Clogging of soft particles

Xia Hong, Dandan Chen, Ken Desmond, Piotr Habdas, Anisa Hofert, Yonglun Jiang, Pablo Illing, Meghan Kohne, Ben Lonial, Mia Morrell, Ran Tao, Haoran Wang, Madelyn Wilson, and Eric Weeks
Recent work in collaboration with Corey O'Hern, Jack Treado, Yuxuan Cheng (Yale), and Mark Shattuck (CCNY)

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This page describes work published in: Clogging occurs in a variety of situations: people exiting a crowded room, particles passing through a filter, or corn exiting the bottom of a silo. In general, you can think of clogging as occuring when a dense collection of objects tries to leave a container through a small opening. Often, there is a chance that the objects can form an arch and block the ones behind them from exiting -- for example, the glass marbles in the picture below.

marbles in a quasi-two-dimensional funnel
(photo from Ran Tao.)

Clogging has been studied for decades, mostly by engineers who need to understand solid particles flowing out of containers -- think corn, coal, gravel, etc. Our work has focused on soft particles such as oil droplets and hydrogel particles, as shown in the next two pictures:

Picture at right: Oil droplets forming clogs as they exit a funnel. The droplets are between two parallel glass plates, so they are deformed into pancakes. Click here to see a movie of the clogging event shown in the bottom row of images. (Photos and video from Xia Hong.) oil droplets forming clogs as they exit a funnel
Picture at right: Hydrogel particles forming a clog. The particles are about 1.5 cm in diameter, and the exit opening width is 2.88 cm. The apparatus is tilted so that it is nearly horizontal to reduce the driving force of gravity (10 degrees inclined from horizontal). (Photo from Mia Morrell.) hydrogel particles forming a clog as they exit a funnel

Inspired by the work of Kiwing To, Pik-Yin Lai, and H. K. Pak, we examine the flow of these various types of particles as they drained out of quasi-two-dimensional hoppers (the technical term for these funnels shown in the pictures above). In all cases, we control the opening size w and compare that to the particle diameter d. If w/d is small, then the system always clogs: the particles form an arch at the exit and flow permanently stops. If w/d is large, then the system never clogs: all the particles exit through the bottom. For intermediate values of w/d, sometimes the system clogs and sometimes not.

We do a bunch of experiments at different values of w/d and measure the clogging probability, which leads to the graphs shown at right. The top graph is for oil droplets: these rarely clog, and require opening sizes less than about 1.5 times a particle diameter to see clogging. The middle graph is for hydrogel particles. We vary gravity by changing the tilt of the experiment relative to vertical; the image below shows Haoran tilting an older version of our sample chamber. For a fully vertical experiment, it is harder to clog: this is the left-most triangle symbols labeled 1.0g in the graph. For a nearly horizontal experiment, it is much easier to clog: this is the right-most curve labeled 0.17g in the graph.

Haoran tilting the chamber

graphs of clogging probability, showing that as
w/d increases the probability decreases

The bottom graph shows our simulation data. We use the Durian bubble model to simulate the flow of soft particles; you can click here to download our IDL code for these simulations. Click here to see an animated GIF movie of one of our simulations. And this is a close-up movie of the same data, with inter-droplet forces highlighted. For these movies, w/d=2.2 and the data correspond to the blue circles of the bottom clogging graph.

The simulation lets us vary gravity by three orders of magnitude. As with the hydrogel particles, the lower the gravity, the easier it is to clog -- we can get clogging even with large values of w/d, more than three diameters wide.

The main idea here is that when gravity is big (or the particles are very soft), the weight of the particles on top will make the particles underneath deform. The soft particles can't form an arch, or at least, if they try to form an arch, the weight causes that arch to break. But when gravity is small (or the particles are harder), it is easier to form a permanent arch that can support the weight of the particles above it.

We need to see if the experiments and simulations are giving similar results. To do this, we measure how much a single particle deforms under its own weight. That's some distance delta, and we divide that by the particle diameter d so that we have a nondimensional quantity. We then determine the value of w/d for which clogging occurs half the time for each experiment or simulation, and plot that special value of w/d as a function of delta/d. The data are shown at right. The 2017 hydrogel data are from our 2017 paper (Hong et al), and the other data are from our 2021 paper (Tao et al). data collapse is nice

What's fun about our results is that they are the exact opposite of what people have seen for years with hard particles! With hard particles, there's a phenomenon called "faster is slower." This is easiest to understand with people trying to leave a crowded room through a narrow doorway. If nobody is in a hurry, then people can exit fairly efficiently. If people are rushing, then you can form an arch of people at the doorway, and the crush of people from behind can prevent the people in the arch from being able to move and disrupt their arch. Thus, the flow of people out of the room is actually slower than when people aren't in a hurry.

The key difference is that with people exiting a room, they are moving somewhat randomly. If they form an arch, they're going to continue to jostle each other to break free. And if coal flows out of a container and gets stuck, you'll bang on the container to break the clog. In this case, the pressure of coal above will stabilize the arch against being jostled by your banging on the container. In contrast, with soft particles, we don't have random jostling or banging. If a clog forms, it is stable. And instead, if we have a larger driving force (larger gravity), this causes the arch particles to deform and rearrange enough to break the arch and flow will resume.

This does raise the question of whether adding vibrations to our system will cause it to unclog. Mia Morrell did some experiments showing that indeed this is the case, although we did not ever see the "faster is slower" effect.

We did some additional experiments and simulations related to flowing oil droplets. Briefly, in these cases we allowed the pressure to build up if the system clogged, until the pressure causes the arch to break, at which point the pressure drops. Thus, we never had permanent clogs. Instead, we found that the flow rate was intermittent, especially when we tried to pump the droplets at low flow rates. In these cases we'd get a clog followed by a big avalanche where many droplets flowed out. When we tried to pump faster, the flow was steadier. We were able to explain these results in terms of the system compliance; see the 2022 paper by Xia Hong for details (link at the top of this page).

For fun, here's a simulation picture where the clogging occured early on, when the hopper was nearly full (almost 800 particles):

clogged system

For more information, please contact Eric Weeks <weeks(at)>