A multicomponent lattice Boltzmann model recently introduced [R. Benzi et al., Phys. Rev. Lett. 102, 026002 (2009)] to describe some dynamical behaviors of soft-flowing materials is theoretically analyzed. Equilibrium and transport properties are derived within the framework of a continuum free-energy formulation and checked against numerical simulations. Due to the competition between short-range interspecies repulsion and midrange intraspecies attraction, the model is shown to give rise to a very rich configurational dynamics of the density field, exhibiting numerous features of soft-flowing materials such as long-time relaxation due to caging effects, enhanced viscosity and structural arrest, aging under moderate shear, and shear-thinning flow above a critical shear threshold. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3216105
The purpose of this paper is to give an overview in the realm of numerical computations of polydispersed turbulent two-phase flows, using a mean-field/PDF approach. In this approach, the numerical solution is obtained by resorting to a hybrid method, where the mean fluid properties are computed by solving mean-field (RANS) equations with a classical finite volume procedure whereas the local instantaneous properties of the particles are determined by solving stochastic differential equations (SDEs). The fundamentals of the general formalism are recalled and particular attention is focused on a specific theoretical issue: the treatment of the multiscale character of the dynamics of the discrete particles, i.e. the consistency of the system of SDEs in asymptotic cases. Then, the main lines of the particle/mesh algorithm are given and some specific problems, related to the integration of the SDEs, are discussed, for example, issues related to the specificity of the treatment of the averaging and projection operators, the time integration of the SDEs (weak numerical schemes consistent with all asymptotic cases), and the computation of the source terms. Practical simulations, for three different flows, are performed in order to demonstrate the ability of both the models and the numericals to cope with the stringent specificities of polydispersed turbulent two-phase flows. q
The dynamical behavior of a conÐguration consisting of a plane Ñuid wake Ñowing in a current sheet embedded in a plasma sheet that is denser than its surroundings is discussed. This conÐguration is a useful model for a number of structures of astrophysical interest, such as solar coronal streamers, cometary tails, the EarthÏs magnetotail and Galactic center nonthermal Ðlaments. In this paper, the results are applied to the study of the formation and initial motion of the plasma density enhancements observed by the Large-Angle Spectrometric Coronagraph (LASCO) instrument onboard the Solar and Heliospheric Observatory (SOHO) spacecraft. It is found that beyond the helmet cusp of a coronal streamer, the magnetized wake conÐguration is resistively unstable, that a traveling magnetic island develops at the center of the streamer, and that density enhancements occur within the magnetic islands. As the massive magnetic island travels outward, both its speed and width increase. The island passively traces the acceleration of the inner part of the wake. The values of the acceleration and density contrasts are in good agreement with LASCO observations.
A mesoscopic multi-component lattice Boltzmann model with short-range repulsion between different species and short/mid-ranged attractive/repulsive interactions between like-molecules is introduced. The interplay between these composite interactions gives rise to a rich configurational dynamics of the density field, exhibiting many features of disordered liquid dispersions (microemulsions) and soft-glassy materials, such as long-time relaxation due to caging effects, anomalous enhanced viscosity, ageing effects under moderate shear and flow above a critical shear rate. PACS numbers:The rheology of flowing soft systems, such as emulsions, foams, gels, slurries, colloidal glasses and related fluids, is a fast-growing sector of modern non-equilibrium thermodynamics, with many applications in material science,chemistry and biology [1].These materials exhibit a number of distinctive features, such as long-time relaxation, anomalous viscosity, aging behaviour, whose quantitative description is likely to require profound extensions of non-equilibrium statistical mechanics. The study of these phenomena sets a pressing challenge for computer simulation as well, since characteristic time-lenghts of disordered fluids can escalade tens of decades over the molecular time scales. To date, the most credited techniques for computational studies of these complex flowing materials are Molecular Dynamics and Monte Carlo simulations [2]. Molecular dynamics in principle provides a fully ab-initio description of the system, but it is limited to space-time scales significantly shorter than experimental ones. Monte Carlo methods are less affected by these limitations, but they are bound to deal with equilibrium states. As a result, neither MD nor MC can easily take into account the non-equilibrium dynamics of complex flowing materials, such as micro-emulsions, on space-time scales of hydrodynamic interest. In the last decade, a new class of mesoscopic methods, based on minimal lattice formulations of Boltzmann's kinetic equation, have captured significant interest as an efficient alternative to continuum methods based on the discretization of the Navier-Stokes equations for non-ideal fluids [3]. To date, a very popular such mesoscopic technique is the socalled pseudo-potential-Lattice-Boltzmann (LB) method, developed over a decade ago by Shan and Chen (SC) [4]. In the SC method, potential energy interactions are represented through a density-dependent mean-field pseudopotential, Ψ[ρ], and phase separation is achieved by imposing a short-range attraction between the light and dense phases. In this Letter, we provide the first numerical evidence that a suitably extended, two-species, mesoscopic lattice Boltzmann model is capable of reproducing many features of soft-glassy (micro-emulsions), such as structural arrest, anomalous viscosity, cage-effects and ageing under shear. The key feature of our model is the where f is is the probability of finding a particle of species s at site r and time t, moving along the ith lattice direction defi...
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