Biased diffusion with aggregation of particles in a narrow channel

We consider a fluid that drags impurities in a narrow channel. The impurities are particles of a size comparable to the channel diameter. When two particles collide they produce a cluster that cannot move through the medium and remain immobile. When the accumulation of clusters saturate the system the entrance of impurities is no longer possible. The system is characterized by the entrance flux of impurities, J, and the jump probability per unit time, P, in the direction of the flow. We study a discretized model, in one dimension, that captures the basic behaviour of the system. Numerical simulations with Monte Carlo method and a continuous description with approximate differential equations were performed. Two different regimes were identified: drift limited regime (J P) and entrance limited regime (J P).