Van Der Waals Equation Research Articles

Equationsof state in multiphase lattice Boltzmann method revisited.

The single-component multiphase fluids can be described by a single equationof state (EOS), and various EOSs have been employed in the multiphase lattice Boltzmann (LB) method. In this work, we revisit five commonly used EOSs, including the van der Waals EOS, the Redlich-Kwong EOS, the Redlich-Kwong-Soave EOS, the Peng-Robinson EOS, and the Carnahan-Starling EOS. The recent multiphase LB model with self-tuning EOS is employed because of its thermodynamic consistency in a strict sense and clear physical picture at the microscopic level. First, the way to incorporate these multiphase EOSs is proposed. Two scaling factors are introduced to independently adjust the surface tension and interface thickness, and the lattice sound speed is EOS-dependent to ensure the numerical stability. Then, numerical tests are conducted to validate the incorporations of these EOSs and compare their numerical performances. The surface tension and interface thickness are set to the same values for different EOSs in the comparisons. The liquid and gas densities, surface tension, and interface thickness by the LB simulation agree well with the thermodynamic results. The maximum density ratios achieved with different EOSs are at the same level and could be very close to each other when the interface thickness is relatively small. The effects of multiphase EOS, density ratio, and dimensionless relaxation time on the spurious current are discussed in detail. It is interesting to find the van der Waals EOS shows the best numerical performance in reducing the spurious current.

ВИЗНАЧЕННЯ ТИСКУ У КАМЕРІ ГАЗИФІКАЦІЇ ГАЗОГЕНЕРАТОРА

The purpose of the work: determination of patterns of pressure changes in the gasification chamber of the gas generator. Methodology of the work: a comprehensive approach, which includes theoretical studies of the processes of changing the thermodynamic parameters of the gas phase in the working chamber of the gas generator, a calculation and analytical method for determining the pressure of the working medium, depending on the temperature and its composition in the gas generator. Results: patterns of pressure changes in the working chamber of the gas generator at different operating modes were obtained. Scientific innovation: modeling and calculation of pressure indicators of the working medium in the working chamber of the gas generator, depending on the environmental factors: temperature and composition of the working medium, humidity of solid fuel, were carried out. It is taken into account that the gaseous phase is a real gas, according to the Van der Waals equation. An algorithm for calculating pressure based on data on quantitative indicators of gases in the mixture is proposed. The regularities of the behavior of the gas medium in the range of operating temperatures of the gas generator have been established. Practical significance: the obtained results made it possible to determine the pressure in the working chamber of the gas generator under different modes of its operation and to develop appropriate design solutions for the corresponding nodes (housing, sealing devices, etc.) of gas generators of narrow standard sizes. Key words: gas generator, combustion chamber, pressure, ideal gas, non-ideal gas, gas-air mixture, temperature.

δ − shocks and vacuum states in the Riemann problem for isothermal van der Waals dusty gas under the flux approximation

In this paper, we analyze the Riemann problem for concentration and cavitation phenomena to the isothermal Euler equations for van der Waals gas with dust particles in the presence of flux approximation. By the Riemann problem, we mean that it is an initial value problem for the system of conservation laws supplemented by constant discontinuous initial data involving one breaking. The existence of δ−shock and vacuum state in the Riemann problem for the system under consideration is examined. Further, it is shown that as the flux approximation and pressure vanish, the Riemann solution containing two shock waves to the isothermal Euler equation for van der Waals gas with dust particles converges to δ−shock solution and the Riemann solution containing two rarefaction waves tends to the vacuum state solution of the transport equations. Numerical simulations presenting the formation of δ−shocks and vacuum states for different flux approximations are also shown.

Nanobubble-induced significant reduction of the interfacial thermal conductance for few-layer graphene.

The heat transport properties of van der Waals layered structures are crucial for ensuring the reliability and longevity of high-performance optoelectronic equipment. Owing to the two-dimensional nature of atomic layers, the presence of bubbles is commonly observed within these structures. Nevertheless, the effect of bubbles on the interfacial thermal conductance remains unclear. Based on the elastic membrane theory and the improved van der Waals gas state equation, we develop an analytical formula to describe the influence of bubble shape on the interfacial thermal conductance. It shows that the presence of bubbles has a considerable impact on reducing the interfacial thermal conductance across graphene/graphene interfaces. More specifically, the presence of nanobubbles can result in a reduction of up to 53% in the interfacial thermal conductance. The validity of the analytical predictions is confirmed through molecular dynamic simulations. These results offer valuable insights into the thermal management of van der Waals layered structures in the application of next-generation electronic nanodevices.

Investigating the solvation behavior of some perchlorates in non-aqueous medium and predicting their ion-solvation thermodynamics using Born formula

A systematic study of volumetric, acoustic properties and thermodynamics of ion solvation, from appropriate data of sound velocity, density and conductivity of RNH3ClO4 (R is Ethyl, n-Propyl, n-Hexyl and n-Octyl) in binary mixtures of acetonitrile (AN) and dimethyl sulfoxide (DMSO) has been made at different temperatures. Various acoustical parameters like relaxation strength (r), Rao’s constant (R), Wada’s constant (W), available volume (Va), van der Waals constant (b) and apparent molal volume (Vɸ) were assessed through the experimental data of density and sound velocity at T = (298, 308, 318 and 328) K and at P = 0.1 MPa pressure. From the data of apparent molal volume, other parameters like limiting apparent molal expansibilities ϕEο and Hepler’s constant (∂ϕEο/∂T)p that helps in determining the structure making and structure breaking ability of solute in the solutions, were evaluated. In the second part of this work, the solvated radii (ri) of alkylammonium (RNH3+) and perchlorate (ClO4-) ions have been determined in the binary mixtures of AN-DMSO solvent system at four investigated temperatures. The solvated radii data is then fitted to modified Born equations, whose provenance and implications are discussed and is utilized to evaluate thermodynamics of solvation in terms of free energy change (ΔGI-S), entropy change (ΔSI-S) and enthalpy change (ΔHI-S) of ion–solvent interactions. It is shown that, the plot of ΔGI-S as a function of 1/ri is linear, indicating the investigated system to follow Born equations. Overall, the results obtained from volumetric, acoustic and thermodynamic data, indicates the possibility of effective solute–solvent interactions amidst the investigated system.

From the vapour–liquid coexistence region to the supercritical fluid: the van der Waals fluid

ABSTRACT In this work the interface system of the van der Waals fluid is investigated by using the density gradient theory incorporated with the mean-field theory. Based on the mean-field dividing interface generated by the Maxwell construction, we propose a highly accurate density profile model for the density gradient theory to facilitate reliable predictions of various properties for the interface region. It is found that the local intrinsic Helmholtz free energy peaks at the interface and that the maximum difference of the normal and tangential components of the pressure tensor corresponds to the maximum of the intrinsic Gibbs free energy. It is also found that the entire phase space is divided into gas-like and liquid-like regions by the single line composed of the mean-field interface and the Widom line. The two-fluid feature of the supercritical fluid is hence inherited from the coexistence region. Phase diagrams extended into the coexistence region in all the temperature-pressure-volume planes are thus completed with the solutions to the vapor–liquid equilibrium problem by the van der Waals equation of state.

Two‐phase states of the generalized van der Waals gas: Conditions of absolute and neutral shock wave stability

AbstractIn this work we discuss an approach to the construction of the areas of two‐phase states for real gases, state equations for which are from the article by Fogelson and Likhachev in 2004 and formulate conditions that define absolute and neutral stability of the shock waves.

Thermodynamic and Thermophysical Properties of Air as a Mixture by Using Schreiber-Pitzer EoS

Air is one of the most important substances used in industrial and technological applications. Applications of air require a consistent set of reliable data on its thermodynamic and thermophysical properties. Over the last few decades, researchers have developed a number of empirical and theoretical models for the correlation and prediction of the thermodynamic and thermophysical properties of pure fluids and mixtures. The ideal gas Equation of State (EoS) is used in gas thermodynamic property calculations extensively, but in applications with higher pressure zones, the error levels are increasing. For most applications, an equation of state with better accuracy of thermodynamic properties will be required for extreme cases. In this study, Schreiber-Pitzer EoS is considered for better accuracy of the thermodynamic properties for air mixture. A set of computer programs were developed in java language to calculate the thermodynamic and thermophysical properties of air as a mixture of Nitrogen, Oxygen and Argon. The Schreiber-Pitzer EoS results are compared with Peng-Robinson EoS, Redlich-Kwong EoS, Van der Waals EoS, and ideal gas EoS utilizing cubic spline curve fitting for cp values. The thermodynamic and thermophysical property results and percentages of differences are calculated. The percentages of differences are increasing with increasing pressure and decreasing temperature.

Global Stability of the Curzon-Ahlborn Engine with a Working Substance That Satisfies the van der Waals Equation of State.

In this paper, we show an analysis of the global stability of a Curzon-Ahlborn engine considering that the working substance of the engine satisfies the Van der Waals equation of state, which is more general than the ideal gas case. We use the Lyapunov stability theory for the case where the engine operates at a maximum power output. We analyze the steady state of the intermediate temperatures as well as the asymptotic behavior of the performance of the engine. Additionally, we study the relationship between the inherent time delay by analyzing the dynamic properties of the system and the stability of the steady state. We present illustrative graphs of the obtained results. Finally, we include a brief discussion of the obtained results and appropriate conclusions.

Mathematical Model Simulation of Non-Linear Equations using MATLAB: Specific Volume of Gas with Van der Waals Equation

Computational physics is concerned with the application of numerical methods in solving physical problems. The van der Waals gas model is one of the most common non-linear models. This study simulated a mathematical model of a non-linear equation using MatLab for the case of the specific volume of gas in the equation of the state of van der Waals. This study aimed to determine the molar volume and compressibility factor, as well as describe the relationship between the compressibility factor and the reduced pressure. The method of the study is experimental. The independent variables are the reduced pressure and temperature values. The dependent variable is the determination of the value of the molar volume (V) and the compressibility factor (Z). The control variable, in the form of a function used in solving this case, is based on van der Waals equation with the gas used is ammonia. The fzero command can be used to solve f(x)=0 with a single variable. This program that has been running successfully can show various predictions in the form of reduction pressure, thus obtaining the values of the molar volume and compressibility factor using the ideal gas equation. There is a deviation in ammonia gas, the Z1 at high reduction pressures and Z1 at medium pressures. This study can provide contributions and benefits in the form of material enrichment of thermodynamics to understand how real gases behave. The ideal gas equation can be modified into the van der Waals equation.

Excluded volume of the system of hard-core spheres revisited: New insights from computer simulations

The role of excluded volume in the equation of state of hard-sphere system is studied by analytical theory and computer simulations. The excluded-volume parameter b(ρ) introduced in the van der Waals equation is examined as a function of density. A number of approximations are considered and tested against Monte Carlo simulations. Parameter b(ρ) is seen to decline by a factor of 2 over the density range in which the system is still in the fluid state. Partial contributions of two- and three-sphere intersections to b(ρ) are analyzed as a function of density. The resulting series is seen to be converging very slowly. An approximation based on Padé approximants is seen to offer best accuracy at the lowest cost. It involves computation of the three lowest virial expansion coefficients B2,B3 and B4. Numerical tests reveal that this approximation is accurate in the case of ellipsoids and a number of hard-core polyhedra, supporting a potential application in phase equilibria studies of molecules with non-spherical shapes, such as cubes, pear-shaped molecules and so on.

Anisotropic model of super dense star with linearized core and Van der Waals envelope

In this research, core envelope model of a super dense spherically symmetric compact star is developed by considering anisotropic matter configuration. The core is represented by a linear equation of state (EOS), whereas the Van der Waals EOS is used in the envelope region. In the core and envelope of the star, all geometrical and physical factors are viable. The three regions, i.e. the core, envelope and outer space satisfy the junction conditions. The proposed model validates with the properties of Vela X-1, Her X-1 and SMC X-1. It is concluded that in the model presented, the core of the star compresses as the mass increases justifying the domination of gravitational effects on massive astronomical objects.

TWO-COMPONENT STATISTICAL MODEL OF A NUCLEAR FIREBALL IN THE COOLING STAGE (FREEZEOUT)

The saddle point method is applied to the statistical integral of the Grand Canonical Ensemble for the cases of one-component and two-component van der Waals gas. This made it possible to obtain the state equation and corrections to the pressure and density of the final statistical system. These contributions, taking into account the realistic effective potential, make it possible to take into account the finite dimensions of the system and, as expected, can be used, in particular, in the case of a nuclear fireball that occurs in high-energy nucleus-nucleus collisions. The corrections depending on the size of the system were compared with the corresponding fluctuations. These corrections become insignificant at the thermodynamic boundary, where, according to statistical physics, the difference between the observed thermodynamic quantities obtained in different statistical ensembles disappears. Taking into account modern estimates of the sizes of mesons and nucleons, as well as realistic estimates for the potentials of their effective interactions, formulas for pressure with a transparent nonrelativistic constraint are obtained. It is expected that they can be used to analyze experimental data on the quantitative characteristics of the yield of particles of various types in the final state from the final stages of the freezeout and to determine the critical parameters of the system in high-energy nucleus-nucleus collisions.

Symmetry and self-similar analysis of natural convection of van der Waals gases over a vertical plate

In this work, the symmetry method was first applied to the study of the problem of free convection of van der Waals gas with physical properties that differ from an ideal gas under steady-state conditions. Using the previously obtained simplified form of the equation of state for a van der Waals gas, the nature of the influence of its parameters on the process of convective heat transfer is studied in comparison with the case of using the equation of state for an ideal gas. While solving the problem, it was revealed that nonlinear parameters in the equation of state for van der Waals gas can intensify or worsen the heat transfer process. This feature is associated with the influence of the parameters of the van der Waals gas equation of state on the flow in the boundary layer. The data obtained based on the transport equations in a self-similar form are compared with the results of the previously obtained analytical solution. It is shown that the trends of the influence of the parameters of the simplified equation of state for a van der Waals gas on the Nusselt number agree well with the analytical studies.

Phase transition and quantum corrections of quintessential Kerr–Newman black hole with cloud of strings

The purpose of this manuscript is to inspecting the phase transition and the critical phenomenon of charged quintessential Kerr-Newman-anti-de Sitter black hole with cloud of strings. In this regard, we evaluate the thermodynamic factors (Hawking temperature, angular momentum and entropy) in the framework of extended phase space. These factors fulfill the Smarr-Gibbs-Dehum equation in the existence of quintessence and cloud of strings. The critical behavior of thermodynamic factors is discussed via two techniques such as Maxwell equal-area law and Van-der Waal like equation of state . It is obtained that the former one is more effective to observe the critical nature of the complex black holes. Further, we study the phase diagram in T − S plane using equal-area law and obtain an isobar depicting the coexistence era of two phases. It is concluded that black holes lower than the critical temperature exhibit the phase transition same as that of Van-der Waal fluid. At the end, we analyze the influence of thermal variations on the black hole’s stability. • We inspect the critical phenomenon of quintessential string Kerr-Newman-AdS BH. • The critical behavior via Maxwell equal-area law and Van-der Waal EoS is studied. • Below the critical temperature, BHs show the VdW fluid like phase transition. • At the end, we analyze the influence of thermal variations on the black hole’s stability.

Tunable electronic structures of covalent triazine frameworks/GaS van der Waals heterostructures via a perpendicular electric field and parallel strain

This study employs the density functional theory to verify the electronic structures of covalent triazine frameworks (CTF)/GaS van der Waals heterostructures (vdWhs) in response to parallel strain and the perpendicular external electric field. The CTF/GaS vdWh is an indirect-semiconductor containing a type-II band alignment at an electric field from −1.5 to 1.4 V/Å. Additionally, a semiconductor to metal transition appeared at −1.6 and 1.5 V/Å. Furthermore, the CTF/GaS vdWhs exhibit a direct-semiconductor to indirect-semiconductor transition at −3% parallel strain. These results indicate the ability of CTF/GaS vdWhs in new high-efficiency optoelectronic devices.

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme (DUGKS) for simulations of multiphase fluid flow, we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS. Due to the flux reconstruction procedure, additional terms that break the isotropic requirements of the pseudopotential model will be introduced. To eliminate the influences of nonisotropic terms, the expression of equilibrium distribution functions is reformulated in a moment-based form. With the isotropy-preserving parameter appropriately tuned, the nonisotropic effects can be properly canceled out. The fundamental capabilities are validated by the flat interface test and the quiescent droplet test. It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces. The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition. Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state. By directly incorporating the intermolecular interactions, the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors, which could help gain fresh insights into multiphase fluid flow.

Janus van der waals equations for real molecules with two-sided phase transitions

We obtained families of generalized van der Waals equations characterized by an even number n = 2, 4, 6 and a continuous free parameter, which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature Tc and arbitrarily two close critical densities. The critical phase transitions are naturally two-sided: the critical exponents are αP=γP=23 and βP=δ−1=13 for T > Tc and αP=γP=nn+1 and βP=δ−1=1n+1 for T < Tc. In contrast with the original van der Waals equation, our novel equations all reduce consistently to the classical ideal gas law in the low-density limit. We tested our formulas against the NIST data for 11 major molecules and showed agreements better than the original van der Waals equation, not only near to the critical points but also in low-density regions.

A first order hyperbolic reformulation of the Navier-Stokes-Korteweg system based on the GPR model and an augmented Lagrangian approach

In this paper we present a novel first order hyperbolic reformulation of the barotropic Navier-Stokes-Korteweg system. The new formulation is based on a combination of the first order hyperbolic Godunov-Peshkov-Romenski (GPR) model of continuum mechanics with an augmented Lagrangian approach that allows to rewrite nonlinear dispersive systems in first order hyperbolic form at the aid of new evolution variables. The governing equations for the new evolution variables introduced by the rewriting of the dispersive part are endowed with curl involutions that need to be taken care of. In this paper, we account for the curl involutions at the aid of a thermodynamically compatible generalized Lagrangian multiplier (GLM) approach, similar to the GLM divergence cleaning introduced by Munz et al. for the divergence constraint of the magnetic field in the Maxwell and MHD equations. A key feature of the new mathematical model presented in this paper is its ability to restore hyperbolicity even for non-convex equations of state, such as the van der Waals equation of state, thanks to the use of an augmented Lagrangian approach and the resulting inclusion of surface tension terms into the hyperbolic flux.The governing PDE system proposed in this paper is solved at the aid of a high order ADER discontinuous Galerkin finite element scheme with a posteriori subcell finite volume limiter in order to deal with shock waves, discontinuities and steep gradients in the numerical solution. We propose an exact solution of our new mathematical model, show numerical convergence rates of up to sixth order of accuracy and show numerical results for several standard benchmark problems, including travelling wave solutions, stationary bubbles and Ostwald ripening in one and two space dimensions.

The expansion of a non‐ideal gas around a sharp corner for 2‐D compressible Euler system

In this paper, we consider the problem of expansion of a non‐ideal gas turning around corresponding large or small sharp corner for 2‐D compressible Euler system. We focus on extending the results of this problem for polytropic gas to that for a more realistic gas, that is, van der Waals gas. In this case, rarefaction waves, shock wave, fan–jump composite waves, or fan–jump–fan composite waves may be appeared. The flow expands to vacuum state when the inclination angle is small enough, that is, a zone of cavitation will come into being. Otherwise, the flow will arrive at a zone of constant state. The corresponding problem can be transformed into interaction of a planar rarefaction wave with a planar centered wave and interaction of a simple wave with rigid wall, which are actually characteristic boundary value problems for 2‐D self‐similar Euler system. The estimates of solution are obtained by making use of characteristic analysis, corresponding characteristic decompositions and invariant region of solution. Furthermore, by extending the local solution, and combining with those estimates and hyperbolicity, the existence of global classical solution up to the interface of non‐ideal gas with vacuum is obtained.