A particulate basis for a lattice-gas model of amphiphilic fluids

Abstract

We show that the flux-field expansion derived by for the Rothman-Keller immiscible fluid model can be derived in a simpler and more general way in terms of the completely symmetric tensor kernels introduced by those authors. Using this generalised flux-field expansion we show that the more complex amphiphilic model of Boghosian, can also be derived from an underlying model of particle interactions. The consequences of this derivation are discussed in the context of previous equilibrium Ising-like lattice models and other non-equilibrium mesoscale models.

On the dependence of the Navier–Stokes equations on the distribution of molecular velocities

“…per [4,1] = y f (y h y i y j δ kl + y h y i y k δ jl + y h y i y l δ jk + y h y j y k δ il + y h y j y l δ ik + y h y k y l δ ij + y i y j y k δ hl + y i y k y l δ jh + y i y l y j δ hk + y j y k y l δ ih ) + y i y j y k y l δ hf + y h y j y k y l δ if + y h y i y k y l δ jf + y h y i y j y l δ kf + y h y i y j y k δ lf .…”

“…These lowest order moments are precisely the hydrodynamic variables, and so we obtain an autonomous macroscopic description under very mild assumptions about the form of the local equilibrium distribution. Our results will follow from a remarkable property of the Taylor expansion of isotropic functions, which is proved in [1]. We first introduce some notation.…”

“…As we shall see in a moment, the tensors T n associated with the Taylor expansion of such isotropic functions take a particularly simple form. We follow the notation of [1] and define the nth-rank completely symmetric tensor kernel…”

“…We then write the first and second order solutions in terms of moments of the distribution function. In Section 3 we introduce the "fluxfield" expansion defined in [13] and the recursion relation proved in [1], and use this recursion to evaluate the moments, thereby obtaining the hydrodynamic equations for an arbitrary isotropic local equilibrium, in terms of the low order moments of that distribution. We close the paper with some further discussion and directions for future work.…”

Large-scale lattice Boltzmann simulations of complex fluids: advances through the advent of computational Grids

“…These techniques do not attempt to keep track of the state of every single constituent element of a system, nor do they use an entirely macroscopic description; instead, an intermediate, mesoscale model of the fluid is developed, coarse-graining microscopic interactions enough that they are rendered amenable to simulation and analysis, but not so much that the important details are lost. Such approaches include lattice gas automata (Frisch et al 1986;Rothman & Keller 1988;Rivet & Boon 2001;Love 2002), LBE (McNamara & Zanetti 1988Higuera & Jimènez 1989;Higuera et al 1989;Benzi et al 1992;Shan & Chen 1993;Lamura et al 1999;Chen et al 2000;Succi 2001;Chin & Coveney 2002), dissipative particle dynamics (Hoogerbrugge & Koelman 1992;Español & Warren 1995;Jury et al 1999), or the Malevanets-Kapral real-coded lattice gas (Malevanets & Kapral 1998;Hashimoto et al 2000;Malevanets & Yeomans 2000;Sakai et al 2000). Recently developed techniques (Garcia et al 1999;Delgado-Buscalioni & Coveney 2003) which use hybrid algorithms have shown much promise.…”