Mesoscopic Lattice Boltzmann Modeling of Flowing Soft Systems

Abstract

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...

Galilean invariant fluid–solid interfacial dynamics in lattice Boltzmann simulations

“…The lattice Boltzmann equation (LBE) [3][4][5][6] eliminated this artifact with the use of a proper equilibrium distribution function in the collision term, and in some investigations a few high-order, even complete Galilean invariant LBE models have been achieved [7][8][9]. Nowadays, LBE is particularly successful in simulations involving interfacial dynamics [10][11][12][13], microflows [14,15], multiphase flows [16][17][18], and complex fluid flows [19][20][21].…”

Mesoscopic model for microscale hydrodynamics and interfacial phenomena: Slip, films, and contact-angle hysteresis

“…The model we propose is based on the Boltzmann-BGK equation for a single-component fluid [10,12] ∂f ∂t…”

“…For the class of LB models we employ [11,12], the volumetric body force ρg = ψ(x, t)∇ w(|r|)ψ(x + r, t)dr is determined by a spatial convolution of the pseudo-potentials ψ with the Gaussian kernel w(|r|) = (2πκθ) −2/D exp(−|r| 2 /2κθ). The characteristic length scale √ κθ of the interaction kernel determines the thickness of the resulting interfaces (in all our computations we use κ = 1).…”

“…(8) The long-range fluid-solid interactions thus receive similar treatment to that described in [12], using different pseudo-potentials for cross interactions between species. Hereafter, we refer to all those microscopic interactions that act beyond an atomic radius as long-range; in this work long-range forces are mainly associated to van der Waals interactions and ionic double layers.…”

Shear banding from lattice kinetic models with competing interactions

“…In the recent past, we presented a new conceptual/computational scheme for the numerical simulation of soft-flowing materials [12][13][14][15]. The scheme is based on a (lattice) Boltzmann (LB) formulation [16][17][18] for interacting binary fluids [19,20], in which, by a proper combination of short-range attraction and mid-range repulsion (competing self-interactions), an effective form of frustration was encoded within the physics of the binary mixture [12,13].…”