### Pinning in a Drainage Simulation

The following is a simulation using Immiscible Lattice Gas (ILG) of two liquid phases in which there is an external constant pressure applied to the left edge of the box. The initial conditions are a particle density of d=0.7, system size of 128x256, and periodic boundary conditions on all walls and particles that wrap from the right to the left boundary are converted from red into blue particles, and vice versa. This assures particle conservation while mimicking two liquids that move to the right.

When the system is just a simple ILG of two liquids with input pressure, the interface between the liquids roughens up and moves to the right under a constant acceleration. After barely 4,000 steps, the front almost disappears from the simulation.

 t=1,000 t=4,000 No Obstacles

The same simulation, but now with a porous media-type of obstacles, with coverage at around 25% brings in another totally different view on the subject. The movement of the interface is seriously slowed down when the blue phase is pushed (under the same pressure on all cases above and below) and the obstacles are wettable by the red phase. Even after 10 times the time of the above no-obstacle simulation, the front seems not to move very much, perhaps it becomes pinned.

The porous media used in the last two simulations, the "Annealed Obs", are obstained by first running a phase-separation simulation of an ILG at a 20-80% concentration of blue-red for t=100 and t=500 steps, and then saving the blue configuration to be used as obstacles for the present simulation. This scheme allows for the use of the "annealed" time as a parameter to control the characteristic size of the obstacles as well as their characteristic separation distance.

 t=1,000 t=11,000 t=21,000 t=31,000 t=41,000 Random Blocks Annealed Obs, t=100 Annealed Obs, t=500

The subject of whether the front gets pinned, the value of the critical pressure above which the front start moving, and the porosity and obstacle geometry that affect the dynamics, is a topic of current research.