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

Abstract

We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value $N$, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the $n$ particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particle and their time correlation. We generalize previous results for $N=2$ to an arbitrary distribution of entry times and obtain new, exact solutions for $N=3$ for a Poisson distribution and partial results for $N\ge 4$.

13 pages, 9 figures

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Cited by in corpus (4)

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• Continuous Gated First-Passage Processes
• Optimizing the Throughput of Particulate Streams Subject to Blocking
• Recurrence dynamics of particulate transport with reversible blockage: from a single channel to a bundle of coupled channels