Clogging: The self-sabotage of suspensions

Generally, clogging mechanisms include sieving, when particles are too large to pass a constriction; bridging, when particles jam each other at a constriction and form a stable arch; and aggregation, the successive deposition of small cohesive particles at a constriction.⁶ One or two of those mechanisms may be more common in certain systems, but generally all of them happen during the clogging process, as can be seen in figure 2, which adds to the complexity of establishing a general picture.

To understand clogging, keep in mind some common parameters. The particles’ size, shape, and deformability, and the geometry of the system in which the suspension flows influence the clogging dynamics. When a particle is quasi-spherical, its size is often described by a diameter D, though more complex shapes, such as fibers or particle aggregates, can also jam a constriction. Equally important is a constriction’s minimum dimension W, which could represent the diameter of a filter pore, a reduction in a pipe’s cross section, or the width of an emergency exit. The volume fraction Φ of particles in a suspension also influences the probability of clogging. (Think about volume fraction as how close, on average, the particles are to each other.) Finally, the physical and chemical properties of the particles—for instance, their roughness, adhesion, and cohesion—also play a crucial role, especially in determining which mechanism dominates.

The combination of those mechanisms establishes a unified framework for the physics of clogging. Nevertheless, each one can be isolated for a more fundamental understanding.

The simplest case of clogging happens when one dimension of a particle is too large for the particle to pass a constriction. For a rigid spherical particle of diameter D passing through a constriction of width W, clogging occurs for W/D ≤ 1. That mechanism is one of the most common, as it is routinely used to separate small particles from larger ones with a screen. Because most industrial suspensions are polydisperse—made of different particle sizes—the presence of only a few large particles in the suspensions can greatly hinder the performance of a system with constrictions.

Although sieving seems to be a simple mechanism for spherical particles, it becomes less straightforward when more complex shapes are involved. Anisotropic particles, such as fibers or leaves, may enter a system in a given orientation but later clog the channel after shifting position. That’s why gutters must be periodically cleaned. For anisotropic particles, an approach to predict the clogging of a constriction of width W is to characterize the particles’ shape using so-called Feret diameters, which entail measuring an object along a specified direction. An anisotropic particle has a maximal Feret diameter L_F along its largest dimension and a minimal Feret diameter l_F along its smallest dimension, as illustrated in figure 3a.

Such a rigid particle will always clog by sieving at a constriction if l_F > W, and it will never clog if W > L_F. For an intermediate size constriction, l_F < W < L_F, however, the particle’s orientation determines what happens when the particle reaches the constriction. If the particle passes the constriction with its minor axis aligned with the flow, it won’t clog, but if it’s aligned perpendicularly to the flow, sieving will occur.

Another complexity arises when the particles are deformable. If larger than the constriction, such a particle can still enter it and may even squeeze through when a large enough pressure is applied,⁷ as illustrated in figure 3b. That situation is particularly relevant to biological applications that include deformable vesicles, cells, and protein aggregates.

Clogging by sieving can be described as a random process that depends on the number of particles larger than the constriction or pore sizes. For systems with many pores, sieving can usually be modeled as a Poisson distribution, in which the clogging of each pore represents an independent event. The probability of that event depends on the size distribution of suspended particles.⁸ Overall, the most common way to prevent sieving is to stop large particles from entering the system—usually through upstream filtration. Even then, sieving still happens at the filter, where small pores prevent the passage of large particles.

For dilute suspensions—typically of a volume fraction smaller than a few percent—particles tend to pass through constrictions one at a time. But clogging by bridging generally occurs at higher volume fractions when particles arrive at a constriction simultaneously.⁹ If too many particles arrive at once, they can jam each other, spontaneously forming a bridge, as illustrated in the three time-lapsed frames in figures 4a–c. An arch is formed when constrictions are of size W—larger than the particle size D, but of the same order of magnitude.

For spherical noncohesive particles, researchers have observed bridging experimentally only when W/D < 5. For highly anisotropic particles, such as fibers, flakes, or cohesive particles, such as powders, that threshold can be higher because of differences in the particles’ arrangement and the resulting force network at the bridge. Clogging by bridging shares many features with the clogging of silos, in which particles smaller than the constriction can form stable arches. The main difference is that silo clogs occur only at large packing densities because the dry particles are subject to gravity.

An approach commonly used to describe such systems is to measure the number of particles s or the volume of suspension that flows through the constriction before a bridge is formed. The two relevant quantities are the average number of particles <s> (or the average volume of suspension) before clogging occurs and the resulting distribution of the number of particles escaping. The latter exhibits an exponential decay because of the constant probability of clogging during the flow.¹⁰ As a result, the probability of clogging also follows an exponential distribution, illustrated in figure 4d.

An approach to predict the average number of particles, or the average volume of fluid, flowing through the constriction before bridging occurs is to assume a random distribution of particles in the channel and imagine that a sufficient number of them reach the constriction at the same time. For instance, in a 2D system and particles of diameter D, a constriction of width W will clog by bridging if the number of particles arriving simultaneously is greater than or equal to floor(W/D + 1). For a given particle density, it is then possible to show that before the system clogs the average volume of fluid will increase if the width of the constriction is increased (figure 4e). Similarly, clogging will be delayed if one decreases the volume fraction of the suspension.¹¹ Clogging by bridging exhibits a particular feature of intermittency, in which the flow clogs and unclogs periodically, when some perturbations exist in the system. Those conditions provide a framework to minimize clogging by bridging.

Very small particles can stick to surfaces and to each other. If a particle attaches to the wall of a constriction, that constriction becomes a little smaller,¹² as shown in figure 5. When the deposition happens repeatedly, particles aggregate, eventually leading to severely reduced constrictions that are more susceptible to both bridging and sieving.¹³ Although initial deposition depends on the interaction between the particle and the wall, interparticle interactions can significantly increase the aggregation. The particle–fluid interaction is also an important parameter, because the flow determines how quickly particles will arrive and the shear forces they experience. And that force may influence whether or not the particles can be eroded.

For particles such as sediment or microplastics, aggregation is primarily caused by van der Waals forces, which are short-range forces from distance-dependent interactions between atoms and molecules. Other small particles, such as bacteria and algae, can also be sticky. While still subject to van der Waals forces, bioparticles are often decorated by a variety of adhesion molecules on their exterior, which allow them to attach to surfaces or each other with greater force than abiotic particles. Once attached, many bioparticles can also multiply along the surface while excreting chemicals that serve as a glue to bind them there.

Sieving and bridging are governed primarily by interactions caused by spatial arrangements, but aggregation is more complicated and sensitive to chemistry. For particles in pure water, aggregation is often limited by an electric double-layer repulsion. But pure water is extremely rare outside of specialized applications, such as wafer processing and scientific research. Changes in pH or the addition of salt increase ion availability in suspensions and can drastically reduce double-layer repulsion, allowing van der Waals interactions to dominate. Even small concentrations (<0.1 mol/l) of monovalent salt can significantly increase the aggregation rate.¹⁴ Usually, clogging by aggregation can be observed even for constrictions much larger than the particle diameter and for very dilute suspensions. This clogging mechanism, however, usually takes place over long periods of time—from hours to years.

Because clogging is such a problem in a broad range of fluid systems, much of contemporary research investigates new techniques for preventing or mitigating it. Just as different systems experience different clogging dynamics, techniques to prevent sieving, bridging, and aggregation also vary depending on the predominant mechanism at work.

A common way to prevent sieving is to filter particles upstream. Most suspensions, however, are not ideal. Many particles, such as cells or protein aggregates, are anisotropic in shape and may be deformable. Nonetheless, those imperfections are actually opportunities to prevent clogging.

For deformable particles, or rigid particles flowing through a deformable constriction, elevated pressure can squeeze them through the passageway.⁷ When that happens, the deformation of the particle, constriction, or both results in an adjustment of W/D that allows the particle to pass. Humans and other mammals rely on that phenomenon, as red blood cells must deform to flow through capillaries. In fact, numerous diseases alter the deformability of red blood cells, increasing the risk of blood clots and stroke if those cells become so stiff that they can no longer flow freely through small capillaries.

Highly anisotropic particles may clog a constriction in one orientation but flow freely in another orientation. To prevent sieving in that case, the particle must become aligned so that it can pass the constriction. For some shapes, particularly those with high aspect ratios, hydrodynamics provides a mechanism. At low volume fractions, slender particles subject to a shear flow tend to align their longest dimension with the flow direction. At higher volume fractions or turbulent, high flow rates, however, the motion of anisotropic particles in confined systems is less certain and remains an active research topic.

The simplest way to prevent bridging is to ensure that the suspension volume fraction is sufficiently low and the constriction is sufficiently large. In the case of grain silos or emergency exits, however, achieving either may be impractical or even impossible. Fortunately, other ways help prevent suspended particles from bridging. Indeed, once a bridge has formed in a static system, all the kinetic energy dissipates and the bridge remains stable with an unclogging probability of zero. But the stability of that bridge can be broken by introducing perturbations to the system.

One way to periodically perturb dry granular media is through vibrations using a piezoelectric device or, in the case of a liquid suspension, by adding fluctuations to the flow. Researchers have shown that, depending on its frequency and intensity, such vibration increases the unclogging probability. Thus, systems that rely on vibration to break bridges often exhibit an intermittent flow, which reflects both clogged and unclogged states.

Another passive method to prevent bridging in silos is to place an obstacle just upstream of the constriction. Researchers have shown that proper placement reduces the bridging probability by a factor of 100 without reducing the flow rate. Furthermore, that technique works for both passive particles, such as grains in a silo, as well as active particles, such as sheep or humans rushing through a constriction.¹⁵ The addition of an obstacle reduces the pressure upstream of the outlet and modifies the conditions for bridging, with the ultimate effect of reduced bridging probability, even for dense suspensions.

Preventing aggregation has proven to be a more difficult task thus far. Nevertheless, there are some promising techniques. For a long time, the best way to prevent aggregation has been to introduce chemicals into a system. Some examples include adjusting the system’s pH to reduce mineral precipitation in hard water, or adding biocides, such as chlorine, which kill bacteria and algae and prevent them from proliferating. Adding chemicals is far from ideal, however, as many chemicals are only compatible with specific systems. Furthermore, adding chemicals to large flows presents an environmental risk, because they could run off and invade nearby ecosystems. More robust techniques are therefore being investigated.

In some cases, surface treatment can help prevent aggregation. Modifying the surface roughness or surface energy—and often both—significantly reduces the aggregation rate. But it is difficult to develop surface treatments that maintain anticlogging properties for a long time, because of either erosion or fouling of the surface.

Another technique that researchers have proposed leverages capillary forces to remove particles.¹⁶ For instance, passing a slow-moving bubble through a system can do the trick. As the bubble passes over particles, it exerts an inward capillary pressure that can peel particles from the surface. The process of capillary peeling has been shown to work for both inert particles and bioparticles. And although researchers have demonstrated the process for short-term removal of particles, no one has yet tested it as a long-term solution to curb aggregation. Additional methods to locally increase the fluid shear are being developed for future applications.

Finally, yet another promising solution to mitigate clogging is to incorporate pulsating flows into the system.¹⁷ Studies dating as far back as the 1980s report on their anticlogging potential. Over time, researchers have observed that the unsteady shear environment associated with pulsatile flows may help mitigate all three mechanisms of clogging. With pulsation, anisotropic particles can rotate so that they pass a constriction and do not sieve. And although particle bridges are often stable in a steady flow, pulsation can reorient or break apart a bridge and restore flow to the channel. The mechanism is similar to how vibrations prevent bridging. Finally, pulsatile flows may mitigate aggregation by periodically increasing the fluid velocity and eroding particles with a temporarily elevated shear.

Many different systems can clog in distinctly different ways, so no one-size-fits-all solution exists, and a lot of work remains to obtain a unified picture of how it happens. Understanding the impact of different parameters on clogging is important for designing resilient systems, thus saving time, money, and energy.

Ideally, as our understanding of clogging becomes increasingly comprehensive, general guidelines for its risk can be established. For bridging and sieving, we know that the size ratio W/D and the volume fraction Φ are the dominant parameters that determine whether or not a system will clog. Therefore, it may soon be possible to describe a phase diagram for the phenomenon. Eventually, parameters such as roughness, particle anisotropy, and deformability may be incorporated into such a diagram. The influence of channel geometry, such as the angle of a constriction, needs to be considered as well.

Aggregation is more complex, but it may be handled in a similar way. We can assume that W/D ≪ 1, which makes the constriction width a less important consideration for an aggregation phase diagram, though it would change the time it takes the channel to become fully clogged. Similarly, increasing the volume fraction Φ should simply increase the aggregation rate. The proper phase diagram would indicate when to expect aggregation, given the competition between attachment forces—due to a combination of van der Waals forces and an additional adhesive force—and erosion forces from the shear exerted by the fluid. If the erosion force exceeds the attachment force, we would expect minimal aggregation or an upper limit to the size of the average aggregate. But if the attachment force exceeds the erosion force, we would expect continual aggregation and eventually a complete clog.

To fully understand those processes requires an interdisciplinary approach. Clogging can be sensitive to hydrodynamics, biology, chemistry, and physics all at once. Suspensions may contain billions or more of polydisperse particles with varying properties, and their specific locations in the suspension are unknown. Thus, as in turbulence modeling, advanced clogging models require extensive validation and iteration to be predictive. And although simplified systems are essential for isolating specific aspects of clogging, complex systems must be investigated as well. Real suspensions are polydisperse and flow through a wide variety of geometries. Field research and case studies that focus on such real systems should be extremely useful for helping scientists design relevant experiments while also serving as validation sources for clogging models.

Brian Dincau is a doctoral student, Emilie Dressaire is an assistant professor, and Alban Sauret is an associate professor, all in the department of mechanical engineering at the University of California, Santa Barbara.