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

TL;DR

This paper develops a generalized stochastic model for particle flow through a channel, analyzing blockage phenomena when particle count exceeds a critical threshold, and provides exact solutions for various entry time distributions.

Contribution

It introduces an integral representation for survival probabilities and extends previous models to arbitrary entry time distributions, including new solutions for N=3 and partial results for N≥4.

Findings

Exact survival probabilities derived for arbitrary distributions.

New solutions obtained for N=3 with Poisson entry times.

Partial results provided for N≥4.

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 $N\ge 4$.