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.

Flow response of a segregating mixture by interacting lattice gas simulation

“…Understanding the global patterns from the mobility of individual constituents are difficult to monitor experimentally [24]. However, it is relatively easier to investigate flow and patterns [25,26] in such a complex particulate mixture by computer simulation methods such as lattice gas [27,28], molecular dynamics [29,30], and Monte Carlo [31] methods. Most of the particulate driven system [13][14][15][16][17][18][19][20][21][22][23] deal with conservative systems with a constant number of constituents.…”

Thermodynamic consistency in deriving lattice Boltzmann models for describing segregation in non-ideal mixtures

“…A model for this term was discussed by Santos et al [5]. Finally, f (p) MB (u) is the Maxwell-Boltzmann equilibrium distribution centred around n (p) , u and T ,…”

“…Gunstensen et al [1] and Gunstensen & Rothman [2] with their colour model, Shan & Chen [3,4] and the effectivemass model, and Santos et al [5] with a model based on field mediators. A model based on a temperature shift besides Shan & Chen's velocity shift was proposed by Sbrabaglia et al [6] for non-isothermal two-phase flows.…”

Structural response in steady-state flow of a multi-component driven system: interacting lattice gas simulation

“…A variety of patterns [6] have been observed in many different mixtures including granular systems by simple computer simulation models [7,8], e.g., pattern-forming segregation [9], lane formation [10], segregation and mixing [11][12][13][14][15][16]. Enormous efforts have been made in recent years to understand the structural evolutions in particulate mixtures by lattice gas [17,18], molecular dynamics [19,20], and Monte Carlo [21] methods. Distribution of dissimilar constituent particles leads to random yet well-defined structural patterns [22,16] as a function of parameters such as interaction and temperature.…”