Modified Van Der Waals Model Research Articles

Study of Shock-Compressed Argon Plasma Using Microwave Diagnostics

A microwave diagnostics method and radio interferometers with wavelengths of 3.2 and 2.1 mm are used to study the kinematic and electrophysical characteristics of shock-compressed argon plasma, which is initially at atmospheric pressure. This research study is carried out at pressures of 12–56 MPa, shock wave velocities of 3.1–6.2 km/s, temperatures 9000–19 000 K, and densities 0.006–0.012 g/cm3 for powers of Coulomb nonideality from 10−4 to 0.2. The data obtained on the shock-wave compressibility of argon are consistent with the known measurement results and calculations using the modified van der Waals model and the chemical plasma model. A set of values of the reflection coefficient of electromagnetic radiation from the shock wave front at wavelengths of 3.2 and 2.1 mm is obtained, which serves as a basis for estimating the conductivity and electron concentration behind the shock wave front. The experimental data are consistent with calculation results in a wave velocity range of 3.1–3.6 km/s. It is established that with a further increase in the velocity has no effect on the reflection coefficient.

Construction of global phase diagrams for binary mixtures with equal and unequal size of molecules by using the modified van der Waals model

The global phase diagram or master diagram is constructed for binary mixtures consist of the equal and unequal size of molecules by using the modified van der Waals model. The Griffiths shield region is also presented on the master diagram. The influence of various size differences ratio of molecules on the master diagram is investigated and discussed. It is observed that the GPD are symmetrical around ζ=0 for the equal-size of molecules and the deterioration in the symmetric behavior of GPD increases as differences of size of molecules increase. From the master diagram, all possible main types of phase behavior for every given interaction energy parameters and various size differences ratio of molecules can be seen directly without long and difficult calculations.

Estimating the self-diffusion and mutual diffusion coefficients of binary mixtures on the basis of a modified van der Waals model

The previously proposed model is used to determine the values of the self-diffusion coefficient of He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO2, NH3, and CH4 in the liquid and dense gaseous states, which were compared with the experimental data obtained at a pressure of ≈200 MPa and a temperature of ≈500 K. The calculations are carried out with the use of the equation of state of these substances in the form of a modified van der Waals model. The self-diffusion model was generalized for the case of mutual diffusion in binary mixtures, which is based on the modified model of the van der Waals state equation for mixtures. The modeled coefficient of mutual diffusion for a great number of binary mixtures of the above-mentioned individual substances is determined, and the results are compared with the known data. Without special calibration for the experiment, the model correctly predicts the relationship of the self-diffusion and mutual diffusion coefficients (with their variation by several orders of magnitude in the case where the density changes from gaseous to liquid) with both pressure and temperature. For most substances considered in the paper, the maximum deviations of calculations from the experiment do not exceed 30–50%.

Equation of state of silicon dioxide with allowance for evaporation, dissociation, and ionization

Based on a previously proposed modified van der Waals model for a mixture, a widerange semi-empirical equation of state for silicon dioxide with due allowance for evaporation, dissociation, and ionization is constructed. In the low-density limit, it transforms to Saha’s equation of state for a mixture of ideal gases consisting of ions and electrons. The model and simplifying assumptions used in constructing the equation of state are described. The values of constitutive parameters are given. Results of model calculations are compared with data obtained in experiments on shock compression of solid and porous quartz samples, isentropic unloading, etc.

GASFLOW analysis for the HySIM hydrogen refueling benchmark

Cryo-compressed hydrogen vessels for automotive application were simulated by means of the GASFLOW Simulation Code by using real gas equations of state for hydrogen based on Leachman’s NIST model and a modified van der Waals Model. The hydrogen tank systems here considered are those based on hydrogen storage concepts developed by the Bayerische Motoren Werke (BMW) Group and produced by the Lawrence Livermore National Laboratory (LLNL) and the Structural Composite Industries (SCI). In order to validate the GASFLOW simulations, the data and the simulation results provided in the frame of the HySIM project were used. The GASFLOW simulations show good agreement with data as well as with the HySIM simulations. The two real gas equations of state, Leachman’s NIST and modified van de Waals used in this study produced nearly identical results.

Shock-wave front thickness in a liquid estimated on the basis of the Navier-Stokes equations using a modified van der Waals model

Stationary plane shock-wave profiles in liquid argon are calculated by solution of the Navier-Stokes equations with the use of the equation of state and transport coefficients defined by a modified van der Waals model. The results are compared with previous molecular dynamics calculations and calculations based on the Navier-Stokes solution with the use of the Lennard-Jones potential. Their good agreement is shown in the pressure range ≈1–40 GPa. Apparently, for other simple liquids, the accuracy of estimates of the shock-wave thickness is expected to be the similar to that for argon. An advantage of this approach is the relative simplicity of the expressions for the thermodynamic and kinetic characteristics of the liquid, whose parameters can be easily calibrated base on available experimental data on compressibility.

Equation of State and Transport Coefficients of Argon, Based on a Modified Van der Waals Model up to Pressures of 100 GPa

A modified Van der Waals model of the equation of state and a model of transport coefficients (of viscosity, thermal conductivity, diffusion, and electrical conductivity) based on this modified Van der Waals model are described. The approach is used to describe the characteristics of liquid and gaseous argon. As a whole, model calculations are in reasonable agreement with results of various experiments up to pressures of the order of 100 GPa.

A modified Van der Waals model for the coexistence curve of expanded metals

Recent measurements for expanded Hg, Cs and Rb have shown that the liquid - vapour coexistence curves for these metals do not obey the `law of rectilinear diameters'. It is shown here that a two-state Van der Waals equation with a density-dependent cohesive energy will lead to compositional fluctuations that result in a breakdown of the `law'. Calculations predict that Hg and the alkali metals will exhibit similar behaviour near the critical point. However, in the case of Hg the 6p - 6s band-gap closure, which occurs at higher than critical densities, leads to an anomalous behaviour not observed in the alkali metals. The influence of this transition on the rectilinear behaviour is treated by introducing a further modification of the two-state model.

Non-classical interfacial tension and fluid phase behaviour

Gradient theory, as originally introduced by van der Waals [1], was used to predict interfacial tensions at temperatures close to the critical region of the pure components nitrogen, carbon dioxide, methane, propane, octane, decane, tetradecane, ethanol, butanol, and water, and of the binary system carbon dioxide + butane. A modified van der Waals model was introduced using an expression that incorporates the proper temperature dependence for the influence parameter. The Helmholtz free energy density of the homogeneous fluid of pure components was modelled using the modified Peng-Robinson equation of state as suggested by Chou and Prausnitz [2]. This model improves the description of the behaviour of equilibrium densities near critical points up to a reduced temperature of 0.99, and yields for the critical exponent β a value of 0.34, which is close to the experimental value of 0.325. Along the coexistence curve β is defined by ( ϱ l− ϱ v)∼(T c−T) β . The interfacial tension behaviour could be described with deviations less then 3%, for reduced temperatures lower than 0.99. However, the calculation of interfacial tensions at reduced temperatures above 0.99, shows a critical scaling exponent μ equal to 1.38, while experiments give μ=1.26. The exponent μ is defined by γ∼(T c−T) μ .

Molecular theory of fluid interfaces

A new description of fluid interfaces, the local correlation model, is developed in a gradient approximation to the interfacial density distribution but otherwise rests on fewer assumptions than either the modified Van der Waals model or Toxvaerd's mean field perturbation theory, with both of which it is compared. Its numerical predictions agree quantitatively with those of the modified Van der Waals model for a Lennard-Jones fluid. The differential equation for the density profile, which results from the gradient approximation, provides a particularly simple description of an interface: the intermolecular contributions to interface structure are divided among (1) interactions occurring in homogeneous fluid, and (2) interactions peculiar to inhomogeneous fluid, the latter being represented by an influence factor c and the total thermodynamic potential density ω of inhomogeneous fluid. Numerical results indicate that for a wide range of temperatures the differential equation gives interfacial density profiles and tensions in good agreement with the more rigorous integral equations.

Electric Field Effect on Critical Opalescence of Dipolar Binary Mixture

A modified van der Waals model is used to describe the effect of a time-varying external electric field on the critical mixing-point properties of a dipolar binary mixture. Assuming that the behavior of the concentration fluctuations about equilibrium is governed by linearized hydrodynamic equations and that the diffusion coefficient is determined by the instantaneous equilibrium state, the decay of the fluctuations is described. The relaxation time characterizing the electric field effect upon the light scattering by critical opalescence is related to the free relaxation of the concentration fluctuations.