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Compressibility

About: Compressibility is a research topic. Over the lifetime, 18112 publications have been published within this topic receiving 390880 citations. The topic is also known as: coefficient of compressibility & bulk compressibility.


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TL;DR: In this article, the authors developed a theory of convection from maintained and instantaneous sources of buoyancy, using methods which are applicable to stratified body fluids with any variation of density with height; detailed solutions have been presented for the case of a stably stratified fluid with a linear density gradient.
Abstract: Theories of convection from maintained and instantaneous sources of buoyancy are developed, using methods which are applicable to stratified body fluids with any variation of density with height; detailed solutions have been presented for the case of a stably stratified fluid with a linear density gradient. The three main assumptions involved are (i) that the profiles of vertical velocity and buoyancy are similar at all heights, (ii) that the rate of entrainment of fluid at any height is proportional to a characteristic velocity at that height, and (iii) that the fluids are incompressible and do not change volume on mixing, and that local variations in density throughout the motion are small compared to some reference density. The governing equations are derived in non-dimensional form from the conditions of conservation of volume, momentum and buoyancy, and a numerical solution is obtained for the case of the maintained source, This leads to a prediction of the final height to which a plume of light fluid will rise in a stably stratified fluid. Estimates of the constant governing the rate of entrainment are made by comparing the theory with some previous results in uniform fluids, and with the results of new experiments carried out in a stratified salt solution. For the case of an instantaneous source of buoyancy there is an exact solution; the entrainment constant is again estimated from laboratory results for a stratified fluid Finally, the analysis is applied to the (compressible) atmosphere, by making the customary substitution of potential temperature for temperature. Predictions are made of the height to which smoke plumes from typical sources of heat should rise in a still, stably stratified atmosphere under various conditions.

2,408 citations

01 Jan 1998
TL;DR: In this article, the authors presented a revised and updated data set of 154 mineral end-members, 13 silicate liquid endmembers and 22 aqueous fluid species, which is used for the calculation of uncertainties on mineral reactions to be performed.
Abstract: The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral-fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order-disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha-beta quartz transition to be handled more satisfactorily. Several melt end- members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data. kinetics which apply to determining directly the greatest majority of such equilibria in the laboratory, for forming solid solutions, and inclusion of aqueous and silicate melt species), and provides uncertainties especially at lower temperatures, as well as the diYculty of establishing reversals of reactions involving solid allowing the likely uncertainties on the results of thermodynamic calculations to be estimated. This is a solutions. The levels of precision and accuracy required of thermodynamic data in order to be able to forward- critical issue in that calculations using data sets should always involve uncertainty propagation to help evalu- model synthetic and natural mineral assemblages mean that the continuing upgrading and expansion of the ate the results. Because the experimental phase equilib- ria involve overlapping subsets of compositional space, data set by incorporation of new phase equilibrium constraints, calorimetry and new measurements of the derived thermodynamic data are highly correlated, and it is only the inclusion of the correlations which molar volume, thermal expansion and compressibility are more than justified. enables the reliable calculation of uncertainties on mineral reactions to be performed. Earlier work on mineral thermodynamic data sets for rock-forming minerals includes compilations of The thermodynamic data extraction involves using weighted least squares on the diVerent types of data

2,374 citations

Journal ArticleDOI
TL;DR: In this article, an equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus-Yevick integral equation.
Abstract: An equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus–Yevick integral equation for the mixture of hard spheres. Compressibility and other equilibrium properties of the binary mixtures of hard spheres are calculated and they are compared with the related machine‐calculated (Monte Carlo and molecular dynamics) data. The comparison shows excellent agreement between the proposed equation of state and the machine‐calculated data.

1,894 citations

Journal ArticleDOI
TL;DR: In this paper, a study of the formulation, some basic solutions, and applications of the Biot linearized quasistatic elasticity theory of fluid-infiltrated porous materials is presented.
Abstract: This is a study of the formulation, some basic solutions, and applications of the Biot linearized quasistatic elasticity theory of fluid-infiltrated porous materials. Whereas most previously solved problems are based on idealizing the fluid and solid constituents as separately incompressible, full account is taken here of constituent compressibility. Previous studies are reviewed and the Biot constitutive equations relating strain and fluid mass content to stress and pore pressure are recast in terms of new material parameters, more directly open to physical interpretation as the Poisson ratio and induced pore pressure coefficient in undrained deformation. Different formulations of the coupled deformation/diffusion field equations and their analogues in coupled thermoelasticity are discussed, and a new formulation with stress and pore pressure as basic variables is presented that leads, for plane problems, to a convenient complex variable representation of solutions. The problems solved include those of the suddenly introduced edge dislocation and concentrated line force and of the suddenly pressurized cylindrical and spherical cavity. The dislocation solution is employed to represent that for quasi-static motions along a shear fault, and a discussion is given, based on fracture mechanics models for fault propagation, of phenomena involving coupled behavior between the rupturing solid and its pore fluid, which could serve to stabilize a fault against rapid spreading. Also, the solution for a pressurized cylindrical cavity leads to a time-dependent stress field near the cavity wall, and its relevance to time effects in the inception of hydraulic fractures from boreholes, or from drilled holes in laboratory specimens, is discussed. Various limiting cases are identified, and numerical values of the controlling porous media elastic parameters are given for several rocks.

1,863 citations

Journal ArticleDOI
TL;DR: In this paper, a moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented, where the motion of each particle is calculated through interactions with neighboring particles covered with the kernel function.
Abstract: A moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. Deterministic particle interaction models representing gradient, Laplacian, and free surfaces are proposed. Fluid density is implicitly required to be constant as the incompressibility condition, while the other terms are explicitly calculated. The Poisson equation of pressure is solved by the incomplete Cholesky conjugate gradient method. Collapse of a water column is calculated using MPS. The effect of parameters in the models is investigated in test calculations. Good agreement with an experiment is obtained even if fragmentation and coalescence of the fluid take place.

1,653 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231,334
20222,968
2021694
2020648
2019643
2018616