Analytical Expressions For Pressure Research Articles

Fluid-fluid phase behaviour in the explicit hard spherocylinder solvent ionic model confined in a disordered porous medium

We propose a theoretical approach that takes into account the effects of a disordered porous confinement on the liquid–liquid phase behavior of the ionic solution modelled by the restricted primitive model with an explicit consideration of the neutral hard spherocylinder solvent. The theory is based on a combination of two approaches: the scale particle theory for the description of the reference system represented by a mixture of hard spheres and hard spherocylinders confined in a disordered hard-sphere matrix and the associative mean-spherical approximation for taking into account Coulomb interactions between ions. Alternatively, the mean spherical approximation is applied for the description of the ionic subsystem for comparison. For the considered solvent explicit model in a matrix, analytical expressions for pressure, free energy and partial chemical potentials are derived for the first time. Using these expressions, the liquid–liquid phase transition is studied, where one phase is enriched with ions and another one – with solvent particles. In the solvent-rich phase, the isotropic-nematic phase transition is observed due to the orientational ordering of the spherocylinder solvent particles at different porosities of a matrix. The effects of the matrix confinement and of the solvent particle elongation on the liquid–liquid and isotropic-nematric phase transitions are studied at different pressures. The role of association phenomena appearing between positively and negatively charged ions in phase behavior of the considered ionic solutions under confinement is discussed.

Diagnostic Relations between Pressure and Entropy Perturbations for Acoustic and Entropy Modes

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered and applied to numerical modelling with the direct possibility to use in atmosphere monitoring especially in such strong events which follow magnetic storms and other large scale atmospheric phenomena. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on a vertical coordinate, which essentially complicates the diagnostics. The relations connecting perturbations for acoustic and entropy (stationary) modes are analytically established and led to the solvable diagnostic equations. These equations specify acoustic and entropy modes in an arbitrary stratified gas under the condition of stability. The diagnostic relations are independent of time and specify the acoustic and the entropy modes. They provide the ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts uniquely at any instant within the total accessible heights range. As a prospective model, we consider the diagnostics at the height interval 120–180 km, where the equilibrium temperature of a gas depends linearly on the vertical coordinate. For such a heights range it is possible to proceed with analytical expressions for pressure and entropy perturbations of gas variables. Individual profiles of acoustic and entropy parts for some data are illustrated by the plots for the pure numerical data against those obtained by the model. The total energy of a flow is determined for both approaches and its vertical profiles are compared.

Alternative thermodynamic cycle for the Stirling machine

We develop an alternative thermodynamic cycle for the Stirling machine, where the polytropic process plays a central role. Analytical expressions for pressure and temperatures of the working gas are obtained as a function of the volume and the parameter that characterizes the polytropic process. This approach achieves closer agreement with the experimental pressure-volume diagram and can be adapted to any type of Stirling engine.

Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state

Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the approximation of the fourth order in temperature gradients. It is shown that the gradient contributions to the internal energy depend on the volume, while the entropy satisfies the second law of thermodynamics for nonequilibrium processes. The calculations are performed for dimensions 3D, 2D, and 1D.

Scaled Particle Theory for Multicomponent Hard Sphere Fluids Confined in Random Porous Media.

The formulation of scaled particle theory (SPT) is presented for a quite general model of fluids confined in a random porous media, i.e., a multicomponent hard sphere (HS) fluid in a multicomponent hard sphere or a multicomponent overlapping hard sphere (OHS) matrix. The analytical expressions for pressure, Helmholtz free energy, and chemical potential are derived. The thermodynamic consistency of the proposed theory is established. Moreover, we show that there is an isomorphism between the SPT for a multicomponent system and that for a one-component system. Results from grand canonical ensemble Monte Carlo simulations are also presented for a binary HS mixture in a one-component HS or a one-component OHS matrix. The accuracy of various variants derived from the basic SPT formulation is appraised against the simulation results. Scaled particle theory, initially formulated for a bulk HS fluid, has not only provided an analytical tool for calculating thermodynamic properties of HS fluid but also helped to gain very useful insight for elaborating other theoretical approaches such as the fundamental measure theory (FMT). We expect that the general SPT for multicomponent systems developed in this work can contribute to the study of confined fluids in a similar way.

Analytical and Experimental Investigation of Squeeze-Film Dampers Executing Circular Orbits

We have referred here the first results obtained in the course of an experimental research intended to examine oil film pressure of a squeeze film damper (with inertialess lubricant) executing circular orbits. An analytical expression for pressure arising into the gap was obtained before, for the short bearing SFD, in the general case of offset circular orbits. The expression obtained has permitted, in a simple way, the examination of the influence of the offset on pressure. Two approximated expressions for pressure (the one for pressure as a function of time at a fixed measuring section, the other for pressure along the circumference of the bearing at a given time), corresponding to centered orbits, were compared with the exact ones. We observed that the limits within which the nondimensional offset can be considered negligible, change according to comparisons between circumferential pressure diagrams or between pressure diagrams as functions of time. In the second case they are much wider. The experimental results concerned offset orbits with nominal radius r = 0.5C and offset δ < 0.1. Good accordance between theoretical and experimental pressure trends has been found, as concerns the positive part of dynamic pressure. As concerns the negative part of dynamic pressure, tests have shown that cavitation takes place for a more or less wide length, depending on feeding groove pressure, other conditions being equal. Complete effective pressure diagram coinciding with the theoretical one has been found for particular feeding conditions. Oil film tensile stresses have been frequently detected with both complete and incomplete diagrams owing to cavitation. Maximum measured tensile stress was about 220 kN/m2. It was finally found that theoretical and experimental trends are coincident only if the SFD is not starved. Analytical expression for pressure in the long bearing SFD executing offset circular orbits is referred in the appendix.

Unsteady Flow of Solid-Liquid Suspensions

Basic energy and momentum relationships are used to obtain analytical expressions for pressure and flow variations in suspended solid-liquid flow. The suspended flow occurs in a pressurized conduit system and transients are introduced into the system by rapidly closing a terminal valve. Pressure wave magnitudes and wave stapes generated by this action are investigated. Expressions are obtained describing the momentum exchange resulting from viscous action between the phases that occurs behind the wave front. Experimental results are obtained for several solid-liquid suspensions. The suspending liquid utilized is water and solid rubber, plastic, and sand particles with widely varied properties are used for the solid phase. Pressure wave magnitudes and wave shapes resulting from rapid closure of a terminal valve are recorded. Good agreement between the theoretical and experimental results is obtained.

Tangential Newtonian flow in annuli—II: Stead state pressure profiles

It is shown how the pressure distribution for isothermal, tangential flow of an incompressible fluid in an annulus may be calculated by first solving the problem for a compressible fluid and then taking the limit as the deviation from incompressibility vanishes. An analytical expression for pressure vs. the radial co-ordinate is obtained for either or both of the cylinders in motion.