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Critical indices beta, gamma delta, nv, etc. are defined and calculated for self-organized critical phenomena. Scaling relations are derived and checked numerically. The order-parameter exponent beta describes the spontaneous current and the relaxation to the criticl point. The power spectrum has 'l/f' behavior with the exponent phi = nv x z, where z is the dynamical critical exponent.
Critical phenomena in the Arnold Engineering Development Center (AEDC) High Performance Demonstration Experiment (HPDE) and the U.S. U-25 Experiment, are analyzed. The performance of a NASA specified 500 MW(th) flow train is analyzed. Critical phenomena analyzed include: Hall voltage overshoots; optimal load schedules; parametric dependence of the electrode voltage drops; boundary layer behavior; near electrode phenomena with finite electrode segmentation; current distribution in the end regions; scale up rules; optimum Mach number distribution; and the effects of alternative cross sectional shapes.
The predictions of theoretical models for a critical-point phase transistion in fluids, namely the classical equation with third-degree critical isotherm, that with fifth-degree critical isotherm, and the lattice gas, are reviewed. The renormalization group theory of critical phenomena and the hypothesis of universality of critical behavior supported by this theory are discussed as well as the nature of gravity effects and how they affect cricital-region experimentation in fluids. The behavior of the thermodynamic properties and the correlation function is formulated in terms of scaling laws. The predictions of these scaling laws and of the hypothesis of universality of critical behavior are compared with experimental data for one-component fluids and it is indicated how the methods can be extended to describe critical phenomena in fluid mixtures.
The paper analyzes several types of critical phenomena in fluids, shows how they are affected by the presence of gravity, and describes how experiments conducted in an orbiting laboratory under low gravity conditions could extend the range of measurements needed to study critical phenomena. Future experiments are proposed. One would be a careful measurement of the dielectric constant in a low gravity environment. Two basic problems that can benefit especially from space experiments are the specific heat near the critical point and the shear viscosity at the gas-liquid critical point.
This review provides an overview of the progress in using the low-gravity environment of space to explore critical phenomena and test modern theoretical predictions. Gravity-induced variations in the hydrostatic pressure and the resulting density gradients adversely affect ground-based measurements near fluid critical points. Performing measurements in a low-gravity environment can significantly reduce these difficulties. A number of significant experiments have been performed in low-Earth orbit. Experiments near the lambda transition in liquid helium explored the regime of large correlation lengths and tested the theoretical predictions to a level of precision that could not be obtained on Earth. Other studies have validated theoretical predictions for the divergence in the viscosity as well as the unexpected critical speeding up of the thermal equilibrium process in pure fluids near the liquid-gas critical point. We describe the scientific content of previously flown low-gravity investigations of critical phenomena as well as those in the development stage, and associated ground-based work.
The first-year progress for the project of precise measurements of the density and critical phenomena of helium near phase transitions is summarized below: (1) completion of a cryogenic sample probe for the proposed measurements, and the rehabilitation of a designated laboratory at Caltech for this project; (2) construction and testing of a superconducting niobium cavity; (3) acquisition of one phase-locked-loop system for high-resolution frequency control and read- out; (4) setting up high-resolution thermometry (HRT) for temperature readout and control; (5) developing new approaches for calibrating the coefficient between the resonant frequency shift (delta f) and the helium density (rho), as well as for measuring the effect of gravity on T(sub lambda) to a much better precision; (6) programming of the interface control of all instruments for automatic data acquisition; and (7) improving data analyses and fitting procedures.
Various types of critical point phenomena are discussed including the gas-liquid phase transition of a fluid, the spontaneous magnetization of a ferromagnet below the Curie temperature, and structural phase transitions of solid materials. The interrelation of thermodynamic properties by scaling laws is considered noting theories for the validity of scaling laws and the principle of universality. Gravity effects are reviewed noting that in earth-based experiments the phenomena are significantly influenced by the earth's gravitational field and that fluid samples that are spatially homogeneous cannot be realized near the gas-liquid critical point.
The objective of this research project is to characterize by experiment and theoretically both the kinetics of phase separation and the metastable structures produced during phase separation in a microgravity environment. The particular systems we are currently studying are mixtures of water, nonionic surfactants, and compressible supercritical fluids at temperatures and pressures where the coexisting liquid phases have equal densities (isopycnic phases). In this report, we describe experiments to locate equilibrium isopycnic phases and to determine the 'local' phase behavior and critical phenomena at nearby conditions of temperature, pressure, and composition. In addition, we report the results of preliminary small angle neutron scattering (SANS) experiments to characterize microstructures that exist in these mixtures at different fluid densities.
Studies of anomalous thermodynamic, transport, and structural phenomena in multibody systems near critical points are reviewed. The nomenclature used to describe critical points is explained; theoretical predictions of the thermodynamic properties of bulk systems are presented; and experimental tests of these predictions systems are discussed, considering equilibration and gravity effects in fluid systems and emphasizing the value of experiments conducted in a reduced-gravity environment. Several such experiments are described, and the available academic-research opportunities are briefly surveyed.
Pure fluids and fluid mixtures near critical points are identified and are related to the progress of several disciplines. Consideration is given to thermodynamic properties, transport properties, and the complex nonlinear phenomena which occur when fluids undergo phase transitions in the critical region. The distinction is made between practical limits which may be extended by advances in technology and intrinsic ones which arise from the modification of fluid properties by the earth's gravitational field. The kinds of experiments near critical points which could best exploit the low gravity environment of an orbiting laboratory are identified. These include studies of the index of refraction, constant volume specific heat, and phase separation.
Interferometric procedures have been used to measure the thickness of the wetting layers of liquid SF6 which intrude between SF6 vapor and the walls of an interferometer. Close to the critical temperature the measurements show that the layers become thicker as the height at which they are observed approaches the height of the bulk liquid-vapor meniscus. The functional form of the thickness increase agrees with the dependence expected from models in which the layers' thicknesses are governed by a competition between gravitational and van der Waals forces. The layers are a factor of three thicker than a simple estimate based on such models. No evidence is found of a transition from three-dimensional critical behavior towards two-dimensional critical behavior in the available temperature and size ranges. This contrasts with the interpretation of experiments in binary liquid mixtures carried out with comparable size and temperature resolution.
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We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.
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A high resolution thermometer was developed using dilute aloy of Mn in Pd as the magnetic sensing element instead of the traditional paramagnetic salt.
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A ground based (1-g) experiment is in progress that will measure the turbidity of a density-matched, binary fluid mixture extremely close to its liquid-liquid critical point. By covering the range of reduced temperatures t equivalent to (T-T(sub c)) / T(sub c) from 10(exp -8) to 10(exp -2), the turbidity measurements will allow the critical exponent eta to be determined. No experiment has precisely determined a value of the critical exponent eta, yet its value is significant to theorists in critical phenomena. Relatively simple critical phenomena, as in the liquid-liquid system studied here, serve as model systems for more complex systems near a critical point.