Cascading blockages in channel bundles

Abstract

Flow in channel networks may involve a redistribution of flux following the blockage or failure of an individual link. Here we consider a simplified model consisting of N(c) parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and an individual channel blocks if more than N particles are simultaneously present. The behavior of the composite system depends strongly on how the flux of entering particles is redistributed following a blockage. We consider two cases. In the first, the intensity on each open channel remains constant while in the second the total intensity is evenly redistributed over the open channels. We obtain exact results for arbitrary N(c) and N for a system of independent channels and for arbitrary N(c) and N=1 for coupled channels. For N>1 we present approximate analytical as well as numerical results. Independent channels block at a decreasing rate due to a simple combinatorial effect, while for coupled channels the interval between successive blockages remains constant for N=1 but decreases for N>1. This accelerating cascade is due to the nonlinear dependence of the mean blocking time of a single channel on the entering particle flux that more than compensates for the decrease in the number of active channels.

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

“…We encounter different behaviors, such as clogging in finite time, depending on the type of feedback in the system and the boundary conditions. We show that the results obtained from a simple mean-field model agree with those of previous probabilistic studies on related problems [30].…”

“…The clogging of individual channels is modeled by prescribing the probability that an open channel becomes instantaneously clogged by a cell. This generalizes the model of [30], in which only a single column of channels was considered, to the case of an arbitrary number of columns connected in series.…”

“…Our model focuses on a grid-like geometry composed of rows and columns (see Figure 1). This geometry is similar to the one used in previous research on clogging in microfluidic channels in parallel rows (or bundles) [30]. The clogging of individual channels is modeled by prescribing the probability that an open channel becomes instantaneously clogged by a cell.…”

“…We obtain exact solutions for all these cases for single-column devices (and multiple-column devices belonging to case 3) by using tools from probability theory and reliability engineering [31,30]. We expand on these results to develop an exact solution that tests our mean-field model for multiple-column devices for the constant flow rate devices.…”

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

“…Particles enter at random times according to a Poisson process of intensity λ and exit, if no blockage occurs, after a fixed transit time τ . Subsequently, several generalizations were studied, including a higher blocking threshold (N > 2) [22], an inhomogeneous entering flux [23], and multiple channels [24,25]. When the blockage is reversible, the system is reactivated after a constant waiting time, τ b .…”