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

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.

arXiv comment14 pages, 15 figures

References in corpus (13)

• Large Deviations in Single File Diffusion
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Modeling Supply Networks and Business Cycles as Unstable Transport Phenomena
• Tracer diffusion in crowded narrow channels. Topical review
• Some Exact Results for the Exclusion Process
• Clogging Time of a Filter
• Non-Markovian Models of Blocking in Concurrent and Countercurrent Flows
• Dynamics of Run-and-Tumble Particles in Dense Single-File Systems
• Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic
• Generalized model of blockage in particulate flow limited by channel carrying capacity
• Stochastic models of multi-channel particulate transport with blockage
• Unbinding transition of probes in single-file systems
• Optimizing the Throughput of Particulate Streams Subject to Blocking

Cited by in corpus (1)

• Multiscale Model of Clogging in Microfluidic Devices with Grid-Like Geometries