Showing papers on "Compressibility published in 1983"

The approximation of the pressure by a mixed method in the simulation of miscible displacement

Abstract: The miscible displacement ofone incompressible fluid by another in a porous medium is governedby a System oftwo equations, one ofelliptic formfor the pressure and the other of par abolie formfor the concentration ofone ofthefluids. The pressure appears in the concentration only through its velocity field, and it is appropriate to choose a numerical method that approximates the velocity directly. The pressure is approximated by a mixed finite element method and the concentration by a standard Galerkin method. Optimal order estimâtes are derived when the imposed externalflows are smoothly distributed. A modification of the mixed method is proposed when the flow is located at sources and sinks (i.e., wells), and convergence is established at reduced rates in the special case when the viscosity of the mixture is independent of the concentration.

Theory of earth tide and barometric effects in porous formations with compressible grains

Abstract: The general three-dimensional equations for pore pressure, stress, and strain in a homogeneous porous medium with compressible grains are used to derive expressions for the response of fluid pressure to the stress changes due to earth tides and barometric loading effects. The analysis constitutes a generalization of earlier derivations. The formation is assumed to be of large extent laterally so that horizontal flow may be neglected. It is shown that vertical flow induced by the pore pressure changes can be analyzed by means of a diffusion equation. An expression for the specific storage coefficient is derived which is valid if horizontal deformations are negligible and which includes the effect of the compressibility of the solid grains. Measurements of earth tide and barometric effects constitute two in situ tests of bulk formation properties. Such measurements can therefore make an important contribution to the characterization of the hydraulic and elastic properties of a particular formation.

Fundamentals of Flight

Abstract: 1 Conversion Factors Between SI Units and English Units 2 Nomenclature 3 A Brief History of Aeronautics 4 The Anatomy of the Airplane 5 The Nature of Aerodynamic Forces: Dimensional Analysis 6 Theory and Experiment Wind Tunnels 7 The Atmosphere 8 Incompressible One-Dimensional Flow 9 One-Dimensional Flow in a Compressible Fluid 10 Two-Dimensional Flow: Lift and Drag 11 The Finite Wing 12 Effects of Viscosity 13 Determination of Total Incompressible Drag 14 Compressibility Drag 15 Airfoils and Wings 16 High-Lift Systems 17 Aerodynamic Performance 18 Stability and Control 19 Propulsion 20 Structures 21 Hypersonic Flow 22 Rocket Trajectories and Orbits Appendix A: Characteristics of the Standard Atmosphere (SI units) Characteristics of the Standard Atmosphere (English Units) Appendix B: Derivation of the Compressible Fluid Bernoulli Equation Appendix C: Summary of State and One-Dimensional Flow Equations Index

Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties

Abstract: Properties of the crystal and liquid phases have been measured for a system of particles interacting through a modified Lennard‐Jones potential. Through constant pressure molecular dynamics, we have evaluated the density and internal energy of these phases at a pressure that approximates that of the vapor phase. The free energy of the crystal is obtained with the Einstein crystal as a reference state, and the liquid free energy is measured relative to the ideal gas. The triple point temperature is obtained. Compressibilities and Gruneisen parameters are obtained at zero temperature and the triple point. Dynamic properties of the supercooled liquid state are also calculated. These results are applied in forthcoming publications which calculate surface excess quantities and dynamic properties of the fcc (111), (100), and (110) faces.

Calculation of the Lennard-Jones n–m potential energy parameters for metals

Abstract: A new approach is developed to calculate the Lennard-Jones n–m potential energy parameters for metals whose structure are f.c.c., b.c.c., or h.c.p. using available experimental data. The potential parameters are fitted to the cohesive energy, zero point volume, and zero point compressibility. The results show improved consistency in comparison with previous work.

Adiabatic compressibility of globular proteins.

Abstract: The adiabatic compressibility of several globular proteins has been measured by using an ultrasonic technique in the frequency range 0.5 to 10 MHz. The contributions to the measured compressibility from the protein matrix and from surface processes involving ionization of side chains and solvation effects are discussed. The internal protein compressibility is very low, indicating the existence of "dynamic domains" which are tentatively assigned to secondary structure elements.

Solar System Magnetohydrodynamics

Abstract: Continuum mechanics is that branch of physics that treats the motions of infinitely deformable matter It embraces hydrodynamics, aerodynamics, magnetohydrodynamics (MHD), and magnetogasdynamics The first two differ in that the former is incompressible and the latter compressible fluid dynamics The prefix, magneto, signifies the addition of the ponderemotive force (colloquially called the J-cross-B force) to the usual pressure gradient, gravitational and viscous forces of fluid dynamics Magnetofluid mechanics applies to fluids that can carry electrical currents, such as liquid metals and plasmas Our interest in Solar System MHD is confined to the latter

Toward understanding microemulsion microstructure: A small‐angle x‐ray scattering study

Abstract: The microemulsion phases formed in solutions of octane, commercial surfactant, and alcohol with various brines are examined with small‐angle x‐ray scattering (SAXS), electrical conductivity, and viscosity techniques. Models based on monodisperse populations of swollen micelles or microemulsion ‘‘droplets’’ adequately represent the SAXS data at low volume fractions of brine. Introduction of hard‐sphere interactions with the Percus–Yevick approximation allows us to model the composition dependence of the radius of gyration and isothermal compressibility up to volume fractions of brine near a percolation threshold for electrical conductivity. For brine volume fractions above the percolation threshold, a mean field attractive interaction term is needed to model the variation of isothermal compressibility; however, the same theory fails to model the composition dependence of the apparent radius of gyration. But predictions from a model for a bicontinuous microemulsion structure that is geometrically irregular yet topologically ordered and that evolves continuously into swollen (inverted) micellar solutions at low volume fraction of water (oil) are in good agreement with the SAXS and electrical conductivity data over a wide range of brine volume fractions.

Effect of compressibility on the Rayleigh–Taylor instability

Abstract: Eigenfrequencies are calculated for infinitesimal perturbations of the system consisting of two semi‐infinite regions, each filled with a constant‐temperature ideal polytrope stratified exponentially against gravity. The linear growth rate for the Rayleigh–Taylor instability which occurs when the density above the interface exceeds that below it is shown in the model to vary linearly with wavenumber k as k→0. The incompressible fluid result is obtained when the adiabatic index γ approaches ∞. For finite γ (i.e., compressible fluids), the growth rates are in general larger than in the incompressible case. Numerical results and limiting cases are described which illustrate this conclusion.

Wall pressure fluctuations in attached boundary-layer flow

Abstract: An examination has been made to derive a correlation for an aeroacoustic environment associated with attached compressible flow conditions. It was determined that fluctuating pressure characteristics described by incompressible theory as well as empirical correlations could be modified to a compressible state through a transformation function. In this manner, compressible data were transformed to the incompressible plane where direct use of more tractable prediction techniques are available for engineering design analyses. The investigation centered on algorithms associated with pressure magnitude and power spectral density. The method and subsequent prediction techniques are shown to be in excellent agreement with both incompressible and compressible flow data.

Rationalization of Skempton's compressibility equation

Abstract: Soils primarily being paniculate media, any attempt to understand, interpret, generalize and predict their volume change behaviour would greatly enhance the rational approach to geotechnical engineering problems. This Paper deals with the development of a scientific basis for assessing the volume change response of fine grained, uncemented, normally consolidated, saturated soil systems. A generalized e-log10 p equation has been derived for the compressibility of saturated, normally, consolidated uncemented soil systems based on the Gouy–Chapman diffuse double layer theory. It has been shown that Skempton's compressibility equation is a logical consequence of development from the diffuse double layer theory. At present this equation is extensively employed to obtain the ranges of Cc values of soil systems with only liquid limit water contents known. An engineering approach has been developed in the present investigation to identify the natural systems under equilibrium for any one of the three material sta...

Collapse of branched polymers

Abstract: Exact calculations using transfer matrices on finite strips are performed to study the two-dimensional problem of one lattice animal with an attractive nearest neighbour interaction. Thermodynamic quantities such as specific heat, compressibility, thermal expansion are calculated. Finite size scaling with two strips of different widths yields very accurate approximations of the critical line. Using three different strip widths or the two largest eigenvalues of the transfer matrix, we present two ways of obtaining the tricritical point and its exponents. Our estimations are quite stable when we increase the strip width and we can give rather accurate predictions. Lastly our model can also be interpreted as a gel whose parameters are temperature and pressure showing the experimentally known phenomenon of the collapse.

Zeolite Molecular Sieve 4A: Anomalous Compressibility and Volume Discontinuities at High Pressure.

Abstract: Unit cell parameters of synthetic zeolite 4A were measured at several pressures to 40 kilobars with both water and an alcohol mixture as hydrostatic pressure media. Compression in water was normal, with no observed phase transitions. Compression in alcohols was twice as great as in water, and three volume discontinuities were observed. These volume changes in alcohol were rapid with increasing pressure but sluggish in reverse. High-pressure "phases," all of which are dimensionally cubic, are progressively more compressible at high pressure. These unusual high-pressure phenomena, which indicate significant interactions between zeolite 4A and the hydrostatic media, are consistent with differences in zeolite adsorption of water alcohols.

Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid

Abstract: Etude du probleme d'un barreau infiniment long subissant des oscillations longitudinales et de torsion dans un fluide incompressible et homogene du second ordre

Equation of state and thermodynamic properties of liquid methanol from 298 to 489 K and pressures to 1040 bars

Abstract: The PVT properties of liquid methanol have been measured with a direct-weighing PVT apparatus, from 298 to 489 K and pressures to 1040 bar. The apparatus and the method are described. The results have been fitted to a 16-constant equation of state that has been used, together with published data for vapor pressure and saturated-vapor densities, to calculate the following properties of saturated and compressed liquid methanol over the experimental range: specific volume, isothermal compressibility, thermal expansion coefficient, thermal pressure coefficient, enthalpy, entropy, and constant-pressure heat capacity. The calculated properties are presented in tabular form, at round values of P and T.

Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model

Abstract: The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.

A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme

Abstract: This paper presents the finite element method for the analysis of unsteady viscous flow of fluid at high Reynolds numbers. The method is based on the explicit numerical integration scheme in time and uses three node triangular finite elements. For the convenience of the formulation, slight compressibility is considered. For the explicit scheme, the selective lumping two step scheme has been successfully employed. Vortex shedding behind a cylinder has been computed and compared with the conventional experimental results. The results agree favourably when both schemes are compared.

On the failure of certain integral equation theories to account for complete wetting at solid-fluid interfaces

Abstract: We examine the usefulness of the integral equations derived from the HNC and PY closures of the wall-particle Ornstein-Zernike equation for describing the density profile and pairwise distribution function of models of the solid-fluid interface. It is shown that these, and closely related closure approximations, cannot account for complete wetting of a solid-gas interface by liquid or complete wetting by gas of a purely repulsive substrate at a solid-liquid interface. The closure approximation to the first YBG equation which sets the total pairwise correlation function equal to that of the bulk fluid exhibits the same failings. Since none of these approaches can describe liquid-gas coexistence, they cannot be used as a basis for a self consistent theory of contact angle and wetting phenomena. Moreover, they cannot account for the growth of thick, liquid-like, adsorbed films which develop at solid-gas interfaces at temperatures T above the wetting transition temperature Tw. Such approaches also give an inadequate description of pairwise correlations in the interface. This is illustrated by the introduction of a ' surface ' compressibility sum rule which relates an integral over the interracial part of the pairwise distribution function to (SI'/~/~)T, the derivative with respect to chemical potential/~ of the coverage r. For T> T,¢ r and, hence, (er/~,)T diverge as p~ approaches its value at saturation with exponents that reflect the asymptotic behaviour of the attractive part of the solid-gas potential. The sum rule shows that the range of transverse (parallel to the surface) pairwise correlations must diverge in an equivalent fashion. Divergences of this kind are not predicted by the integral equation approaches. The growth of long-ranged transverse correlations has important repercussions for computer simulations of thick adsorbed films. It iS the purpose of this paper to point out the limitations of several widely used theories of solid-fluid interfaces. In particular we show that these theories cannot account for the phenomenon of complete wetting by liquid or by gas. There are three main theoretical approaches employed in calculations of the microscopic structure of simple fluids near model solid substrates. The first of these makes use of closure approximations to the wall-particle OrnsteinZernike equation. This approach was pioneered by Perram and White [I] and Henderson et al. [2] and has been applied to a variety of model systemssee, for example, [3, 4] and references therein. Two of the simplest and most commonly used closures are the hypernetted-chai n (HNC) and Percus-Yevick

Small-angle scattering from colloidal dispersions

Abstract: A theory of the small-q behaviour of the static structure factor S(q) for monodisperse colloidal dispersions is presented in which the long-range forces between the colloid particles are treated in the random phase approximation. By using a hard-sphere reference fluid, explicit results for the coefficients to (q4) in a small-q expansion of c(q), the Fourier transform of the direct correlation function, are obtained.The theory gives an expression for the osmotic compressibility of a dispersion that is equivalent to an empirical relation used to interpret light-scattering experiments on microemulsions. When applied to charge-stabilised dispersions the theory predicts the existence of a phase diagram closely analogous to one normally observed in molecular systems.

A theory of the anomalous thermodynamic properties of liquid water

Abstract: A theory of the anomalous thermodynamic properties of liquid water is presented. The theory is based on a simple model intermolecular potential that contains short‐ranged repulsions, hydrogen‐bonding attractions, and longer ranged interactions. Cluster theory approximations derived in the previous paper [J. Chem. Phys. 77,1962 (1982)] are used to calculate the thermodynamic energy and free energy for the model fluid as a function of temperature and density. The model fluid is found to have many of the anomalous properties of real water, such as a density maximum at low pressure, a compressibility minimum, and high heat capacity. The model is not a quantitatively accurate one for real water, nor does it have the anomalous properties observed for supercooled water. The reasons for the anomalies of the model fluid are discussed in order to shed some light on the physical basis for these anomalies in real water.

Determination of the thermodynamic properties of water from measurements of the speed of sound in the temperature range 251.15–293.15 K and the pressure range 0.1–350 MPa

Abstract: The speed of sound in water has been measured in a broad region around the liquid-solid transition, that is, in the temperature range from 251.15 K to 293.15 K and in the pressure range from 0.1 to 350 MPa. An iterative method of calculation was used to determine the thermodynamic properties in the same P-T diagram. Anomalies observed for the isothermal compressibility and the specific heat at constant pressure are discussed in terms of statistical mechanical considerations.

Helical shear of an elastic, circular tube with a non-convex stored energy

Abstract: In 1949, in one of his pioneering studies on large elastic deformations, Rivlin [1] applied the general theory of non-linear elasticity for an incompressible, isotropic, homogeneous body to study the helical shearing of a circular tube for a Mooney material. Approximately 25 years later, Ogden, Chadwick & Haddon [2] reconsidered this problem in some detail for more general materials, but in neither of these works was there an emphasis placed upon the structure of the stored energy function and, in particular, on its convexity. In the present work, we wish to emphasize the case of a non-convex stored energy function and the related emergence of equilibrium states with discontinuous deformation gradients. It is most convenient to consider the problem as one of minimization, and we shall seek to characterize the uniqueness, existence, and detailed structural properties of an absolute minimizer.

Compressible Rayleigh–Taylor instability

Abstract: The role of compressibility in modifying the growth rate of Rayleigh–Taylor instability is discussed. Compressibility can either enhance or decrease the growth rate. If the sound speeds in the two media are the same, compressibility can still have an effect, in contrast to ‘‘first‐order’’ theory. Compressibility becomes less important as the density ratio between the fluids increases. Experimental results have shown that compressibility can enhance growth rates compared to the incompressible value.