ILG simulation on a 128x512 lattice, obstacles with 25% coverage. The system has periodic boundary conditions and momentum is injected at a constant rate on the left boundary of the system. Red particles that leave the system re-enter the system on the left side as blue particles. The pressure drop accross the system is P=0.0058, which corresponds to an input of 0.05 units of momentum per vertical site (low pressure).
The "annealed" obstacles come from a previous phase-separation simulation in which the low concentration phase (27%, annealed for t=500 steps) was saved in a file to serve as obstacles for the present simulation.
The variable in the simulations below is the overall particle density. The density ranges from 0.5 to 0.8 particle density per site. This translates into a range of 3.5 to 5.6 particles per site. Notes to take into account is that although the surface tension between red and blue particles is an inverted parabola of particle density (Rothman-Keller), the viscosity is a decreasing function of density (Kadanoff-McNamara). The effect on the capillary number is yet to be determined, as well as the correlation between the roughness of the interfase as a function of density.
Snapshots of different simulations as a function of particle density. The snapshots capture the interfase at approximately the same x position, but the running times are t=9100, 13500, 16500, and 23000, respectively. (i.e. the interfase velocity decreases with particle density)
(I'll put movies of the time evolutions of the pictures below when I figure out a convenient format. Animated gifs are currently too big to post)
Same simulations, but only the interfase between the liquids are shown. Click on the pictures for an animated gif of the time evolution of the interfase.
The dark pixels below represent those pixels that contain red and blue particles at the same time. This representation gives an impression of the interfase between the liquids although is not a strict definition. Loose dark pixels are itinerant mixed sites that wander from the interfase. Note the smoothness of the interfase as a function of particle density.
Graph of the percentage of mixed sites as a function of simulation time for the particle densities shown above. The black, red, green, and blue curves are this percentage for particle densities of d=0.5, 0.6, 0.7, and 0.8 per site.
Note that this percentage seems to saturate at sequentially lower values for increased densities. Longer runs are by necessity required to confirm this observation, as well as bigger and more numerous simulations.
(Click on the image for an enlarged picture)