Clogging of cohesive particles in a two-dimensional hopper

TL;DR

The study investigates clogging of cohesive, buoyant droplets flowing through a quasi-2D hopper, combining experiments and simulations to vary droplet diameter $d$, cohesion (via micelle concentration) and hopper opening $w$. A cohesive length scale $\delta = \sqrt{{\mathscr{A}}/{\Delta\rho \tilde{g}}}$ governs arch stability, enabling data collapse when using the dimensionless ratio $w/\delta$ rather than $w/d$; clogging probability $P_\text{clog}$ follows a sigmoidal form while the mean avalanche size $\langle s\rangle$ grows exponentially with $(w/\delta)^\alpha$. Higher cohesion increases clogging propensity and shifts the clogging threshold to larger $w$, with quantitative agreement between experiments and quasi-2D Durian-model simulations. This work provides a predictive framework for cohesive particulate flows in confined geometries, highlighting the cohesive length scale as a central control parameter for clogging and enabling predictions of clogging even at large openings when cohesion is strong.

Abstract

We study clogging of cohesive particles in a 2D hopper with experiments and simulations. The system consists of buoyant, monodisperse oil droplets in an aqueous solution, where the droplet size, buoyant force, cohesion, and hopper opening are varied. Stronger cohesion enhances clogging, a trend confirmed in simulations. Balancing buoyant and cohesive forces defines a cohesive length scale that collapses the data onto a master curve. Thus, under strong cohesion, we find that clogging is governed not by particle diameter, but by the cohesive length scale.

Figures (4)

• Figure 1: a) Schematic of the experimental chamber. Droplets float into the hopper while the chamber is held horizontal. b) The chamber is rotated to a desired tilt angle which drives the buoyant droplets through the hopper. c) Representative experimental image showing a clog with a false color overlay: red droplets indicate the clogging arch, blue droplets represent remaining droplets, yellow droplets remain attached to the aggregate due to cohesion ($w/d = 8.8$, $w/\delta = 2.86 \pm 0.07$). d) Representative simulation image ($w/d=3.25$, $w/\delta = 3.54$). e) An array of images of the final state of the hopper for 20 trials with $w/d =$ 3.0, $C_\text{m} = 71$ mM; here 15 out of 20 experiments clogged, so $P_\textrm{clog} = 0.75$.
• Figure 2: Clogging probability of a) experiments with $w= 162~\mu$m and $d=56~\mu$m and b) simulations with $w/d = 3.0$, for a range of cohesive strengths as a function of the effective gravitational acceleration (error is calculated based on a finite number of trials $N = 20$ and $N = 100$ for a Poisson process). Solid lines are fits of Eq. (\ref{['eqn:P_clog']}) to the data. The effective gravitational acceleration where the probability of clogging is $1/2$, $g_0$, vs cohesive strength for c) experiment and d) simulation.
• Figure 3: Probability of clogging as a function of $w/\delta$ for (a) experiments and (b) simulations. The solid lines represents a fit to Eq. (\ref{['P_c']}). (c) Mean avalanche size before a clog occurs as a function of $w/\delta$ for experiments and (d) simulations. Solid lines are Eq. (\ref{['sfinal']}) fit to the data. Dashed lines show a plateau at 190 droplets. Error bars on $P_c$ are calculated based on a finite number of trials $N = 20$ for experiments and $N = 100$ for simulations for a Poisson process. Error bars on $\langle s \rangle$ represent standard error on the mean. Error bars on $\delta$ are representative of experimental data measuring the cohesive strength between droplets hoggarth2025simple. For these data, smaller $w/\delta$ represents a smaller opening or stickier droplets, both of which make clogging likelier.
• Figure 4: Probability of clogging as a function of $w/d$ for (a) experiments and (b) simulations. (c) Mean avalanche size before a clog occurs as a function of $w/d$ for experiments and (d) simulations. Dashed lines show a plateau at 190 droplets. Error bars represent standard error on the mean. For these data, we see that simply plotting as a function of $w/d$ does not nicely collapse our data which contains different cohesion strengths. In short, $d$ cannot normalize the data, while $\delta$ does.