Entropy production in thermal phase separation: a kinetic-theory approach

Abstract

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

“…It should be stressed that kinetic effects are significant and traditional hydrodynamic models are not sufficient for fluid flows with small characteristic scales or large Knudsen numbers [26][27][28][29][30][31][32][33][34][35][36][37][38]. The TNE becomes crucial and even dominant in the evolution of multicomponent flows due to the existence of various complex material and/or mechanical interfaces [26][27][28][29][30][31][32][33][34][35][36][37][38]. In such complicated cases, to investigate the TNE is a significant and convenient way to study the fundamental kinetic processes.…”

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

“…From a computational resource perspective, the remarkable merits are brevity of programming, numerical potency, inherent parallelism, and ease treatment of intricate boundary conditions. This kind of method has comprehensive capacities in quite several fields, from phonon transport [13] to approximate incompressible flows [14][15][16][17][18][19][20][21][22][23][24][25], full compressible flows [26][27][28][29][30][31][32][33][34][35][36][37], dendrite growth [38,39] and thermal multiphase flows [40]. Recently, the mesoscopic kinetics method is also becoming increasingly popular in computational mathematics and engineering science for solving certain NPDEs, including Burgers' equations [41,42], Korteweg-de Vries equation [43], Gross-Pitaevskii equation [44], convection-diffusion equation [45][46][47][48][49][50][51], Kuramoto-Sivashinsky equation [52], wave equation [53,54], Dirac equation [55], Poisson equation…”

Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects

“…The collision term becomes complicated with increasing kinetic moments required due to the simplicity of the discrete equilibrium distribution function and the lattice symmetry [63,64]. In fact, a more direct way is to invoke a novel methodology, the discrete Boltzmann method (DBM), which is regarded as a modern variant of the standard LBM [10][11][12][13][65][66][67][68][69][70][71][72][73]. The DBM is based on the discrete Boltzmann equation, which can be solved with various numerical approaches.…”

“…Standard LBMs mainly serve as solvers of (incompressible or slightly compressible) Navier-Stokes (NS) equations or other partial differential equations and aim to be loyal to these original equations. The DBM is equivalent to a modified hydrodynamic model plus a coarse-grained model of the thermodynamic nonequilibrium behaviors [10][11][12][13][14][65][66][67][68][69][70][71][72][73]. In other words, the DBM kinetic modeling goes beyond traditional macroscopic governing equations in terms of physics recovered.…”