A Mean-Field Pressure Formulation for Liquid-Vapor Flows

2006 ◽  
Vol 129 (7) ◽  
pp. 894-901 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Capillary Waves ◽  
Wave Number ◽  
Density Profiles ◽  
Pressure Formulation ◽  
Boltzmann Method ◽  
Relationship Of ◽  
The Relationship ◽  
Liquid Vapor

A nonlocal pressure equation is derived from mean-field free energy theory for calculating liquid-vapor systems. The proposed equation is validated analytically by showing that it reduces to van der Waals’ square-gradient approximation under the assumption of slow density variations. The proposed nonlocal pressure is implemented in the mean-field free energy lattice Boltzmann method (LBM). The LBM is applied to simulate equilibrium liquid-vapor interface properties and interface dynamics of capillary waves and oscillating droplets in vapor. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, Laplace’s law of capillarity, dispersion relationship between frequency and wave number of capillary waves, and the relationship between radius and the oscillating frequency of droplets in vapor. It is shown that the nonlocal pressure formulation gives excellent agreement with theory.

A Mean-Field Free-Energy Lattice Boltzmann Model for Liquid-Vapor Interfaces

2006 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann ◽  
Mean Field Theory ◽  
Mean Field ◽  
Capillary Waves ◽  
Lattice Boltzmann Model ◽  
Wave Number ◽  
Gradient Theory ◽  
Pressure Equation ◽  
Liquid Vapor

A nonlocal pressure equation is proposed for liquid-vapor interfaces based on mean-field theory. The new nonlocal pressure equation is shown to be a generalized form of the nonlocal pressure equation of the van der Waals theory or the “square-gradient theory”. The proposed nonlocal pressure is implemented in the mean-field free-energy lattice Boltzmann method (LBM) proposed by Zhang et al (2004). The modified LBM is applied to simulate equilibrium interface properties and the interface dynamics of capillary waves. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, and the dispersion relation between frequency and wave number describing the dynamics of capillary waves. It is shown that the modified LBM gives very good agreement with the theories. In addition, preliminary calculations of phase transition and binary droplet coalescence are also presented.

First and second laws of thermodynamics: relationship, “inconsistency”, hidden effects

2020 ◽  
pp. 63-73
Author(s):  
A. M. Savchenko ◽  
Yu. V. Konovalov ◽  
A. V. Laushkin
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Entropy Of Mixing ◽  
Ideal Mixing ◽  
Laws Of Thermodynamics ◽  
Relationship Of ◽  
The Relationship

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

scholarly journals Simulation of phase separation in a Van der Waals fluid under gravitational force with Lattice Boltzmann method

2019 ◽  
Vol 29 (9) ◽  
pp. 3095-3109 ◽  
Author(s):  
Ezequiel Oscar Fogliatto ◽  
Alejandro Clausse ◽  
Federico Eduardo Teruel
Keyword(s):  
Phase Separation ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Van Der Waals ◽  
Numerical Results ◽  
Density Profiles ◽  
Content Type ◽  
Boltzmann Method ◽  
Liquid Vapor

PurposeThis paper aims to assess the accuracy of Lattice Boltzmann method (LBM) for numerical simulation of the stratification of a Van der Waals (VdW) fluid subjected to a gravity field and non-uniform temperature distribution. A sensitivity analysis of the influence of the pseudopotential parameters and the grid resolution is presented. The effect of gravity force on interface densities, density profiles and liquid volume fraction is studied.Design/methodology/approachThe D2Q9 multiple-relaxation-time pseudopotential LBM for two-phase flow is proposed to simulate the phase separation. The analytical solution for density profiles in a one-dimensional problem is derived and used as a benchmark case to validate the numerical results.FindingsThe numerical results reproduce the analytical density profiles with great accuracy over a wide range of simulation conditions, including variations of the gravity and temperature fields. Particularly, the numerical simulations are able to represent the effect of gravity on the existence and position of the liquid–vapor boundary of an ideal pure substance in thermodynamic equilibrium. The sensitivity of the results to variations of the calibration parameters of the VdW pseudopotential was assessed.Research limitations/implicationsThe numerical simulations were performed assuming a VdW fluid in a 2-D cavity with one periodic direction for which analytical solutions for benchmarking purposes are possible to obtain.Originality/valueThe following fundamental question is addressed: Is the pseudopotential LBM capable of simulating accurately the liquid–vapor equilibrium under gravity forces and temperature gradients? Moreover, regarding that the pseudopotential model requires the calibration of several internal parameters to achieve thermodynamic consistency, the sensitivity of the results to variations of these parameters is assessed.

Containment forces in low energy states of plasmoids

1987 ◽  
Vol 38 (2) ◽  
pp. 263-274 ◽  
Author(s):  
Daniel R. Wells ◽  
Lawrence Carl Hawkins
Keyword(s):  
Free Energy ◽  
Vector Fields ◽  
Energy State ◽  
Lagrange Equations ◽  
Magnus Force ◽  
Side Condition ◽  
Gas Laws ◽  
Relationship Of ◽  
The Relationship

The application of Hamilton's principle to the problem of the determination of the structure of low free energy state plasmoids is discussed. It is shown that Clebsch representations of the vector fields and representations involving side conditions on the functional result in the same sets of Euler–Lagrange equations. The relationship of these representations to the problem of containment forces in vortex structures (plasmoids) is considered. It is demonstrated that the lowest free energy state of an incompressible plasma is always Lorentz force and Magnus force free. For a compressible plasma obeying the adiabatic gas laws, the Magnus force is finite. Introduction of conservation of angular momentum as an additional side condition also results in finite containment forces.

PHENOMENOLOGICAL IMPLICATIONS OF HIGH-Tc SUPERCONDUCTIVITY

1992 ◽  
Vol 06 (14) ◽  
pp. 2499-2519 ◽  
Author(s):  
Y. L. MA ◽  
X. X. DAI
Keyword(s):  
Specific Heat ◽  
Lattice Structure ◽  
Equations Of Motion ◽  
Mean Field ◽  
Soliton Solutions ◽  
Real Space ◽  
Field Equations ◽  
Critical Magnetic Fields ◽  
Relationship Of ◽  
The Relationship

We develop a phenomenological model for high-T c superconductors. Some main features are emerging in copper oxides: characteristic quasi two-dimensional Cu-O planes, strong correlation of antiferromagnetism, existence of a vortex lattice structure, and observation of a small coherence length and a large penetration depth. These features indicate that the superconductive pair is reasonably constrained to a small volume in real space and may be conceived of as a string-carrying vortex, and therefore can be well simulated by the dual phenomenological local boson fields [Formula: see text] and Φ. The various mean-field ground states of the system are discussed. The field equations of motion are originally solved to get approximate analytical soliton solutions. The effective Hamiltonian is formulated by a variational method for finite temperatures. The model parameter behaviour described by the relationship of the variational parameters is investigated. We discuss the critical temperature T c , the specific heat cV and its jump Δc at T c , and the critical magnetic fields H c1 and H c2 . These results are in agreement with experimental observations, especially the critical behaviours and the zero temperature values. The model also allows interpretation of the variation of T c with oxygen vacancy x and that with doping fraction δ in Cu-O planes, as well as the dependence of γ (defined as the specific heat coefficient of the T-linear term) on δ.

A Mean-Field Free-Energy Approach to Lattice Boltzmann Method for Liquid-Vapor and Solid-Fluid Interfaces in Micro and Nanofluidics

2004 ◽  
Author(s):  
Junfeng Zhang ◽  
Baoming Li ◽  
Daniel Y. Kwok
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Mean Field ◽  
Contact Angles ◽  
Energy Approach ◽  
Fluid Interfaces ◽  
Field Representation ◽  
Fluid Systems ◽  
Boltzmann Method

We presented a lattice Boltzmann method (LBM) using a mean-field representation of the free energy for fluid systems. This free-energy approach provides more realistic contact angles and fluid density profiles near the vicinity of an impenetrable wall, which cannot be easily obtained by other LBM schemes. Our method was tested against various criteria and the results are in good agreement with those from thermodynamics and molecular dynamics considerations. This mean-field approach to LBM can have important implication on studies where the solid-fluid interactions are crucial to fluidic behaviors.

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