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 Nc 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 Nc, 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.

Multi-scale model of clogging in microfluidic devices with grid-like geometries

“…Our consideration of grid-like structures may be viewed as an extension to the geometry previously studied in works such as [24][25][26] where Sauret et al (2018) follow similar calculations presented by Talbot & Barré (2015) and confirm their results by experiments. We apply our model to this simpler geometry of parallel channels and show that it agrees with these previous works.…”

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

“…Microfluidic devices play an important role in various disciplines, with applications ranging from inkjet printing, cooling of integrated circuits, mimicking porous structures in studies of soil improvement, and biomedical instruments [1,2,3,4,5]. In some cases, clogging hinders the performance of these microfluidic devices or decreases their efficiency in transporting particles [6]. For instance, in microfluidic cell sorters that sort sickle red blood cells based on their deformability, clogging leads to greater unpredictability in the device behavior [7].…”

“…We acknowledge that this assumption may not be appropriate in other contexts, such as the gradual aggregation of small particles that progressively occlude and eventually clog a channel. For example, such gradual clogging is the subject of the model of Talbot and Barré [6] who consider a more general particle transit time instead of limiting their work to instantaneous clogging.…”