Steady state hydrodynamics of a lattice Boltzmann immiscible lattice gas

Role of inertia in two-dimensional deformation and breakdown of a droplet

“…While lattice Boltzmann fully treats inertial effects, a stationary zero Reynolds number flow can also be simulated (essentially by switching off the term in the algorithm that handles fluid convection). In contrast to previous suggestions [6,11], we found that a two-dimensional droplet in a shear flow at zero Re does not break up by any fluidmechanical process. Instead it continues to deform (Figure 1) until the width of the droplet is comparable to the interface width, at which point dissolution-assisted breakup occurs.…”

“…Much of this work uses a flow protocol based on sudden onset of shearing at different flow rates, rather than a gradual ramping up of the rate; this saves much time numerically but describes a distinct physical situation from the slow ramp studied here; both are of interest experimentally.The situation is somewhat different in two dimensions. Although not realizable directly in laboratory experiments, this case is more accessible by simulation [6,7], and is interesting because the nonlinear physics involved in breakup may not be the same as in 3D. In 2D, the Rayleigh instability is effectively switched off, because periodic variations in the width of the droplet (at fixed volume) always increases the amount of interface.…”

“…The situation is somewhat different in two dimensions. Although not realizable directly in laboratory experiments, this case is more accessible by simulation [6,7], and is interesting because the nonlinear physics involved in breakup may not be the same as in 3D. In 2D, the Rayleigh instability is effectively switched off, because periodic variations in the width of the droplet (at fixed volume) always increases the amount of interface.…”

Macroscopic surface tension in a lattice Bhatnagar-Gross-Krook model of two immiscible fluids

“…1. Then, for example, the prioritization of links 1-9 that results when f គ (x,t) is found to lie in angular interval ␤ is, in descending order, i ϭ3, 4,5,2,9,6,1,8,7. The need to resolve f គ (x,t) into 16 intervals emerges as one attempts to determine which of links i ϭ2 or 5 is third most favorable for red occupation, for such prioritization can be made only after determining the direction onto which short link 2 and long link 5 have equal projection.…”

“…The influence of such microcurrents upon the macroscopic behaviour of LBILG fluids is therefore of interest. In this paper an analysis similar to that of Gunstensen et al ͓7,8͔ is applied to calculate the tension in the interface generated between two D2Q9 BGK fluids.…”