Two dimensional versus one dimensional behavior for biased diffusion and aggregation in a network of channels

We present an extension to two dimensions of a one-dimensional model for a fluid that drags particles in a narrow channel [V. Ruiz Barlett, M. Hoyuelos, H.O. Mártin, Physica A 387 (2008) 4623–4629]. We consider a network of narrow channels on a strip. There is a flux rate J of particles that enter in the left end of the system; particles move to the right, up or down with a jumping rate P. When two particles collide, they produce a cluster that remains immobile because the size of the cluster is greater than the channel diameter. After some time, the accumulation of clusters plugs the system up. We analyze the clogging time against J/P with results obtained from numerical simulations and from a continuous description with approximate differential equations. A transition from a 2D to a 1D behaviour is observed for J/P≪1. The transition point depends on the value of the number of longitudinal channels in the network, w. For J/P≫1, we demonstrate analytically, and confirm numerically, that the clogging time behaves as lnw.