Combined equation of state for liquids and gases, which includes the classical and scaling parts

A new equation of state is suggested, which describes the P-ρ-T data for ⁴He and SF₆ in the ranges of reduced densities ?1 < (ρ?ρ _c )/ρ _c < 1 and of reduced temperatures ?0.3 < (T-T _c )/T _c < 0.3 (ρ _c and T _c are the critical values). This equation includes the regular equation of state approximating the P-ρ-T data outside of the critical region and the nonparametric scaling equation of state adequately describing the P-ρ-T data in the vicinity of the critical points, which are combined by the crossover function. The classical function of damping of fluctuations of density and temperature when moving away from the critical point is suggested as the crossover function. Two equations of state are used for the regular part of combined equation, namely, the new cubic equation of state suggested by us and the equation of state of Kaplun and Meshalkin. The nonparametric scaling equation of state with three system-dependent constants is used as the scaling part of the combined equation. The conditions (?P/?v) _T = 0 and (?² P/?v ² ) _T = 0 are valid for the combined equation at the critical point; binodal and spinodal are present, as is the case in classical equations of state. The approximation of the most exact data on ⁴He and SF₆ using the new equation reveals that the latter equation correctly describes the P-ρ-T data with mean-square error with respect to pressure of ±0.5%.     

Study of Edge Effect to Stop Liquid Spillage for Microgravity Application

The ability of a micro-groove to prevent the spreading of HFE-7100 fluid (C₄F₉OCH₃) having low surface tension (γ?= 13.6 mN/m) on a surface is studied. In this study, micro-grooves were made around square openings of a plate made of either polycarbonate or 316 stainless steel. To verify effectiveness of micro-grooves to stop the spread of HFE-7100, experiments were done under non-saturated and saturated conditions. Under non-saturated conditions the micro-grooves on both materials confined the liquid up to apparent angle of 55 ± 5° due to the edge effect. Saturated gas-vapor mixture with vapor mass fraction of w _v = 88% and w _v = 97% did not significantly influence the confinement of the liquid by the micro-groove. This result is promising for application of micro-grooved plates in CIMEX experiment planned for ISS.     

A thermodynamic property formulation for nitrogen from the freezing line to 2000 K at pressures to 1000 MPa

A new fundamental equation explicit in Helmholtz energy for thermodynamic properties of nitrogen from the freezing line to 2000 K at pressures to 1000 MPa is presented. A new vapor pressure equation and equations for the saturated liquid and vapor densities as functions of temperature are also included. The techniques used for development of the fundamental equation are those reported in a companion paper for ethylene. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (C _v), isobaric heat capacity (C _p), and velocity of sound are also included in that paper. The property formulation using the fundamental equation reported here may generally be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ± 2%, and velocity of sound values within ±2%. The fundamental equation is not intended for use near the critical point.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

A Thermodynamic Equation of State for Pentafluoroethane (R-125)

We developed a fundamental equation of state for pentafluoroethane (R-125, CHF₂CF₃) which is represented in terms of a non-dimensional Helmholtz free energy. The equation has been established on the basis of selected measurements of the pressure-density-temperature relation, speed of sound, heat capacities, and saturation properties. Linear and non-linear regression analysis was employed to determine the functional form and the numerical parameters. The equation represents all the thermodynamic properties of R-125 in the liquid and gaseous phases for temperatures between the triple point and 470 K, and pressures up to 35 MPa. The uncertainties are estimated to be about ±0.05% or 0.1 kPa for the vapor pressure, ± 0.05 % for the liquid and vapor densities, about ± 1 % for the isobaric and isochoric heat capacities in the liquid, and ± 0.5 % or ± 0.02 % for the speed of sound in the liquid and vapor, respectively.     

Equations of State for the Ozone-Safe Refrigerants R32 and R125

Equations of state for gaseous and liquid difluoromethane (R32) and pentafluoroethane (R125) were developed. The coefficients of the equations were determined using experimental density data and heat capacities c _v and c _s. The equations satisfy Maxwell's rule. The equations describe the thermodynamic properties of R32 and R125 at temperatures from 140 to 433 K and from 178 to 480 K, respectively, and at pressures up to 70 MPa within the experimental uncertainties. In particular, the root-mean-square deviations of the calculated values of density from the most reliable experimental data are equal to 0.10% for R32 and 0.12% for R125.     

Fracture mechanics approach to fatigue crack initiation from deep notches

Fracture mechanics approach is applied to fatigue crack initiation at the tips of deep, blunt notches including those with very small notch-tip radius. The theoretical relations between the stress intensity range ΔK_ρ and the notch-tip radius ρ for a fixed life for crack initiation were derived based on the models of dislocation-dipole accumulation and blocked slip-band. Those are approximated by a simpler equation: $\text{ΔK}{}_{\mathrm{\rho }}\text{ΔK}{}_{\mathrm{o}}\text{= (1 + ρ/ρ0)}\text{1}\text{2}$ where ΔK₀ and ρ0 are material constants which are related to the fatigue strength of smooth specimens Δρ0 as $\text{Δρ0 =}\text{2ΔK}{}_0\text{(πρ0)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The results of experiments done with bluntly notched compact tension specimens of a structural low-carbon steel agree with the above relation between $\text{ΔK}{}_{\mathrm{gr}}\text{ΔK}{}_{\mathrm{o}}$ and ρ/ρ_o. The method to predict ΔK_o, ρ_o and Δρ_o from the fatigue data of cracked and smooth specimens is proposed.     

A principle of corresponding states for the viscosity of non-quantum mono- and diatomic condensed gases

The reduced viscosity coefficient η_R for the saturated liquid state of argon, neon, krypton, xenon, oxygen, nitrogen, and fluorine is examined as a function of T_R and as a function of 1/ρ_R ? 1/ρ_oR. The reduction parameters are the critical ones: η_R = η/η_c where η_c is the viscosity of the liquid calculated at the critical point supposing there is no anomalous behaviour; T_R = T/T_c, ρ_R = ρ/ρ_c and ρ_oR = ρ_o/ρ_c. The density ρ_o is the density of the liquid where η = ∞.For the inert gases there is a good η_R(T_R) correspondence. From this fact the viscosity of radon is calculated.Where η_R is plotted as a function of 1/ρ_R ? 1/ρ_oR, a principle of corresponding states is found for the investigated condensed gases. For densities greater than about 2ρ_c the reduced fluidity φ_R = 1.868 (1/ρ_R ? 1/ρ_oR). In this range the overall average deviation between the calculated and the experimental fluidity is 2.6%.     

The explosive oxidation of hydrocarbons in a supercritical water

The kinetics of oxidation of naphthalene and a heavy oil residue (upon vacuum distillation) by oxygen dissolved in supercritical water is studied in a wide range of temperatures (663 K≤T≤1075 K) and pressures (31MPa≤P≤67MPa). It is established that the oxidation process exhibits an explosive (blow-up) character. The kinetic constants characterizing the thermal explosion are determined. For naphthalene, the heat evolution rate during the explosive oxidation obeys the law W _N=10^13.10±0.30exp((170.4±1.0 kJ/mol)/RT)×[C₁₀H₈]^0.46±0.01[O₂]^0.63±0.01[H₂O]^1.66±0.03kJ/(l s).     

Nonlinear Dynamics of Superflow in 3He-B: The Coupling of Sound and Helmholtz Oscillations

The nonlinear relation between supercurrent and superfluid velocity:j_s(v_s)=_sv_s (1-(v_s/v_c)²/3)provides a coupling mechanism between the sound and Helmholtz modes of a short cylindrical cavity closed by a superleak at the centre of one end. Appropriate nonlinear equations have been formulated and solved numerically. The simulations reveal an interesting coupling of sound and Helmholtz oscillations at large amplitude. If the driving frequency of the sound is above the (large amplitude) resonance by twice the (large amplitude) Helmholtz frequency, only an initial Helmholtz drive is required to set up combined Helmholtz and sound oscillations, which can then be sustained by off-resonance sound drive alone. The combined motion, in which Helmholtz oscillations are amplified by sound drive, has been observed experimentally, but it decays when the Helmholtz drive is switched off, although it is sustained for a while by Helmholtz drive alone. Modified simulations that allow for quasiparticle relaxation show that slow relaxation is the probable reason that the combined motion decays without Helmholtz drive even at the lowest temperatures where the resonance Q is high. Comparison of simulations and experiment also gives evidence for larger dissipation at large amplitudes and associated memory effects. The simulations show that in the combined motion the negative slope region of j_s(v_s) for v_s>v _c is being explored.     

Isochoric Heat Capacities of Propane + Isobutane Mixtures at Temperatures from 280 to 420 K and at Pressures to 30 MPa

The isochoric heat capacity (c_v) and pressure–volume–temperature-composition (pvTx) properties were measured for propane + isobutane mixtures in the liquid phase and in the supercritical region. The expanded uncertainty (k = 2) of temperature measurements is estimated to be ±13 mK, and that of pressure measurements is ±8 kPa. The expanded relative uncertainty for c_v is ±3.2% for the liquid phase, increasing to ±4.8% for near-critical densities. The expanded uncertainty for density is estimated to be ±0.16%. The present measurements for {xC₃H₈ +(1−x)i-C₄H₁₀} with x = 0.0, 0.498, 0.756, and 1.0, were obtained at 659 state points at temperatures from 270 to 420 K and at pressures up to 30 MPa. The experimental data were compared with a published equation of state. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal expansion,velocity of sound,and compressibility in liquid3He under pressure

We have measured the pressure at constant volumeP _v(T), of liquid³He as a function of temperature from 10 to 600 mK and at starting pressures from 1.6 to 28.1 bar. Simultaneously, we determined the hydrodynamic sound velocityc ₁, at the same pressures and temperatures. From these data we have derived very accurate values of the isobaric expansion coefficient α _p and the adiabatic compressibility κ.     

Phase transformations in water-aliphatic alcohol binary systems

The parameters of liquid-vapor phase transitions p _s , ρ _s , T _s and critical points p _c, ρ_c, T _c were determined from the experimental data on the p, ρ, T, x-dependences of aqueous solutions of aliphatic alcohols (methanol, ethanol, n-propanol) that contain 0.2,0.5, and 0.8 mole fractions (x) of ethanol and correspond to single-phase (gas, liquid), two-phase, or subcritical areas. The dependence of the pressure of saturated vapor in solutions on the temperature and density was described by means of the expansion of the compressibility factor Z = p/RTρ _m in powers of the density and temperature along the coexistence curve away from the critical point. The temperature dependence of the density of solutions along the coexistence curve and inside the critical area was fitted using the power functions of parameters ω ～ $\tau ^{\beta _i } $ , τ = (T ? T _c) and ω = (ρ_1,v ? ρ_c)/ρ_c.     

A thermodynamic property formulation for ethylene from the freezing line to 450 K at pressures to 260 MPa

A new thermodynamic property formulation based upon a fundamental equation explicit in Helmholtz energy of the form A=A(, T) for ethylene from the freezing line to 450 K at pressures to 260 MPa is presented. A vapor pressure equation, equations for the saturated liquid and vapor densities as functions of temperature, and an equation for the ideal-gas heat capacity are also included. The fundamental equation was selected from a comprehensive function of 100 terms on the basis of a statistical analysis of the quality of the fit. The coefficients of the fundamental equation were determined by a weighted least-squares fit to selected P--T data, saturated liquid and saturated vapor density data to define the phase equilibrium criteria for coexistence, C _v data, velocity of sound data, and second virial coefficients. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (C _v), isobaric heat capacity (C _p), and velocity of sound are included. The fundamental equation reported here may be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ±3 %, and velocity of sound values within ±1 %, except in the region near the critical point. The fundamental equation is not intended for use near the critical point. This formulation is proposed as part of a new international standard for thermodynamic properties of ethylene.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Isentropic exponents of real gases and application for the air at temperatures from 150 K to 450 K

Summary Three real gas isentropic exponentsk _Tv,k _rv,k _pT are introduced, which when used in place of the classical isentropic exponentk=c _p/c in the ideal gas isentropic change equations, the latter may describe very accurately the isentropic change of real gases. The usual practice of employing exponentk may lead to considerably incorrect results even when the value ofk corresponds to the correct local value ofc _p/c _v of the real gas under examination. The numerical values of the new exponents are calculated in the case of real air for temperatures from 150 K to 450 K and pressures from 1 bar to 1000 bar. It is seen that at low temperatures and high pressures the values of the new exponents differ considerably from the values of the classical exponentk. Therefore, the error resulting by approximating, as is usually the case, the behaviour of real gases by the ideal gas isentropic change equations in a stepwise fashion with exponentk instead of the new exponents, is considerable. It follows that exponentk, which appears in various relations in thermodynamics, fluid mechanics, gasdynamics, heat transfer etc., should be suitably replaced by combinations of the three exponents. Related numerical examples, made in the case of real air, showed that the use ofk leads (in the temperature and pressure ranges examined) to a 5% error in the calculation of blowby rate in internal combustion enginers, high pressure compressors or steam turbines and to a 50% error in the calculation of the isentropic expansion or compression.Nomenclature A _ij,B _i,N _ij,O _ij,Q _ij Coefficients - c Velocity - c _p Specific heat under constant pressure - c _v Specific heat under constant volume - h Specific enthalpy - k Isentropic exponent,k=c _p/c _v - k _pT Real gas isentropic exponent corresponding to the pair of variablesp,T - k _pv Real gas isentropic exponent corresponding to the pair of variablesp, v - k _Tv Real gas isentropic exponent corresponding to the pair of variablesT,v - M Mach number,M=c/ - p Pressure - p _c Pressure at the critical point - R Constant of the air,R=287.22 J/kg K - s Specific entropy - T Temperature - T _c Temperature at the critical point - v Specific volume - v _c Specific volume at the critical point - z Compressibility factor - Sound velocity - T Temperature increment With 14 Figures     

High-pressure,high-temperature study of GeS2 and GeSe2

Phase transitions of the GeX₂ (X = S, Se) dichalcogenides have been studied at pressures of up to p ? 8 GPa and temperatures from 675 to 1375 K, and portions of their p-T phase diagrams have been constructed using our and previous experimental data. The crystal structure of the GeS₂-III phase has been refined by the Rietveld method (HgI₂ structure, P4₂/nmc, a = 3.46906(2) Å, c = 10.9745(1) Å, Z = 2, D _x = 3.438 g/cm³, R = 0.06). GeSe₂-III crystals have been grown for the first time at p ? 7 GPa in the temperature range 875–1275 K. The unit-cell parameters of GeSe₂-III (hex) are a = 6.468 ± 0.004 Å and c = 24.49 ± 0.10 Å (D _meas = 5.16 g/cm³, D _x = 5.18 g/cm³, Z = 12).     

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

In the petroleum industry, measurements of the density and viscosity of petroleum reservoir fluids are required to determine the value of the produced fluid and the production strategy. Measurements of the density and viscosity of petroleum fluids require a transducer that can operate at reservoir conditions, and results with an uncertainty of about ±1% in density and ±10% in viscosity are needed to guide value and exploitation calculations with sufficient rigor. Necessarily, these specifications place robustness as a superior priority to accuracy for the design. A vibrating plate, with dimensions of the order of 1 mm and a mass of about 0.12 mg, clamped along one edge, has been fabricated, with the methods of Microelectromechanical (MEMS) technology, to provide measurements of both density and viscosity of fluids in which it is immersed. The resonance frequency (at pressure p = 0 is about 12 kHz) and quality factor (at p = 0 is about 2800) of the first order bending (flexural) mode of the plate are combined with semi-empirical working equations, coefficients obtained by calibration, and the mechanical properties of the plate to provide the density and viscosity of the fluid into which it is immersed. When the device was surrounded by argon at temperatures between 348 and 423 K and at pressures between 20 and 68 MPa, the density and viscosity were determined with an expanded (k = 2) uncertainty, including the calibration, of about ±0.35% and ±3%, respectively. These results, when compared with accepted correlations for argon reported in the literature, were found to lie within ±0.8% for density and less than ±5% for viscosity of literature values, which are within a reasonable multiple of the relative combined expanded (k = 2) uncertainty.     

Molar Heat Capacity (Cv) for Saturated and Compressed Liquid and Vapor Nitrogen from 65 to 300 K at Pressures to 35 MPa

Molar heat capacities at constant volume (C_v,) for nitrogen have been measured with an automated adiabatic calorimeter. The temperatures ranged from 65 to 300 K, while pressures were as high as 35 MPa. Calorimetric data were obtained for a total of 276 state conditions on 14 isochores. Extensive results which were obtained in the saturated liquid region (C_v⁽²⁾ and C_σ) demonstrate the internal consistency of the C_v (ρ,T) data and also show satisfactory agreement with published heat capacity data. The overall uncertainty of the C_v values ranges from 2% in the vapor to 0.5% in the liquid.     

Percolation of interacting particles deposited onto a planar substrate

A model for the diffusion of interacting particles deposited onto a planar substrate is analysed near its percolation threshold. In the Monte Carlo simulations on square lattices, the movement of particles depends on w/kT, where k is the Boltzmann constant, T the temperature and w is the lateral interaction energy of nearest neighbours; w>0 and w<0 correspond to the attractive and repulsive cases respectively. The extrapolated results for the infinite system show that the critical concentration ψ_c decreases continuously with w/kT, from ψ_c ≈ 0.661 (for w/kT = - 2.0) to ψ_c ≈ 0.512 (for w/kT = 2.0). Some details of the internal structure of clusters at ψ_c as well as the initial non-equilibrium regime are also studied as a function of w/kT.     

Study on Isochoric Specific Heat Capacity of Liquid R-410A and HFE-347pcf2

The isochoric heat capacity (c _v ) of R-410A [a mixture of 49.81 mass% difluoromethane (HFC-32) + 50.19 mass% pentafluoroethane (HFC-125)] and 1,1,2,2-tetrafluoroethyl-2,2,2-trifluoroethylether (HFE-347pcf2) was measured at temperatures from 277 K to 400 K and at pressures up to 30 MPa. The reported density measurements for R-410A and HFE-347pcf2 are in the single-phase region and cover a density range above 0.92 g·cm^?3 and 1.33 g·cm^?3, respectively. The measured data of R-410A are compared with data reported by other researchers. Also, the measured data of R-410A are examined with an available equation of state. As a result, it is found that the present c _v data for R-410A agree well with those by other researchers and the calculated values with the equation of state in the measurement range except near the critical isochore.