Lattice Boltzmann Simulation of Nonideal Fluids

Abstract

A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase How is described. Thermodynamic consistency is ensured by introducing a nonideal pressure tensor directly into the collision operator. We also show how an external chemical potential can be used to supplement standard boundary conditions in order to investigate the effect of wetting on phase separation and fluid Aow in confined geometries.The approach has the additional advantage of reducing many of the unphysical discetrization problems common to previous lattice Boltzmann methods. The hydrodynamics and kinetics of two-component Auids present a wealth of physical problems of both fundamental and technological importance [1]. There is much current interest in the relevance of hydrodynamics to spinodal decomposition [2] and the effects of substrates with different wetting properties on phase separation and domain growth [3]. In addition, the fiow properties of multicomponent systems, particularly in porous media, have been intensively studied and are of great relevance to oil recovery [4]. Conventional methods for simulating two-phase How include numerical integration of the Navier-Stokes equations and molecular dynamics simulations [5]. These techniques are extremely computationally intensive and particularly difficult to implement in random geometries. A newer approach, the lattice Boltzmann method, has recently proved competitive [6]. Here a set of distribution functions defined on a lattice is allowed to relax to equilibrium via a Boltzmann equation, discrete in both space and time. The correct choice of equilibrium distribution ensures that in the long wavelength limit the Navier-Stokes equations are recovered. Several authors have set up lattice Boltzmann schemes for two-phase systems. In most approaches interface formation has been introduced phenomenologically by modifying the Boltzmann collision operator to impose phase separation [7]. Recent work by Shan and Chen [8] has attempted to relate phase separation to microscopic interactions by redefining the equilibrium velocity distribution so as to simulate a Quid with a nonideal equation of state. However, their approach leads to inconsistent thermodynamics unless a particular equation of state is chosen. In addition, all current schemes reach equilibrium distributions which have unphysical velocity fluctuations within the interfacial region [9].In this Letter we show for the first time that it is possible to set up a lattice Boltzmann scheme modeling isothermal hydrodynamics for two-phase systems. This is achieved by introducing directly into the collision operator the equilibrium pressure tensor for a nonideal quid. The resulting phase transition is pressure driven, as pertinent to a liquid-vapor system quenched to well below the critical point [10]. The lluid reaches the correct thermodynamic equilibrium as determined by the equation of state and a Maxwell construction.We first summarize the relevant results from the van der Waals formulation of quasilocal thermo...

Entropic lattice Boltzmann methods

“…These considerations make it very difficult to add potential interaction to lattice Boltzmann models. If we are willing to give up the idea of an exactly conserved energy, and instead consider isothermal systems, then methods of skirting these difficulties have been known and actively investigated for some time now [16,17]. More recently, a method of incorporating interaction that maintains exact (kinetic plus potential) energy conservation has also been proposed [18].…”

Multiphase lattice Boltzmann simulations for porous media applications

“…Among them, five representative models are the color gradient model [79][80][81], the inter-particle potential model [82][83][84], the free-energy model [85,86], Fig. 1 Single phase flow in a segmented, μCT image of a Dolomite sample including a a rendering of the pore volume (i.e.…”

“…The free-energy model proposed by Swift et al [85,86] is built upon the phase-field theory, in which a free-energy functional is used to account for the interfacial tension effects and describe the evolution of interface dynamics in a thermodynamically consistent manner. Similar to the inter-particle potential model [82], the free-energy model also includes both SCMP model and MCMP models [86].…”

Bubble Motion under Gravity through Lattice Boltzmann Method

“…Several kinds of lattice Boltzmann model for simulating multiphase fluid have been established and applied to the simulations of gas bubbles under gravitysuccessfully. These models include potential method proposed by Shan et al [7], color method proposed by Rothman et al [8], and free energy method proposed by Swift et al [9]and improved byZheng et al [10]. The free energy method [10] was proved to be a good tool for the study of two-phase flows with high viscosity ratios and high density ratio.As shown by Gupta et al [11] and Yu et al [12], in comparison with the case of single bubble, the motion of multiple bubbles under gravity could be much more complex due to hydrodynamic interactions between bubbles.…”