Crossover between linear and volcanic response in a self-organizing driven mixture - interacting lattice gas computer simulation

Transport, flow, and self-organizing structures are studied in a mixture of two immiscible components (A,B) driven by hydrostatic bias from a reservoir source. We consider a cubic lattice with an open top end and a source of particles at the bottom. Initially, particles (A,B) are distributed randomly on about half of the lattice sites with equal proportion. Apart from excluded volume (hard-core), similar particles attract and dissimilar particles repel each other with a nearest neighbor interaction. Empty sites (S) represent an effective medium which attract both components. Hydrostatic pressure bias (H) is implemented probabilistically to drive particles, against gravitational sedimentation, from the source at the bottom to open sink. The Metropolis algorithm is used to move particles stochastically to randomly selected neighboring sites. Periodic boundary conditions are used along the transverse direction. Particles are released into the lattice only from the bottom, but they can escape from top and bottom. A steady-state self-organized structure appears as the sedimentation competes with the hydrostatic bias in continuous flow. At low bias, the flow response is linear and becomes non-linear at high values where the rate of response of the higher molecular weight component diverges while it goes down (in the opposite direction) for the lighter component.