We present the details of a lattice Boltzmann approach to phase separation in nonideal one- and two-component fluids. The collision rules are chosen such that the equilibrium state corresponds to an input foe energy and the bulk flow is governed by the continuity, Navier-Stokes, and, for the binary fluid, a convection-diffusion equation. Numerical results are compared to simple analytic predictions to confirm that the equilibrium state is indeed thermodynamically consistent and that the kinetics of the approach to equilibrium lie within the expected universality classes. The approach is compared to other lattice Boltzmann simulations of nonideal systems

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...

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This paper discusses wetting and capillary condensation transitions on a line and a rectangular array of cylinders using an interface potential formalism. For a line of cylinders, there is a capillary condensation transition followed by complete wetting if the cylinders are sufficiently close together. Both transitions disappear as the cylinder separation is increased. The dependence of the wetting phase diagram of a rectangular array of cylinders is discussed as a function of the chemical potential, substrate-fluid interaction strength and surface tension.PACS: 68.45.Gd and 47.55.Mh