title: Lattice-Boltzmann model based on field mediators for immiscible fluids.
abstract: In this paper, a lattice BGK (Bhatnagar-Gross-Krook) model is proposed for immiscible fluids. Collision operator is decoupled considering mutual and cross collisions between lattice particles, with three independent parameters related to the species diffusivity and to the viscosity of each fluid. Field mediator's concept, described by Santos and Philippi [Phys. Rev. E 65, 046305 (2002)], is extended to the framework of the lattice-Boltzmann equation and interference between mediators and particles is modeled by considering that there is a deviation in particles velocity, proportional to the mediators' distribution at the site. A Chapman-Enskog analysis is performed leading to theoretical predictions of the macroscopic equations inside the transition layer and to the transition-layer thickness. Chapman-Enskog analysis is restricted to near-equilibrium states and was unable to predict the correct second-order interfacial tension dependence on the modeled long-range fields intensity. Interfacial tension was, only, correctly retrieved using a nonequilibrium solution. Theoretical predictions are compared with simulation results and the model is tested considering its ability in describing the dynamical behavior of the interface and Galilean invariance.
authors.affiliation: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, Santa Catarina, Brazil. emerich@lmpt.ufsc.br
authors.forename: L O E
authors.initials: LO
authors.lastname: Santos
authors.forename: P C
authors.initials: PC
authors.lastname: Facin
authors.forename: P C
authors.initials: PC
authors.lastname: Philippi