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

## TL;DR

This paper models particulate flow through channels with reversible blockage, analyzing how system parameters affect throughput and open probability, and compares coupled versus uncoupled channel efficiencies.

## Contribution

It provides analytic solutions for small capacities and numerical analysis for larger systems, revealing complex behaviors and efficiency differences in coupled versus uncoupled channels.

## Key findings

- Exiting flux can increase monotonically or have a maximum depending on deblocking time.
- Large N systems show abrupt transition from few blockages to permanent blockage.
- Coupled channels are more efficient for N=1, with complex behavior for N>1.

## Abstract

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 $N\le 3$ 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.