Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects

Abstract

A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing a detailed inspection of various non-equilibrium observables. Based on the TNE features, we define TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium. The time evolution of the TNE intensity provides a convenient and efficient physical criterion to discriminate the stages of the spinodal decomposition and domain growth. Via the DBM simulation and this criterion, we quantitatively study the effects of latent heat and surface tension on phase separation. It is found that the TNE strength attains its maximum at the end of the spinodal decomposition stage, and it decreases when the latent heat increases from zero. The surface tension effects are threefold, prolong the duration of the spinodal decomposition stage, decrease the maximum TNE intensity, and accelerate the speed of the domain growth stage.

The study of uniaxial–biaxial phase transition of confined hard ellipsoids using density functional theory

“…We plan to investigate the phase transition diagram of the studied system which we expect to see a first order transition for the isotropic-nematic phase transition including a biaxial nematic phase and a continuous phase transition for the U-B one similar to [27,28]. It is good to mention here we have studied the equilibrium physical properties, however, some nonequilibrium behaviors can be examined as it has been done for liquid-vapour separation in [42].…”

Multicomponent Lattice Boltzmann Simulations of Gas Transport in a Coal Reservoir with Dynamic Adsorption

“…The Langmuir pressure varies directly with the adsorption rate constant, and with a larger Langmuir pressure, the adsorbed amount will drop in that the adsorption strength will become weaker with the increasing Langmuir pressure when the desorption rate constant is fixed, as expected from (14). Therefore, both the output concentration and the central concentration increased with the Langmuir pressure.…”

“…The heterogeneity of geometric shapes, the difference of pore size/distribution, and the involved multiple transport mechanism of fluid causing the difficulty of the research and causing the fluid flow and transport in the reservoir are usually treated at the representative elementary volume (REV) scale in experiments and numerical simulation [8][9][10][11][12]. Recently, the Lattice Boltzmann method (LBM) has been widely used in the field relevant to fluid flow and gas transport at the mesoscale because of its efficiency and effectiveness in the implementation of multiple interparticle interactions and complex geometry boundary conditions [13][14][15]. Nithiarasu et al [16] proposed a generalized Navier-Stokes equation for isothermal incompressible flow in porous media, which ignores the detailed structure of the porous media by including an additional term to account for the presence of a porous medium.…”

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

“…The study on the former helps understanding the latter and the nonlinear constitutive relations [35]. The new observations brought by DBM have been used to understand the mechanisms for formation and effects of shock wave, phase transition, energy transformation and entropy increase in various complex flows [30,34,36], to study the influence of compressibility on Rayleigh-Taylor instability [31,32]. In a recent study, it is interesting to find that the maximum value point of the thermodynamic nonequilibrium strength can be used to divide the two stages, spinnodal decomposition and domain growth, of liquid-vapor separation.…”

“…In order to alleviate the heavy computational burden of directly solving Boltzmann equation, a variety of Boltzmann equationbased methods, such as the unified gas-kinetic scheme (UGKS) [10,11], the discrete velocity method (DVM) [12], the discrete unified gas-kinetic scheme (DUGKS) [13,14], the lattice Boltzmann method (LBM) [2,[15][16][17][18][19][20][21][22][23][24][25][26], have been presented and well developed. Recently, Discrete Boltzmann Method (DBM) has also been developed and widely used in various complex flow simulations [27][28][29], such as multiphase flows [30], flow instability [31,32], combustion and detonation [33,34], etc. From the viewpoint of numerical algorithm, similar to finite-different LBM, the velocity space is substituted by a limited number of particle velocities in DBM.…”