Dissipative and Fluctuating Hydrodynamic Interactions between Suspended Solid Particles via Lattice-Gas Cellular Automata

Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation

“…For simulations of particulate suspensions, the lattice-Boltzmann approximation has two important advantages over a nite-di erence approximation to the Navier-Stokes equations. First, the connection to molecular mechanics makes it possible to derive simple local rules for the interactions between the uid and the suspended solid particles (Ladd, 1993b); this was demonstrated in our earlier lattice-gas simulations (Ladd and Frenkel, 1990;Ladd, 1991;van der Hoef et al, 1991). Second, the discrete one-particle distribution function n i contains additional information about the dynamics of the uid beyond that contained in the Navier-Stokes equations; in particular, the uid stress tensor, although dynamically coupled to the velocity gradient (Frisch et al, 1987), has an independent signi cance at short times.…”

“…In comparison with our previous work (Ladd et al 1988;Ladd & Frenkel 1989Ladd 1991 ; van der Hoef et al 1991), here we have chosen to place the boundary nodes on the links connecting the interior and exterior regions, whereas in our latticegas simulations they were located on the nodes closest to the boundary surface. There is little to choose between the two methods; the link method has the advantage that it provides a somewhat higher resolution of the solid boundary surface, as can be seen (figure 2) from the much larger number of boundary nodes compared with the number of lattice nodes just inside the surface.…”

Simulating mesoscopic order

“…[9]). The latter calculations are non-trivial because the simulation of the dynamics of dense colloidal suspensions requires special techniques [10] that I will not go into here.…”

Scientific Issues in the Flow of Gases With Dispersed Solids

“…On the theoretical side, they have recommended research on hydrodynamic interactions between gas and solids, boundary conditions for the disperse phase, collisional interactions amongst particles (Jenkins and Savage, 1983;Lun, et al, 1984), and the role of inhomogeneities (Wang, et al, 1996;Agrawal, et al, 2001). On the numerical side, they have suggested further development of direct numerical simulations for large systems (e.g., Ladd, 1990Ladd, , 1991Ladd, , 1992.…”