Papers in Physics, vol. 6, art. 060014 (2014)

Received: 21 November 2014, Accepted: 5 December 2014
Edited by: L. A. Pugnaloni
Reviewed by: K. To, Institute of Physics, Academia Sinica, Taipei, Taiwan.
Licence: Creative Commons Attribution 3.0
DOI: http://dx.doi.org/10.4279/PIP.060014

www.papersinphysics.org

ISSN 1852-4249

Invited review: Clogging of granular materials in bottlenecks

Iker Zuriguel1∗

During the past decades, notable improvements have been achieved in the understanding of
static and dynamic properties of granular materials, giving rise to appealing new concepts
like jamming, force chains, non-local rheology or the inertial number. The ‘saltcellar’ can
be seen as a canonical example of the characteristic features displayed by granular materi-
als: an apparently smooth flow is interrupted by the formation of a mesoscopic structure
(arch) above the outlet that causes a quick dissipation of all the kinetic energy within the
system. In this manuscript, I will give an overview of this field paying special attention to
the features of statistical distributions appearing in the clogging and unclogging processes.
These distributions are essential to understand the problem and allow subsequent study
of topics such as the influence of particle shape, the structure of the clogging arches and
the possible existence of a critical outlet size above which the outpouring will never stop.
I shall finally offer some hints about general ideas that can be explored in the next few
years.

I. Clogging in bottlenecks, a multi-
scale and multidisciplinary prob-
lem.

When a system of discrete bodies passes through
a constriction, the interactions among the particles
might lead to the development of clogging struc-
tures that, eventually, completely arrest the flow.
This phenomenon is observed in a wide range of
systems with relevant consequences. Clogging of
granular materials in silos may force a production
line to be stopped. Much in the same way, clogging
of suspended hydrated particles is a major issue
concerning oil and gas transport through pipelines
[1]. At a smaller spatial scale, clogging leads to
intermittent flow when a dense suspension of col-
loidal particles passes through a constriction in a

∗E-mail: iker@unav.es

1 Departamento de F́ısica, Facultad de Ciencias, Universi-
dad de Navarra, 31080 Pamplona, Spain.

microchannel [2, 3]. A straightforward application
of the understanding that could be gained concern-
ing clogging in suspensions is found in ecological
engineering. Nowadays, an alternative that is be-
coming widely used for removing pollutants from
wastewater is the use of subsurface flow treatment.
The most important drawback of this technique is
its unpredictable lifetime, mostly limited by clogs
that obstruct the pores [4]. At an even smaller
scale, intermittent flows are observed when elec-
trons on the liquid helium surface pass through
nanoconstrictions [5]. Finally, clogging can also de-
velop when crowds in panic are evacuated through
emergency exits that cannot absorb the amount of
people approaching the doors [6–8].

All these examples of clogging take place in
a broad range of systems where widely different
forces are at play: those concerning the interac-
tions among particles as well as those related to the
interaction between particles and the surrounding
media. For the case of non-cohesive inert grains,
gravity and contact forces are the only relevant

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

ones. For particle suspensions, however, the hydro-
dynamics of the flowing fluid as well as the capillary
effects must be taken into account. Dynamics of
crowds through bottlenecks are even more difficult
to approach theoretically, yet a social force model
has been proved to adequately reproduce the ob-
served behavior in some circumstances.

In the last decade, the number of works published
about clogging has experienced a sudden increase,
which constitutes a gauge of the interest and rele-
vance of this phenomenon. Despite this, the phys-
ical mechanisms behind clogging are still not well
understood. Several issues contribute to this, but
probably the most important one concerns the lo-
cal character of clogging when compared, for ex-
ample, with the global nature of jamming [9], a
scenario that has attracted much more attention
over the last years. This ‘local character of clog-
ging’ seems to complicate the definition of global
extensive variables within the system which could
be used to characterize the phenomenology.

In this manuscript I shall give a brief summary of
the major advances achieved in the understanding
of clogging of non-cohesive inert grains at a bot-
tleneck. I will start by presenting results on the
static silo, then I will move to the case of a vi-
brated silo, and finally I will present some conclu-
sions and mention several questions that —from my
point of view— should be addressed in the forth-
coming years.

II. Clogging in hoppers or silos

The development of clogs that obstruct the flow in
the discharge of bins or silos by gravity is a problem
that has always worried the engineering community
[10–13]. The goal in all these works was finding a
ratio of the outlet to particle size that could guaran-
tee the absence of clogging. For non-cohesive ma-
terials, it was known that this value is around 5
although, depending on the particle properties, it
could increase up to 10. Nevertheless, little was un-
derstood about the mechanism that triggers a clog
and the physical variables that control its devel-
opment. Indeed, it was not until the beginning of
this century when the scientific community started
to carefully investigate this problem [14].

Figure 1: Histogram nR(s) for the number of grains
s that flow between two successive clogs. Data cor-
respond to a circular orifice of 6 mm diameter and
glass beads with a diameter of 2 mm. More than
4000 events were recorded. In the inset, a semilog-
arithmic plot with the solid line indicating an ex-
ponential fit.

i. Avalanche size distribution

One of the first questions that was tackled concerns
the statistics of the avalanche sizes (the usual mea-
sured magnitude is the number of grains that flow
out of the silo from the breakage of a clogging arch,
until the development of a new one). The key fea-
ture of avalanches, which is now well accepted, is
that the distribution of their sizes follows an ex-
ponential decay (see Fig. 1), a result reported for
the first time in [15]. This trend was explained in
[16] by assuming that the probability of clogging
is constant during the whole avalanche, a behav-
ior observed for all the outlet sizes explored. Af-
terward, a many-particle-inspired theory was pro-
posed based on a continuity equation in polar co-
ordinates [17]. Although friction, force networks
or inelastic collapse of the particles were not taken
into account, the authors reproduced the exponen-
tial decay of the avalanche (or burst) sizes. The in-
termittent flows reported were explained in terms of
a random alternation between particle propagation
and gap propagation. Very recently, a probabilis-
tic model —in which the arches were modeled by
a one-dimensional stochastic cellular automaton—
also sheds light on the origin of the exponential
character of the avalanche size distribution [18].

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

The stochastic nature of the clogging process was
also suggested in [19] where it was shown that the
particles that end up forming the clog were totally
uncorrelated at the beginning of the avalanche.

The exponential decay of the avalanche size dis-
tribution has been reported in several arrange-
ments: 2D and 3D silos [16, 20, 21], 2D hoppers
[22, 23], 2D and 3D tilted hoppers and silos [24, 25],
silos with the presence of obstacles [26,27], 2D silos
where the particles were driven by different gravity
forces [28], and fluid driven particles in 2D and 3D
[29, 30]. However, there are some examples where
this exponential tail breaks down. Those situations
are typically related to a breaking of the symmetry
of the problem as in the following cases: 1) usage
of particles with shapes that are not spherical [31];
2) emplacement of multiple orifices [32]; 3) imple-
mentation of slots in 3D silos instead of the normal
circular orifices [33]. In the latter case, a power law
distribution was observed as it will be explained
in section iv. Incidentally, power law distributions
were also numerically obtained when considering
internal avalanches, defined as the number of grains
that move inside the silo between consecutive clogs.
This result was compatible with the idea of Self Or-
ganized Criticality, in analogy with avalanches de-
veloped at the surface of a pile [34]. This work was,
indeed, one of the first approaches to the avalanche
statistics in the silo problem.

ii. Does a critical outlet size exist?

Considering the exponential character of the
avalanche size distribution, its first moment (the
average avalanche size 〈s〉) can be easily calculated
and used to study the dependence of clogging on
the size ratio between the outlet and the particles.
For spherical beads in a 3D silo, a divergence of
the avalanche size was reported for an outlet diam-
eter about 5 times the bead diameter (see Fig. 2)
[31]. This divergence was shown to be robust, as it
holds for particles with widely different properties.
Among these, the shape of the particle was reported
to be the most influential on the critical outlet size
value. Nevertheless, in a subsequent work, the ex-
istence of such a critical outlet size was challenged
by K. To [22]. In a two dimensional silo, it was
shown that several empirical fits agree reasonably
well with the experimental data: some were com-
patible with the existence of a critical outlet, but

others were not (see Fig. 3).
Following this idea, Janda et al. [20] demon-

strated that one of the non-divergent expressions
proposed in [22] could be analytically deduced us-
ing both, the probability that a given number of
particles meet above the outlet —as suggested by
Roussel et al. [35]— and the probability of finding
arches of a given size within a granular deposit —
as found in [36, 37]. Unfortunately, the reasoning
used in two dimensions was not applicable to three
dimensional silos, where the transition seems to ac-
tually exist. Interestingly, this clogging transition
has been also identified for inclined silos and ori-
fices [24, 25], as well as in the discharge of granular
piles through an orifice below its apex [38]. Very
recently, the mean avalanche size has been put on
relation with the fraction of clogging configurations
that are sampled by the orifice, suggesting that 〈s〉
should increase exponentially with the hole width
raised to the system dimensionality [39]. Accord-
ing to these results, clogging is akin to the jamming
and glass transitions in the sense that there is not
any sharp discontinuity in the behavior, but a dra-
matic increase of the relaxation times as the orifice
size is enlarged.

iii. Clogging arches

Complementary to the analysis of the avalanche
sizes, some authors have paid special attention to
the arches that clog the orifices. Clogging arches
are structures of several mutually stabilizing parti-
cles that have to span, at least, the size of the con-
striction. In his seminal work, To et al. introduced
a simple model to explain the clogging probability
based in the geometry of the clogging arches (see
Fig. 4) [14]. They proposed that the position of
particles in a clogging arch is the result of a ran-
dom walk model with some restrictions: 1) the hor-
izontal span of the arch should be larger than the
orifice; 2) the arch has to be convex everywhere; 3)
particles conforming the arch should be in contact
with each other. This model nicely reproduced the
clogging probability for hopper angles below 75◦.
In a subsequent work [40], the same authors intro-
duced an approximation of the arch shape to a cir-
cular arc centered at the apex of the hopper cone.
From this, they calculated detailed properties of
the clogging arches, such as the number of disks
conforming them, finding good agreement with the

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

1 2 3 4 5

0

1x106

2x106

3x106

4x106

0.5 1 2 3
10-1

102

105

108

<
s>

1/(R
c
-R)

 

 

<s
>

R

Figure 2: Mean avalanche size 〈s〉 vs. R, the
ratio between the outlet and particle diameters.
The solid line is a fit with the equation: 〈s〉 =
A(RC−R)−γ; with RC = 4.94±0.03, γ = 6.9±0.2,
and A = 9900 ± 100. Inset: mean avalanche size
〈s〉 vs. 1/(RC − R). Note the logarithmic scale.
Figure reprinted with permission from Ref. [31].
Copyright (2005) by the American Physical Soci-
ety [65].

experimental results. Some of the ideas proposed
by To et al. were corroborated in Ref. [41] where
it was reported that the aspect ratio of the arches
(the height divided by half the span) tends to one, a
result that is compatible with a semicircular shape.
In addition, it was shown that the convexity con-
dition assumed by To is not necessarily fulfilled in
all the particles. Indeed, 17% of the particles had
an associated angle with their two neighbors above
180◦. Hence, arches were locally concave at that
particle, a situation which was named ‘defect’. De-
spite this seemingly mismatch with the restricted
random walk model, a strong inverse correlation of
the angle associated to a particle and the one of
their neighbors was also shown. Apparently, this
inverse correlation compensates the apparition of
defects and preserves the validity of the restricted
random walk model.

Apart from the works mentioned above, where
only the geometry of the arches was evaluated,
there have been preliminary attempts to consider
the forces involved within the particles conform-

Figure 3: Variation of the decay rate α with hopper
or silo exit d. α is obtained from the fittings of the
avalanche sizes with F(s) = e−α(s−s0). The solid

line is the fitted curve α = Ae−Bd
2

with A = 0.846
and B = 0.275. The inset shows the same data
and the fitted curve with d2 plotted in the x axis.
Figure reprinted with permission from Ref. [22].
Copyright (2005) by the American Physical Society
[65].

ing the arches. In [42], force analysis was used to
calculate the jamming probability of mixed sizes
disks that move downwards under gravity in a two-
dimensional hopper. The authors focused in the
simplest case of arches formed by three discs which,
for the outlet size employed, were the most com-
mon. Finally, Hidalgo et al. [43] performed nu-
merical simulations and found that —in clogging
arches— the tangential forces in the ‘defects’ were
very high, while normal forces were abnormally low.
The outcome concerning tangential forces is some-
how expected as friction is necessary to stabilize
defects. On the contrary, the result concerning
the normal forces is rather counterintuitive, but it
was in accord with a previous forecasted predic-
tion based on experimental works on the stability
of arches in a vibrated silo [44].

iv. Orifice geometry.

As stated above, clogging is a local phenomenon
in the sense that it always takes place at the con-
striction. According to this, it seems rather obvious
that the properties of the confining geometry would

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

Figure 4: (a) Image of a typical clogging arch. (b)
Configuration of the arch where ri illustrate the i
steps of the restricted random walk model proposed
in [14]. Figure reprinted with permission from Ref.
[14]. Copyright (2001) by the American Physical
Society [65].

importantly affect the clogging process. An evi-
dence of this can be found in [14] where it is shown
that the clogging probability in a hopper is notably
reduced as the hopper angle increases from 60◦ to
75◦. On the contrary, hopper angles below 60◦ give
rise to similar clogging probabilities. The reason
for this seems to be founded on the fact that, for
sufficiently flat hoppers, the grains develop a spon-
taneous internal angle of repose which acts as an
internal hopper.

The effect of this internal angle of repose is also
relevant in the works of Durian’s group who im-
plemented inclined orifices and silos [24, 25]. This
practice is relatively common in industrial hoppers

and hence, knowing the way in which clogging is
affected, becomes significant. The authors have
proved that increasing the tilting angle of the orifice
or silo augments the propensity to clog according
to a reduction in the projection of the aperture area
against the average flow direction. In addition, a
clogging phase diagram is proposed combining tilt-
ing angle and outlet size. For circular apertures,
the same diagram is found for four grain types (in-
cluding prolate and oblate ones). For slots, how-
ever, the shape of the phase diagram for the case of
lentils and rice seems to be different than for more
isotropic grains, an effect attributed to an align-
ment between grains and slit axes.

The use of slots instead of circular orifices was
already proved to be beneficial to prevent clogging
[45]. In this work, some conservative guidelines are
given to select the minimum outlet size that as-
sures no flow interruption. While for horizontal
and vertical slots the ratio of slot width to parti-
cles size are 3.3 and 4.6 respectively, for horizon-
tal circular outlets the ratio of orifice diameter to
particle size is 6.4. This number may seem consid-
erably larger than the ones reported in [31], but it
should be taken into account that particles of dif-
ferent properties (including anisotropic ones) were
employed. Even more importantly, in a subsequent
work, it was reported that, as the length of the slot
increases, the avalanche size distribution departs
from the exponential behavior displaying a power
law decay [33]. This behavior is explained in terms
of a model where a slot is represented by a series
of statistically independent cells whose length is re-
lated with a hypothetical distance along which par-
ticles’ movement is correlated. Interestingly, the
model matches experimental outcomes for a cor-
relation distance of around 10 particle diameters.
Nevertheless, this result needs to be confirmed as
in other experiments using slots, the avalanche size
distribution has been found to be exponential for
different types of grains [25].

A configuration which is closely related to the
slot geometry is the placement of several aligned
orifices. Very recently it has been reported that
clogging can be significantly reduced by having
more than one exit orifice. In this situation, when
one of the orifices jams, the flow through the ad-
jacent unjammed orifice might cause perturbations
in the clogging arch, destroying it and leading to a
sequence of jamming and unjamming events [46].

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

The necessary condition to observe this behav-
ior is, of course, that orifices are close enough to
each other. In the same line, Mondal and Sharma
[32] have shown that adjacent outlets start affect-
ing each other when the distance is approximately
three times the diameter of the particles. These
authors point toward the importance of stable par-
ticles (adjacent to the arches) resting on the base of
the silo. Remarkably, the role of these particles was
in fact overseen in previous works that analyzed the
properties of clogging arches [14, 40–44].

A smart alternative to alter the clogging process
consists of placing an obstacle just above the outlet.
In [26], it was reported that the clogging probabil-
ity may be reduced up to 100 times if the obstacle
position is properly selected. This dramatic effect
was attributed to a reduction in the pressure (or
particle confinement) in the orifice neighborhood,
which apparently favors arch destabilization. The
explanation given is that particles colliding above
the orifice —which eventually could form a clogging
arch— are not easily stabilized if there is not a cer-
tain confinement that facilitates energy dissipation.
This idea was supported by the observation of a
sudden increase on the number of particles ejected
upwards in the outlet proximities when the obstacle
was placed. In the same work, simulations of a silo
filled with a few layers of grains revealed the same
kind of clogging reduction as the layer of grains
above the orifice was reduced, then confirming the
important role of pressure in the process. In a sub-
sequent work [27], it was shown that the effect of
the obstacle is enhanced as the outlet size enlarges.
It is noteworthy that, in all the cases, the clogging
reduction is achieved with just a tiny alteration of
the flow rate (up to 10% in the worst situation).
In these works, an issue that remains unclear is
the role of the packing fraction above the orifice.
Clearly, the placement of the obstacle affects this
variable which should be, indeed, related to pres-
sure. Nevertheless, robust measurements of volume
fraction are extremely difficult near the outlet due
to the existence of strong gradients.

As far as I know, there has been only one attempt
to unveil the role of volume fraction on clogging in
dry granular media [47]. In this work, a pseudo-
dynamic model was implemented to prepare sam-
ples with different initial configurations by means
of a tapping procedure. Although packing fraction
affects clogging, their main conclusion is that this

is not a good macroscopic parameter to predict the
size of the avalanches that would flow through a
given aperture, suggesting that further information
about the packing properties is necessary. A nice
alternative to study the effect of packing fraction
on the ability of a system to develop clogs is the
use of solid particles suspended in a fluid. This
is precisely what it was done in [48] where it was
proved that the probability of bridge formation in-
creased with the volume fraction. Note that this
system has the advantage of allowing a better con-
trol of the volume fraction than just varying the
initial configuration as done in [47].

v. Effect of polydispersity and particle
shape

A recursive topic that arises in the granular com-
munity is the roles that size polydispersity and par-
ticle shape play on the behavior of such materi-
als. For the case of clogging in silos, in [31] it was
reported that polydisperse samples displayed the
same exponential decay of the avalanche size than
monodisperse ones. Furthermore, it was revealed
that polydispersity had a negligible effect in the
critical outlet size above which clogging would not
occur. In [49], clogging of bidisperse samples was
also shown to be similar to the monodisperse case
as long as segregation is prevented. In addition, the
authors propose that the parameter that should be
considered to characterize the mixture is the parti-
cles volume-average diameter.

Contrary to polydispersity, particle shape seems
to play a major role in clogging development as evi-
denced using prolate (rice) and oblate (lentils) par-
ticles [31]. The critical outlet size increases (i.e.,
clogging is more likely) when anisotropic particles
are employed, a result coherent with that obtained
in fluid driven suspensions of mica flakes when com-
pared with glass beads [48]. An issue that is still
open concerning anisotropic particles in the dis-
charge of a silo is the characteristic particle length
that should be chosen to compare with that of the
orifice. In addition, there is a lack of experiments
or simulations about the effect of using faceted par-
ticles in the clogging probability. Some words have
been written suggesting that faceted particles dra-
matically increase the clogging ability due to their
tendency to align [50, 51], yet there are not system-
atic results on this interesting topic.

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vi. Dynamic signatures of clogging

Provided that clogging in bottlenecks is a conse-
quence of the sudden formation of a stable arch at
the very narrowing, it is a big challenge to find dy-
namical descriptors in the flowing state that can
be used to predict an eventual arrest of the flow.
The first important result about this challenge was
reported by Longhi et al. [52] who studied the im-
pulses recorded by a force transducer at the hopper
boundary near the orifice. Although the distribu-
tion of impulses does not reveal any static signature
of jamming, the distribution of the time intervals
between collisions (τ) produces interesting distinc-
tive features as the outlet size is reduced and ap-
proaches the clogging region (see Fig. 5). In fact,
this distribution tends to a power-law P(τ) ∼ τ−3/2
implying that the mean time interval tends to di-
verge as the outlet is reduced. This is so even when
the average time computed from a finite (albeit
large) data set shows a relatively negligible depen-
dence on the outlet size.

In [53], the flow rate properties were carefully
examined in a two-dimensional silo for outlet sizes
both, above and below the supposed critical out-
let size. Even though the average flow rate be-
haved smoothly and did not display any character-
istic property near the critical size, it was observed
that the flow rate fluctuations are non symmetric
for small apertures. For large orifices, the mea-
surements of the instantaneous flow rate (q) dis-
play Gaussian-like distribution of the fluctuations
around the average. Nevertheless, as the outlet size
is reduced, temporal interruptions of the flow are
evidenced by the development of a peak at q = 0 in
addition to the one that corresponds to the flowing
regime.

In this direction, a step further was performed by
Tewari et al. [54] who implemented event-driven
simulations to analyze the velocity fluctuations of
grains flowing through a hopper. The analysis in
this work was not restricted to the region of the ori-
fice, as all the grains of the silo were studied. Inter-
estingly, although the kinetic temperatures are al-
ways higher at the boundaries of the silo, the corre-
lation times display a tendency that reverses as the
outlet size is reduced: whereas for high flow rates
(far above the critical outlet size) the flow at the
center has longer autocorrelation times than at the
boundary, the opposite is valid for low flow rates as

Figure 5: (A) Probability distributions, P(τ), of
the time intervals τ between collisions, on a log-log
scale for an outlet length 3.3 times the diameter
of the particles. The solid line corresponds to a
power law P(τ) ∼ τ−3/2. The average time interval
between impulses is marked in the figure. (B) P(τ)
on a log-log scale for different opening sizes ranging
from 3 to 16 times the diameter of the particles
(the curves on the top correspond to the smaller
outlet sizes). The curves are displaced vertically
for clarity. The solid line is the power law: P(τ) ∼
τ−3/2. Figure reprinted with permission from Ref.
[52]. Copyright (2002) by the American Physical
Society [65].

fluctuations relax more slowly at the boundaries. In
this work, it is also suggested that clogging is pre-
ceded by the appearance of vortices that nucleate
at the corners of the hopper and extend inwards.

III. Vibrated silos: clogging and un-
clogging

Up to now, I have described investigations related
to the clogging process presuming that, once a clog-
ging bridge is formed, all the kinetic energy is dissi-
pated and the structure is forever stable. Neverthe-
less, an alternative approach can be implemented,
which consists on applying an external input of en-

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

ergy and study its effect on clogging. This strategy
gives rise to a dramatic change in the observed dy-
namics when the orifice is small, i.e., in the region
where clogging is frequent. Unlike the case of a
static silo, the flow in the vibrated silo is character-
ized by the alternation of jamming and unjamming
events. Indeed, apart from the flow rate fluctua-
tions found in a static silo [53], in the vibrated case
long flow interruptions were present. These were
attributed to arches that form and were initially
stable, but destabilize as a consequence of vibra-
tions (see Fig. 6). This behavior suggests that
the intermittent flow in vibrated silos can be split
in two different, independent processes: clogging
and unclogging. Following this line of reasoning,
Mankoc et al. [55] reported that the probability
that a system clogs does not depend on the vi-
bration, which only introduces a non-zero proba-
bility of unclogging once an arch has blocked the
orifice. This probability of unclogging was mea-
sured in three different ways which led to consistent
results whose most conspicuous feature was an in-
crease of the unclogging probability with the outlet
size.

Janda et al. [56] devised a similar experiment in
which the hopper wall of an eccentrically discharged
silo was a piezoelectric, allowing a local perturba-
tion of the clogging arch. In this sense, this work
is conceptually different than that of Mankoc et al.
where the whole silo was vibrated. The most inter-
esting result revealed by Janda et al. was that the
distribution of times that the system takes to get
unclogged exhibits a power law decay. At low vi-
bration accelerations, anomalous statistics for the
jamming times were evidenced as the exponent α
of the power law was below 2 and the first moment
could not be calculated (see Fig. 7). This prop-
erty is, indeed, strongly reminiscent of the anoma-
lous dynamics usually observed for creeping flows
of glassy materials. In a recent work, this behavior
has been shown to be universal in other systems
of macroscopic particles flowing through a bottle-
neck like sheep, a model of pedestrians, and colloids
[57]. Furthermore, for the case of inert grains, sev-
eral variables have been shown to affect the value
of the exponent going from α > 2 to α ≤ 2, i.e.,
from an unclogged situation (where averages can
be defined) to a clogged scenario (where the aver-
age flow rate would tend to zero as the measur-
ing time increases). These variables are: the inten-

Figure 6: Signal from a photosensor at the exit
of a silo: a value of 1 indicates that a particle is
blocking the beam, zero means that the beam is
unobstructed. (a) Static silo. (b) Vibrated silo. (c)
A zoom of the signal shown in (b) during the first
three seconds, the same time stretch as in (a). All
the data were obtained using an orifice of diameter
3.05 times the beads diameter. Figure reprinted
with permission from Ref. [55]. Copyright (2009)
by the American Physical Society [65].

sity of vibration, the outlet size, the height of the
layer of grains above the outlet, and the inclination
of the 2D silo with respect to the vertical which
modifies the component of the gravity affecting the
grains. Increasing the intensity of vibration and
enlarging the outlet size favors the development of
unclogged situations, while increasing the layer of
grains or the silo verticality facilitates the transi-
tion to clogging. A similar idea was anticipated by
Valdés and Santamarina [58] who suggested that
the acceleration that would be required for unclog-
ging increases with increasing skeletal forces in the
particles forming the bridge. Furthermore, they re-
lated this prediction to the higher stability exhib-
ited by the arches formed in a suspension when

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Papers in Physics, vol. 6, art. 060014 (2014) / I. Zuriguel

Figure 7: Histogram, in logarithmic scale, for the
time lapses that the orifice remains blocked in a vi-
brated silo for different vibration accelerations as
indicated in the legend. Data correspond to an
outlet size 1.78 times the particle diameter. The
dashed line has a slope of two evidencing that,
for the smallest acceleration displayed, the slope is
smaller than two. Figure reprinted with permission
from [56]. Copyright (2009) by IOP.

subjected to high fluid velocities [59].
Finally, in a 2D vibrated silo which allowed ob-

servation of the clogging structures, it was estab-
lished a relationship among the bridge geometry
and its resistance to vibration [44]. In particu-
lar, it was revealed that the intensity of vibration
at which the arches collapse is inversely correlated
with the maximum angle among the particles con-
forming it. For the particular case of angles above
1800 (the so called defects), this dependence was
explained in terms of a very simple force analysis.
In summary, from this work it was concluded that
arches break at defects and, the larger the maxi-
mum angle, the weaker is the arch.

IV. Perspectives

After more than a decade of research, significant
advance has been achieved in the understanding of
clogging. Despite all that, the relevance of the re-
maining open issues and the importance of the con-
sequences that clogging has from an applied point
of view, hint about an augment of activity on this
topic in the forthcoming years. Probably, a sensi-

ble approach that should be investigated is isolat-
ing the dynamic and geometric contributions in the
development of clogs. Effectively, a clogging arch
should have a structure compatible with the con-
fined geometry. But in addition, this structure has
to be able to persist until all the kinetic energy of
the system is dissipated. Unfortunately, increasing
the outlet size leads to a modification of the geom-
etry of the problem (as the span of clogging arches
has to increase), but also affects to the velocity of
the particles (which increases with the square root
of the orifice diameter). In a recent work, Arévalo
et al. made initial progress in this direction by ex-
ploring clogging when reducing the driving force up
to 10−3g where g is the gravity; but undoubtedly,
new strategies should be devised to understand the
effect of dynamics in the clogging process.

A situation which seems simpler as dynamic ef-
fects are removed is the study of unclogging as ex-
plained in section III. The power law decays ob-
served in the time that the system needs to be-
come unclogged, suggest a creeping process where
the bridges would age with time, increasing their
endurance. A straightforward way of testing the va-
lidity of these ideas would be an analysis of this pro-
cess using photoelastic particles to evaluate tempo-
ral evolution of the forces within the arch [60]. The
usage of this kind of particles could also be im-
plemented in order to unveil an old question con-
cerning the relationship among clogging arches and
force chains.

Another issue that remains unsolved is, whether
or not, clogging can be seen as a phase transition
and, if so, what kind of transition clogging is. As
explained above, from the measurements of unclog-
ging times in a vibrated silo, a divergence has been
found that can be used to rigourously character-
ize the clogged state through the definition of a
‘flowing parameter’ [57]. A thorough inspection of
the dependence of this parameter on different vari-
ables becomes necessary to corroborate its useful-
ness. Nonetheless, as this approach is based on the
unclogging times, it cannot be used for the ‘singu-
lar’ case of a static silo where, if formed, clogs last
forever. In such scenario, instead of the traditional
way of studying the divergence of the avalanche size
as the outlet is enlarged, I believe that it is perti-
nent to approach the transition from the flowing
region. There, it should exist some parameter that
reveals distinctive behavior when the outlet size is

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reduced as explained in section II.vi. A reminis-
cent problem of this alternative is the difficulty of
choosing a region where to perform the analysis as
the silo is precisely characterized by the existence
of strong spatial and temporal gradients. In this
sense, a geometry that becomes promising is a nar-
row pipe without any constriction where clogs may
develop at any place [61–63]. Apart from a zone
at the top of the pipe where the pressure increases
with depth, a rather homogeneous behavior should
be observed within the rest of the system, allowing
clean measurements of variables like velocity, den-
sity and so on. The study of this geometry can also
be seen as an intermediate stage between clogging
and jamming as it is also the case of ‘jamming by
pinning’ [64] where the increase of the number of
obstacles in the system (and so the characteristic
distance between them) was shown to reduce the
density at which the system jams.

Acknowledgements - I would like to thank
the referee Kiwing To whose comments have, un-
doubtedly, helped to improve the quality of this
manuscript. I am very grateful to Angel Garci-
mart́ın, Diego Maza, Carlos Pérez-Garćıa and Luis
Pugnaloni, without whom this work would never
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