Tait equation

About: Tait equation is a research topic. Over the lifetime, 359 publications have been published within this topic receiving 10081 citations.

An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids

Abstract: The thermodynamic properties of 254 end-members, including 210 mineral end-members, 18 silicate liquid end-members and 26 aqueous fluid species are presented in a revised and updated internally consistent thermodynamic data set. The PVT properties of the data set phases are now based on a modified Tait equation of state (EOS) for the solids and the Pitzer & Sterner (1995) equation for gaseous components. Thermal expansion and compressibility are linked within the modified Tait EOS (TEOS) by a thermal pressure formulation using an Einstein temperature to model the temperature dependence of both the thermal expansion and bulk modulus in a consistent way. The new EOS has led to improved fitting of the phase equilibrium experiments. Many new end-members have been added, including several deep mantle phases and, for the first time, sulphur-bearing minerals. Silicate liquid end-members are in good agreement with both phase equilibrium experiments and measured heat of melting. The new dataset considerably enhances the capabilities for thermodynamic calculation on rocks, melts and aqueous fluids under crustal to deep mantle conditions. Implementations are already available in thermocalc to take advantage of the new data set and its methodologies, as illustrated by example calculations on sapphirine-bearing equilibria, sulphur-bearing equilibria and calculations to 300 kbar and 2000 °C to extend to lower mantle conditions.

The Tait equation: 100 years on

Abstract: The “Tait equation,” which is now widely used to fit liquid density data over wide pressure ranges, is a modification of the original equation of Tait, published 100 years ago, to fit his results on the compressibility of fresh water and seawater at different pressures. The range of applicability of these different equations is discussed and it is concluded that their simplicity and accuracy in reproducing high pressure density data for dense gases, liquids, solids, and liquid mixtures will ensure their continued use.

Pressure-volume-temperature relationships for polymeric liquids : a review of equations of state and their characteristic parameters for 56 polymers

Abstract: A review of theoretical equations of state for polymer liquids is presented Characteristic parameters for six equations of state, as well as parameters for the empirical Tait equation, are given for 56 polymers where pressure–volume–temperature (PVT) data over a wide range of conditions could be found in the literature New PVT data are presented for four polymers: poly(epichlorohydrin), poly(ϵ-caprolactone), poly(vinyl chloride), and atactic polypropylene All six equations of state provide adequate fits of the experimental specific volume data for the 56 polymers in the low pressure range (up to 500 bar) The modified cell model of Dee and Walsh, the Simha–Somcynsky hole theory, the Prigogine cell model, and the semiempirical model of Hartmann and Haque, were all found to provide good fits of polymer liquid PVT data over the full range of experimental pressures The Flory–Orwoll–Vrij and the Sanchez–Lacombe lattice–fluid equations of state were both significantly less accurate over the wider pressure range © 1993 John Wiley & Sons, Inc

A unified simulation of the filling and postfilling stages in injection molding. Part I: Formulation

Abstract: This study employs a unified theoretical model to simulate the filling and postfilling stages of the injection-molding process. Implementation of such a model is based on a hybrid finite-element/finite-difference numerical solution of the generalized Hele-Shaw flow of a compressible viscous fluid under nonisothermal conditions. The shear viscosity of the polymeric material is represented by a Cross model for the shear-rate dependence and a WLF-type functional form for the temperature and pressure dependence, whereas the specific volume is modeled in terms of a double-domain Tait equation. The analysis also handles variable specific heat and thermal conductivity of the polymer as a function of temperature. Complex thin parts of variable thickness can be modeled and discretized by flat, triangular finite elements which may have arbitrary orientation in three-dimensional space, whereas runners and possible round pins or bosses in the part are represented as one-dimensional circular-tube elements. A control-volume scheme is employed that leads to automatic melt-front advancement during the cavity-filling stage.

PρT Measurements of Imidazolium-Based Ionic Liquids

Abstract: Experimental density measurements are reported, and the derived thermodynamic properties, such as the isothermal compressibility, the isobaric expansivity, and the thermal pressure coefficient are presented as Supporting Information for several imidazolium-based ionic liquids (ILs), namely, 1-ethyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [C2mim][NTf2], 1-heptyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [C7mim][NTf2], 1-octyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [C8mim][NTf2], 1-ethyl-3-methyl-imidazolium tetrafluoroborate [C2mim][BF4], and 1-butyl-3-methyl-imidazolium tricyanomethane [C4mim][C(CN)3] in the pressure (0.10 < p/MPa < 30.00) and temperature (293.15 < T/K < 393.15) domains. These ILs were chosen to provide an understanding of the influence of the cation alkyl chain length and the anion influence on the properties under study. Experimental densities are correlated with the Tait equation with an average absolute deviation (AAD) less than 0.04 %. Expe...