Physics and Astronomy
We study a computer-simulation model for driven particles on a discrete lattice where a fraction p of the lattice sites is randomly occupied by frozen impurities (barriers), and an imposed bias governs the particles' hopping through the lattice. These particles (the carriers) are initially released from a source of wetting fluid from one end of the lattice in order to wet and the dry lattice on their trails. We study the transport of particles, frontier of their trail and the growth of the interface between the wet and dry regions as a function of the biased field and the number of carriers. The rms displacements of carriers (R(tr)) and that of their center of mass (R(cm)) show power-law behaviors with time t, with exponents depending on the biased field. At the impurity concentration p=0.30 in two dimensions, we find that the mean wetting front position R(f) moves with a power law R(f) approximately t(2/3) at low values of the biased field, whereas it becomes pinned at higher values. The interface width grows with time to a maximum value before relaxing to a saturation value.
Physical Review E
Pandey, R. B.
(1993). Driven Diffusion of Particles, First-Passage Front, and Interface Growth. Physical Review E, 48(4), 2382-2385.
Available at: https://aquila.usm.edu/fac_pubs/6679