Irreversible blocking in single-file concurrent and countercurrent particulate flows

Filtration and flow in micro/nano-channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. We propose here a concurrent flow model where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, blockage occurs. We obtain the exact solution for the survival probability, the distribution of the number of particles that pass before blockage, the instantaneous flux exiting the channel and the statistics of trapped particles. We then obtain the exact solution of a counterflow model with two opposing Poisson streams. There is no restriction on the number of particles passing in the same direction, but blockage occurs if, at any time, two opposing particles are simultaneously present in the passage.