Showing papers on "Compressibility published in 1986"

Bubble dynamics in a compressible liquid. Part 1. First-order theory

Abstract: The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a simplified singular-perturbation method to first order in the bubble-wall Mach number. It is shown that, at this order, a one-parameter family of approximate equations for the bubble radius exists, which includes those previously derived by Herring and Keller as special cases. The relative merits of these and other equations of the family are judged by comparison with numerical results obtained from the complete partial-differential-equation formulation by the method of characteristics. It is concluded that an equation close to the Keller form, but written in terms of the enthalpy of the liquid at the bubble wall, rather than the pressure, is most accurate, at least for the cases considered of collapse in a constant-pressure field and collapse driven by a Gaussian pressure pulse. A physical discussion of the magnitude and nature of compressibility effects is also given.

Thermoelastic response of fluid-saturated porous rock

Abstract: A linear theory for fluid-saturated, porous, thermoelastic media is developed. The theory allows for compressibility and thermal expansion of both the fluid and solid constituents. A general solution scheme is presented, in which a diffusion equation with a temperature-dependent source term governs a combination of the mean total stress and the fluid pore pressure. In certain special cases, this reduces to a diffusion equation for the pressure alone. In addition, when convective heat transfer and thermoelastic coupling can be neglected, the temperature field can be determined independently, and the source term in the pressure equation is known. Drained and undrained limits are identified, in which fluid flow plays no role in the deformation. In the drained case, the medium behaves as a simple thermoelastic body with the properties of the porous skeleton with no fluid present. In the undrained limit, the fluid is trapped in the pores, and the material responds as a thermoelastic body with effective compressibility and thermal expansivity determined in part by the fluid properties. The theory is further specialized to one-dimensional deformation, and several illustrative problems are solved. In particular, the heating of a half space is explored for constant temperature and constant flux boundary conditions on the thermal field, and for drained (zero pressure) and impermeable (zero flux) conditions on the fluid pressure field. The behavior of these solutions depends critically upon the ratio of the fluid and thermal diffusivities, with very large and very small values of this parameter corresponding to drained and undrained responses, respectively.

Compressibility-structure relationship of globular proteins.

Abstract: The adiabatic compressibility, -beta s, of 11 globular proteins in water was determined by means of sound velocity measurements at 25 degrees C. All the proteins studied except for subtilisin showed positive -beta s values, indicating the large internal compressibility of the protein molecules. The intrinsic compressibility of proteins free from the hydration effect appeared to be comparable to that of normal ice. The compressibility data for 25 proteins, including 14 reported previously [Gekko, K., & Noguchi, H. (1979) J. Phys. Chem. 83, 2706-2714], were statistically analyzed to examine the correlation of the compressibility with some structural parameters and the amino acid compositions of proteins. It was found that -beta s increases with increasing partial specific volume and hydrophobicity of proteins. The helix element also seemed to be a dynamic domain to increase -beta s. Four amino acid residues (Leu, Glu, Phe, and His) greatly increased -beta s, and another four (Asn, Gly, Ser, and Thr) decreased it. Some empirical equations were derived for the estimation of the -beta s values of unknown proteins on the basis of their amino acid compositions. The volume fluctuations of proteins revealed by the compressibility data were in the range of 30-200 mL/mol, which corresponded to about 0.3% of the total protein volume. The conformational fluctuation seemed to enhance the thermal stability of proteins.

Self‐consistent integral equations for fluid pair distribution functions: Another attempt

Abstract: We propose a new mixed integral equation for the pair distribution function of classical fluids, which interpolates continuously between the soft core mean spherical closure at short distances, and the hypernetted chain closure at large distances. Thermodynamic consistency between the virial and compressibility equations of state is achieved by varying a single parameter in a suitably chosen switching function. The new integral equation generalizes a recent suggestion by Rogers and Young to the case of realistic pair potentials containing an attractive part. When compared to available computer simulation data, the new equation is found to yield excellent results for the thermodynamics and pair structure of a wide variety of potential models (including atomic and ionic fluids and mixtures) over an extensive range of temperatures and densities. The equation can also be used to invert structural data to extract effective pair potentials, with reasonable success.

thermodynamic properties for natural waters covering only the limnological range1

Abstract: Dissolved salts affect the thermodynamic properties of lake waters. Equations are given to calculate the following properties over the range of 0-0.6 salinity, 0/sup 0/-30/sup 0/C, and 0-180 bars: density, thermal expansibility, temperature of maximum density, maximum density and minimum specific volume, isothermal compressibility, specific heat at constant pressure, specific heat at constant volume, sound speed, adiabatic compressibility, freezing point, adiabatic temperature gradient, and static stability.

Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads

Abstract: The film thicknesses and pressures in elastohydrodynamically lubricated contacts have been calculated for a line contact by using an improved version of Okamura's approach. The new approach allows for lubricant compressibility, the use of Roelands' viscosity, a general mesh (nonconstant step), and accurate calculations of the elastic deformation. The new approach is described, and the effects on film thickness, pressure, and pressure spike of each of the improvements are discussed. Successful runs have been obtained at high pressure (to 4.8 GPa) with low CPU times.

Fluid pressure response to undrained compression in saturated sedimentary rock

Abstract: The pore pressure response of saturated porous rock subjected to undrained compression at low effective stresses are investigated theoretically and experimentally. This behavior is quantified by the undrained pore pressure buildup coefficient, B = (dPf/dPclld,"f~O' where Pf is fluid pressure, P, is confining pressure, and mf is the mass of fluid per unit bulk volume. The measured values for B for three sandstones and a dolomite are near 1.0 at zero effective stress and decrease with increasing effective stress. In one sandstone, B is 0.62 at 13 MPa effective stress. These results agree with the theories of Gassmann (1951) and Bishop (1966), which assume a locally homogeneous solid framework. The decrease of B with increasing effective stress is probably related to crack closure and to high-compressibility materials within the rock framework. The more general theories of Biot (1955) and Brown and Korringa (1975) introduce an additional parameter, the unjacketed pore compressibility, which can be determined from induced pore pressure results. Values of B close to 1 imply that under appropriate conditions within the crust, zones of low effective pressure characterized by low seismic wave velocity and high wave attenuation could exist. Also, in confined aquifer-reservoir systems at very low effective stress states, the calculated specific storage coefficient is an order of magnitude larger than if less overpressured conditions prevailed.

The Segregated Approach to Predicting Viscous Compressible Fluid Flows

Abstract: The SIMPLE method of Patankar and Spalding and its variants such as SIMPLER, SIMPLEC and SIMPLEX are segregated methods for solving the discrete algebraic equations representing the equations of motion for an incompressible fluid flow. The present paper presents the extension of these methods to the solution of compressible fluid flows within the context of a generalized segregated approach. To provide a framework for better understanding the segregated approach to solving viscous compressible fluid flows an interpretation of the role of pressure in the numerical method is presented. With this interpretation it becomes evident that the linearization of the equation for mass conservation and the approach used to solve the linearized algebraic equations representing the equations of motion are important in determining the performance of the numerical method. The relative performance of the various segregated methods are compared for several subsonic and supersonic compressible fluid flows.Copyright © 1986 by ASME

Crystal structure of magnetite under pressure

Abstract: The crystal structure and the unit-cell parameters of magnetite have been studied at room temperature up to a pressure of 4.5 GPa using a diamond anvil cell and a four-circle X-ray diffractometer. The isothermal bulk modulus (K T ) and its pressure derivative (K' T ) determined by fitting the pressure-volume data to the Murnaghan equation of state are 181(2) GPa and 5.5(15), respectively. The positional parameter u does not vary significantly over the pressure range of this study. The linear compressibilities of the interatomic distances and the bulk moduli of the polyhedra have been calculated from the pressure dependences of the unit-cell edge a and the u parameter. The Bloch equation has been modified to derive a relationship between the Neel temperature and the parameter u. The modified Bloch equation gives a closer agreement with the experimental results than the Weisz equation.

An existence theorem for the flow of a non-newtonian fluid past an infinite porous plate

Abstract: Non-Newtonian fluid mechanics affords an excellent opportunity for studying many of the mathematical methods which have been developed to analyse non-linear problems in mechanics. The flow of an incompressible fluid of grade three past an infinite porous flat plate, subject to suction at the plate, is governed by a non-linear differential equation that is particularly well suited to demonstrate the power and usefulness of three such techniques. We establish an existence theorem using shooting methods. Next, we investigate the problem using a perturbation analysis. It is not clear that the perturbation solution converges and thus may not be the appropriate solution for a certain range of a material constant (which is not the perturbation parameter). Finally, we employ a numerical method which is particularly suited to the problem in question.

Apparatus for controlling a pump to account for compressibility of liquids in obtaining steady flow

Abstract: There is disclosed herein an apparatus and method for controlling a dual piston pump for a liquid chromatography system so as to pump a flow of solvent through the liquid chromatography column at a constant flow rate and with a solvent composition which is substantially equal to the desired solvent composition despite changing conditions of compressibility of the solvent. The control system uses a computer which measures the time it takes the pump shaft to move through an overlap region in the pump cycle when both pistons are simultaneously pumping as normalized to the time taken by the pump to move through a constant velocity portion of the piston travel defined by the user. This time is compared to the time stored in the computer for the particular flow rate used to measure the time defined above for the pump to move through the overlap region for an incompressible solvent at low pressure as normalized to the time taken by the input piston to move through the same user defined segment of the constant velocity portion of the travel of the input piston. The ratio of these two times is then used in an algorithm to derive a correction factor for compressibility. This correction factor is then used to control the flow rate and the makeup of the solvent composition to maintain the correct values over changing conditions of solvent compressibility.

Spinodal curve in highly asymmetrical polyelectrolytes.

Abstract: The study of salt-free polyelectrolytes within the primitive model and with the hypernetted chain integral equation leads to a phase separation at very low concentration. The spinodal line and the critical point are deduced from the compressibility equation and are determined as functions of the polyion charge.

Compressibility route to solvation structure

Abstract: We discuss the basic model of structural colloidal pair-interactions, consisting of a simple fluid confined between a pair of planar walls. A compressibility route to solvation structure follows from the statistical mechanical hierarchy obtained by successive functional differentiation of the grand potential, with respect to the solute-medium interaction. In particular, for short-range wall-fluid forces a shielding approximation to an integral equation for the density profile yields a solution in terms of a product of profiles obtained from the limit of large wall-separation. In one-dimension the shielding solution is exact in the absence of non-nearest-neighbour fluid interactions. In the case of hard wall boundaries, the exact form of both the density profile and the solvation force can be deduced at small wall-separation. The shielding approximation with hard wall boundary conditions leads to a first-order differential equation for the solvation force.

Lattice gas automata for fluid mechanics

Abstract: A lattice gas is the representation of a gas by its restriction on the nodes of a regular lattice for discrete time steps It was recently shown by Frisch, Hasslacher and Pomeau that such very simple models lead to the incompressible Navier-Stokes equation provided the lattice has enough symmetry and the local rules for collisions between particles obey the usual conservation laws of classical mechanics We present here recent results of numerical simulations to illustrate the power of this new approach to fluid mechanics which may give new tools for numerical studies and build a bridge between cellular automata theory and complex physical problems

The response of an incompressible, viscoelastic coating to pressure fluctuations in a turbulent boundary layer

Abstract: The response of the interface between a compliant surface and a turbulent boundary-layer flow is examined theoretically. This response is forced by transient, convected, interfacial pressure pulses that represent the footprints of turbulent flow structures in the boundary layer. Calculations are presented for coatings with a wide range of damping and densities equal to the density of the flow. For coatings with moderate damping, three regimes of response are found. When the flow speed U∞ is less than about 1.2 (non-dimensionalized by the shear wave speed of the coating), the response is stable and primarily localized under the pressure pulse. For flow speeds from 1.2 to as high as 2.8, depending on the damping, the response is also stable, but it includes a wave pattern behind the pressure pulses. For flow speeds above 2.8, the response is unstable and eventually forms a two-dimensional wavetrain moving in the flow direction. At the highest stable flow velocity, the amplitude of the surface displacements reaches 4.0% of the boundary-layer displacement thickness δ* and the energy transfer from the pressure pulse reaches 5.0 × 10−4 U∞2 (δ*)2. For high damping, the coating response is again stable when the flow speed is below 2.8. However, there is no wavelike response regime; the path that is traversed by the pressure pulse is covered by a scar that heals according to the viscous relaxation properties of the material. The amplitude of the response is at most 0.01δ*.

Solvability of the problem of evolution of an isolated volume of viscous, incompressible capillary fluid

Abstract: The initial boundary-value problem for the Navier-Stokes equation describing the flow of a viscous, incompressible capillary fluid bounded only by a free surface is considered At the initial time the region occupied by the fluid and the velocity field of the fluid are given A theorem is formulated regarding the unique solvability of the problem for a finite time interval, and a model linearized problem in a half space is obtained

Computer modeling of large rock slides

Abstract: A computer-based analysis of the runout dynamics of the Madison Canyon rockslide of August 17, 1959, is reported. Three levels of computer representation of the flow are considered. First is a representation of the actual canyon profile, where the model assumes incompressible linear viscous flow. Second is a horizontal profile in which gravitational forces are input by components, and again the flow is approximated by a single viscosity model. Third is a horizontal profile, for which a two viscosity model approaching a Bingham material representation is used. Results of each model are compared to actual slide runout, debris distribution, and maximum speed of the flow. The biviscous model, which depicts an active basal flow layer, also has physical characteristics consistent with measurements made of the Madison Canyon slide following the event.

Compressibility effects on ideal and kinetic ballooning modes and elimination of finite Larmor radius stabilization

Abstract: The dynamics of ideal and kinetic ballooning modes are considered analytically including parallel ion dynamics, but without electron dissipation. For ideal modes and typical tokamak parameters, parallel dynamics predominantly determine the growth rate when β is within ∼20%–40% of the ideal threshold, resulting in a substantial reduction in growth rate. Compressibility also eliminates the stabilization effects of finite Larmor radius (FLR); FLR effects (when temperature gradients are neglected) can even increase the growth rate above the magnetohydrodynamic (MHD) value. Temperature gradients accentuate this by adding a new source of free energy independent of the MHD drive, in the region of ballooning coordinate corresponding in MHD to the continuum. Analytic dispersion relations are derived demonstrating the effects above; the formalism emphasizes the similarities between the ideal MHD and kinetic cases.

An integral method for predicting hydraulic fracture propagation driven by gases or liquids

Abstract: Hydraulic fracture propagation is predicted by a general numerical procedure which satisfies the transport equations in a global or integral sense over the entire fracture and over a small control volume near the leading edge. At each discrete time step the pressure distribution is selected from a four-parameter family of profiles such that the stress intensity is equal to the critical value at the tip of the fracture and the integral equations are satisfied. Comparisons with previous analytical and, numerical solutions indicate accuracy within 10 per cent for a variety of test problems include wedge-shaped and envelope-shaped fractures, laminar and turbulent flows, incompressible liquids and ideal gases, permeable and impermeable media, prescribed inlet pressure and prescribed flow rates. CPU time is typically a few seconds for a tenfold increase in fracture length. The method has been applied to explosively driven and propellant-driven gas fracturing problems as well as the traditional pump-driven hydraulic fracturing problem.

Numerical solution procedure for viscous incompressible flows

Abstract: A calculation procedure for solving the time-dependent incompressible Navier-Stokes equations in arbitrary shapes is presented. The conservative form of the primitive-variable formulation is adopted. The numerical scheme is based on an overlapping grid with forward and backward differencing for mass and pressure gradients, respectively. This structure allows use of the same computational cell for both the continuity and momentum equations and storage of the pressure and velocity components at the same grid location. The result is a stable and accurate algorithm, and no oscillations on the velocity or pressure field are detected. The computed results are compared with numerical and experimental data.

Precise determination of the compressibility factor of methane, nitrogen, and their mixtures from refractive index measurements

Abstract: We show that the absolute determination of the refractive index, when combined with an expansion technique for obtaining the higher-order coefficients of the Lorentz-Lorenz expansion, leads to precise values of density. A grating interferometer has been developed for the refractive index measurements as a function of pressure. The advantage of a grating interferometer is that it performs a reversible counting and generates a DC compensated signal from the interference fringes. The pressure is also measured with an interferometer, previously calibrated with an oil-type precision piston gauge. For the precise determination of the compressibility factor, the absolute measurement of the refractive index is combined with the differential technique to determine the refractivity virial coefficients of the Lorentz-Lorenz expansion. The compressibility factors of methane, nitrogen, and their mixtures have been determined at 323.15 K for pressures up to 335 bar. The optical method for the determination of the compressibility factor not only is shown to be precise, but also has the ability to produce numerous experimental points in a short time as compared to other methods.