Generalized model of blockage in particulate flow limited by channel carrying capacity

Recurrence dynamics of particulate transport with reversible blockage: From a single channel to a bundle of coupled channels

We model a particulate flow of constant velocity through confined geometries, ranging from a single channel to a bundle of N_{c} identical coupled channels, under conditions of reversible blockage. Quantities of interest include the exiting particle flux (or throughput) and the probability that the bundle is open. For a constant entering flux, the bundle evolves through a transient regime to a steady state. We present analytic solutions for the stationary properties of a single channel with capacity N≤3 and for a bundle of channels each of capacity N=1. For larger values of N and N_{c}, the system's steady state behavior is explored by numerical simulation. Depending on the deblocking time, the exiting flux either increases monotonically with intensity or displays a maximum at a finite intensity. For large N we observe an abrupt change from a state with few blockages to one in which the bundle is permanently blocked and the exiting flux is due entirely to the release of blocked particles. We also compare the relative efficiency of coupled and uncoupled bundles. For N=1 the coupled system is always more efficient, but for N>1 the behavior is more complex.

Cascading blockages in channel bundles

Flow in channel networks may involve a redistribution of flux following the blockage or failure of an individual link. Here we consider a simplified model consisting of N(c) parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and an individual channel blocks if more than N particles are simultaneously present. The behavior of the composite system depends strongly on how the flux of entering particles is redistributed following a blockage. We consider two cases. In the first, the intensity on each open channel remains constant while in the second the total intensity is evenly redistributed over the open channels. We obtain exact results for arbitrary N(c) and N for a system of independent channels and for arbitrary N(c) and N=1 for coupled channels. For N>1 we present approximate analytical as well as numerical results. Independent channels block at a decreasing rate due to a simple combinatorial effect, while for coupled channels the interval between successive blockages remains constant for N=1 but decreases for N>1. This accelerating cascade is due to the nonlinear dependence of the mean blocking time of a single channel on the entering particle flux that more than compensates for the decrease in the number of active channels.