxation time and hydrodynamics flows that prompted this experimental investigation. We found that the number of droplets increases rapidly during the intermediate stage of phase separation. We also found that above a cutoff diameter of about 100 microns the size distribution of droplets follows a power law with an exponent close to -2, as predicted from phenomenological considerations.

Imaging critical fluctuations of pure fluids and binary mixtures.

We use optical microscopy techniques to directly visualize the structures that emerge in binary mixtures and pure fluids near their respective critical points. We attempt to understand these structures by studying the image formation using both a phase contrast and a dark field filter to our microscope. We found that images of critical fluctuations for both liquid-liquid and liquid-gas critical systems have gray level intensity histograms with Gaussian shape. For all fluids investigated, the temperature-dependent standard deviation of the Gaussian histogram follows a power law with the same exponent. Since the image intensity fluctuations are determined by order parameter fluctuations, this direct imaging method allowed us to estimate the critical exponent of compressibility with very good accuracy.

Dynamic structure factor of density fluctuations from direct imaging very near (both above and below) the critical point of SF(6).

Large density fluctuations were observed by illuminating a cylindrical cell filled with sulfur hexafluoride (SF(6)), very near its liquid-gas critical point (|T-T(c)|< 300 µK) and recorded using a microscope with 3 µm spatial resolution. Using a dynamic structure factor algorithm, we determined from the recorded images the structure factor (SF), which measures the spatial distribution of fluctuations at different moments, and the correlation time of fluctuations. This method authorizes local measurements in contrast to the classical scattering techniques that average fluctuations over the illuminating beam. We found that during the very early stages of phase separation the SF scales with the wave vector q according to the Lorentzian q(-2), which shows that the liquid and vapor domains are just emerging. The critical wave number, which is related to the characteristic length of fluctuations, steadily decreases over time, supporting a sustained increase in the spatial scale of the fluctuating domains. The scaled evolution of the critical wave number obeys the universal evolution for the interconnected domains at high volume fraction with an apparent power law exponent of -0.35 ± 0.02. We also determined the correlation time of the fluctuations and inferred values for thermal diffusivity coefficient very near the critical point, above and below. The values were used to pinpoint the crossing of T(c) within 13 µK.

Heat can cool near-critical fluids.

We report experiments with very compressible fluids near the liquid-gas critical point. These experiments are performed (i) under microgravity in low Earth orbit by using SF(6) at liquidlike density and (ii) under Earth's gravity with CO(2) at gaslike density. The sample fluid is filled in an interferometer cell with its walls maintained at constant temperature. In situ thermistors measure the local fluid temperature. One of the thermistors is also used as a heat source to generate heat pulses. With no gravity-induced fluid convection, the evolution of fluid temperature is governed by the balance of heat flux between the thermal boundary layer of the heat source, which compresses the bulk fluid, and the thermal boundary layer at the wall, which expands it. When heat pulses are applied to the fluid under weak or Earth's gravity, a long thermal transient is observed at the end of the heat pulse where the bulk fluid temperature reaches significantly below the initial temperature. This unconventional cooling originates from the fast decompression of the fluid, which is induced by the rapid convectively disappearing hot boundary layer at the heat source, and the persistence of an anomalously thin cold boundary layer convectively induced at the cell wall. This striking phenomenon is observed in a large range of temperature, density, and various thermodynamic conditions. This anomalous cooling effect persists for an appreciable period of time corresponding to the diffusive destruction of the cold boundary layer. We found that the effect is also more pronounced when the free fall acceleration is large. We have analyzed the result by using a simple one-dimensional model with ad hoc convective heat losses.

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.

Universality in early-stage growth of phase-separating domains near the critical point.

We present both the experimental and computational methods and results of phase-separating experiments performed with sulfur hexafluoride (SF6) close to its critical density. These experiments were performed in microgravity to suppress buoyancy and convection-driven effects. Phase separation under reduced gravity is analyzed for both 0.3 mK and 3.6 mK temperature quenches in order to derive the early-stage growth law. We found a 1/3 growth law for early stages of phase separation for a volume fraction of minority domains of 50%. Our findings support the hypothesis of a crossover between Brownian motion and hydrodynamic effects in the early stages of phase separation. The temperature inside the bulk of the pure fluid was estimated using a proposed histogram method. Our histogram method allowed temperature estimation below thermistors' sensitivity and detected small temperature variations inside the bulk of the pure fluid.

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.

Mean crossover functions for uniaxial three-dimensional Ising-like systems.

We give simple expressions for the mean of the max and min bounds of the critical-to-classical crossover functions, previously calculated [Bagnuls and Bervillier, Phys. Rev. E 65, 066132 (2002)] within the massive renormalization scheme of the Phi(d)4(n) model in three dimensions (d = 3) and scalar order parameter (n = 1) of the Ising-like universality class. The mean functions are determined relying on the properties of the theoretical functions in the two limiting three-dimensional (3D) Ising-like and mean-field-like descriptions close to the Wilson-Fisher fixed point and to the Gaussian fixed point, respectively. Such descriptions correspond to the preasymptotic domains near each fixed point where a Wegner expansion restricted to two terms (leading and first confluent terms) is valid. The Ising-like preasymptotic domain description includes the correlations between parameters due to the error-bar determination of the exponents and amplitude combinations very close to the Wilson-Fisher fixed point. Adding the equivalent description of the mean field preasymptotic domain close to the Gaussian fixed point leads to define each mean crossover function with three calculated parameters. Fixing a unique value of one parameter whatever the selected mean crossover function, we use this parameter as a relative sensor to estimate the dominant nature, either (Ising-like) critical, or (mean-field-like) classical, of the crossover behavior. Finally, we obtain an explicit criterion to measure the extension of the Ising-like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite, using a well-controlled number of system-dependent parameters (like in the subclass of one-component fluids).

Universality and quantum effects in one-component critical fluids.

Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within phi (4)(d = 3) (n = 1)the model, or based on the crossover parametric equation of state for Ising-like systems.

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.

Wetting film dynamics during evaporation under weightlessness in a near-critical fluid.

By performing near-critical fluid experiments in the weightlessness of an orbiting space vehicle, we have suppressed buoyancy-driven flows and gravitational constraints on the liquid-gas interface of a large gas bubble. At equilibrium, the liquid completely wets the walls of a cylindrical cell, and the bubble is pushed to the sidewall. In these experiments the system's temperature T is increased at a constant rate past the critical temperature T(C), pushing it slightly out of equilibrium. The wetting film shows a large mechanical response to this heating, including contact lines that recede on a solid surface and a spreading bubble. Near T(C), the receding contact lines make the entire bubble appear to spread along the copper sidewall. The spreading bubble is a manifestation of the boiling crisis near the critical point. We present quantitative data of the receding contact lines that are observed prior to the near-critical boiling crisis. We analyze the receding contact lines in detail, and find that they are driven by vapor recoil from evaporation, as is the spreading bubble of the boiling crisis.

High-frequency driven capillary flows speed up the gas-liquid phase transition in zero-gravity conditions.

Under weightlessness conditions, the phase transition of fluids is driven only by slow capillary flows. We investigate the effect of high-frequency vibrations to reproduce some features of gravity effects and show that such vibrations can greatly modify the phase transition kinetics. The investigation is performed in H2 near its critical point (critical temperature 33 K) where critical slowing down enables the phase transition process to be carefully studied. Gravity effects are compensated in a strong magnetic field gradient.