Experiments on granular dynamics

Granular group:

Sára Lévay
PostDoc
(on leave)

Alumni:
Balázs Szabó (MSc 2010, PhD 2015, PostDoc 2015-2017, TB, continued at Mediso Kft)
Katalin Gillemot (PostDoc 2014-2016, TB, continued as MC Fellow at the University of Vienna)
Gábor Törös (MSc 2011, TB, continued at GE Hungary)
Zsolt Kovács (BSc 2011, MSc 2012, TB, continued at Semilab)
Gábor Bíró (BSc 2013, TB, continued at Wigner RMI)
Béla Csengeri (BSc 2014, TB)
Bence Szabó (BSc 2017, TB)
Dávid Kálmán (MSc 2017, ES)
Viktor Nagy (BSc 2018, TB)
Dániel Nagy (BSc 2015, MSc 2017, ES)
Bo Fan (PhD 2023, PostDoc 2023-2024, continued at UCSD, USA)

Aims and techniques:

We study the flow properties of granular materials in various geometries taking benefit of high speed digital imaging, X-Ray Computed Tomography or MRI and Discrete Element Model (DEM) simulations.

Latest results:

The flow rate of a granulate out of a cylindrical container was studied as a function of particle shape for flat and elongated ellipsoids experimentally and numerically. We found a nonmonotonic dependence of the flow rate on the grain aspect ratio a/b. Starting from spheres the flow rate grows and has two maxima around the aspect ratios of a/b ≈ 0.6 (lentil-like ellipsoids) and a/b ≈ 1.5 (ricelike ellipsoids) reaching a flow rate increase of about 15% for lentils compared to spheres. For even more anisometric shapes (a/b = 0.25 and a/b = 4) the flow rate drops. Phys. Rev. Lett. 133, 058201 (2024) (download pdf)

We studied the rotation dynamics of nonspherical particles in a shear flow in the presence of added noise in 3 dimensions. The Jeffery orbits of elongated (uniaxial, prolate) particles subject to noise were explored using Langevin simulations and a Fokker-Planck equation. We examined how the probability distribution of particle orientation changes when changing the rotation diffusion coefficient D (see figure). Various quantities (nematic ordering, biaxiality) are measured as a function of particle elongation and external noise. Phys. Rev. E 110, 044143 (2024) (download pdf)

Shear induced orientational ordering of asymmetric elongated particles was investigated. Corn grains and pegs with one end sharpened were studied using x-ray computed tomography during quasistatic shearing and for silo flow. We have shown that asymmetries can be detected in the orientational distributions of the particles, which are related to the modulated rotation of the particles during shear flow. J. Stat. Mech. 2023 113201 (download pdf)

The flow of elliptical particles out of a 2-dimensional silo when extracted with a conveyor belt was analyzed. The conveyor belt —placed directly below the silo outlet — reduces the flow rate, increases the size of the stagnant zone, and it has a very strong influence on the relative velocity fluctuations as they strongly increase everywhere in the silo with decreasing belt speed. In other words, instead of slower but smooth flow, flow reduction by belt leads to intermittent flow. Interestingly, we show that the intermittency correlates with a strong reduction of the orientational order of the particles at the orifice region. Phys. Rev. E 108, 044902 (2023) (download pdf)

The force on an obstacle exerted by a flowing granular material was investigated in a silo. For frictional hard glass beads, the force on the obstacle was practically flow-rate independent. In contrast, for nearly frictionless soft hydrogel spheres the drag force increases with flow rate. The dependence of the total force on the obstacle diameter is qualitatively different for the two types of material: the force grows quadratically with the obstacle diameter in the soft, low-friction material, while it grows much weaker, nearly linearly with the obstacle diameter, in the bed of glass spheres. Phys. Rev. E 108, L062901 (2023) (download pdf)

Numerical simulations were performed for studying the discharge of elongated grains from a silo with rotating bottom. The introduction of a slight transverse shear reduces the flow rate by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Main findings of our previous experimental studies are recovered. Phys. Rev. E 106, 034904 (2022) (download pdf)

The time evolution of silo discharge was investigated for different granular materials made of spherical or elongated grains in laboratory experiments and with discrete element model (DEM) calculations. For spherical grains, we confirmed the widely known typical behavior with constant discharge rate. For elongated particles we find a peculiar flow rate increase before the end of the discharge process for a certain range of the normalized orifice diameter D/d* (see Figure). New J. Phys. 24,103036 (2022) (download pdf)

Laboratory experiments have been carried out to study the discharge of elongated grains from a silo with a rotating bottom plate. In the continuous flow regime the rotation of the silo base leads to a strong — more than 50% — decrease of the discharge rate, which otherwise depends only weakly on the rotation rate. Phys. Rev. E 103, 062905 (2021) (download pdf)

We analyzed the statistical properties of granular packings to test Edwards approach based on equiprobable jammed states. Identical spheres packed in a nearly two-dimensional geometrical confinement were studied in experiments and numerical simulations. When tapped, the system evolves toward a ground state, but due to incompatible domain structures it gets trapped. Analytical calculations reproduce relatively well our simulation results, which allows us to test Edwards theory on a coupled system of two subsystems with different properties. We find that the joint system can only be described by the Edwards theory if considered as a single system due to the constraints in the stresses. The results show counterintuitive effects as in the coupled system the change in the order parameter is opposite to what is expected from the change in the compactivity. Phys. Rev. E 103, 042901 (2021) (download pdf)

We studied the outflow dynamics and clogging phenomena of mixtures of soft, elastic low-friction spherical grains and hard frictional spheres of similar size in a quasi-two-dimensional (2D) silo with narrow orifice at the bottom. We show that the addition of small amounts, even as low as 5%, of hard grains to an ensemble of soft, low-friction grains already has significant consequences. The mixtures allow a direct comparison of the probabilities of the different types of particles to clog the orifice. We analyze these probabilities for the hard, frictional and the soft, slippery grains on the basis of their participation in the blocking arches, and compare outflow velocities and durations of non-permanent clogs for different compositions of the mixtures. Experimental results are compared with numerical simulations. The latter strongly suggest a significant influence of the inter-species particle friction. Soft Matter 17, 4282 (2021) (download pdf)

We performed laboratory experiments and numerical simulations of silo discharge with traditional (frictional hard) granular materials and grains with reduced surface friction and hardness. We show, that particle stiffness has a strong effect on the qualitative features of flow rate. For deformable grains lowering the friction coefficient leads to a gradual change in the discharge curve: the flow rate becomes filling height dependent, it decreases during the discharge process. For hard grains the flow rate is much less sensitive to the value of the friction coefficient. New J. Phys. 23, 023001 (2021) (download pdf)

Silo discharge was studied numerically for the case of a silo with a rotating bottom plate. We show, that in accordance with recent experimental findings, for intermediate orifice diameter the discharge rate shows a non-monotonic behaviour on the rotation frequency of the bottom plate. Phys. Rev. E 102, 042902 (2020) (download pdf)

We studied the discharge of low friction soft (hydrogel) particles from a 2D silo with narrow orifice experimentally. The outflow velocity and the clogging probability both depend on the filling height, which is different from the case of hard grains where these quantities are fill height independent. The reason is the fill height dependence of the pressure at the orifice. Decreasing orifice size leads to increasing fluctuations of the flow. Decreasing orifice size leads to increasing intermittency of the flow.For an orifice size smaller than 2 particle diameters the outflow can stop completely, but in contrast to clogs formed by rigid particles, these congestions may dissolve spontaneously. This is connected to slow reorganizations of the grains due to the viscoelastic character of the particles. Restarting the flow leads to delayed particle movement at heigher locations above orifice (seee space-time plot). Soft Matter 16, 8013 (2020) (download pdf)

The rheology of frictional spherocylinders was investigated in shear flows. We explored how the effective friction changes with the inertial number and the particle aspect ratio L/D. For frictional grains the effective friction increases with the elongation of the particles, while for low friction particles a non-monotonic behavior is observed. New J. Phys. 22, 073008 (2020) (download pdf)

We used ultrafast X-ray tomography (1000 fps) to study discharge of a granular material from a cylindrical container. In this procedure 2 horizontal slices (separated by 11 mm) can be recorded continuously. Space time plots were used to reconstruct velocity profiles and packing structures for low friction soft grains and frictional hard particles. New J. Phys. 21, 113054 (2019) (download pdf)

We studied the packing and flow profiles of low friction soft grains using X‐ray computed tomography during discharge of a 3D bin. For hard frictional grains (left image), flow is concentrated in the middle part of the bin (red region) with stagnant zones near the wall, for low friction soft grains we find grain motion everywhere in the bin (right image). Granular Matter 21, 56 (2019) (download pdf)

The rheology of elongated frictional particles has been investigated in inclined plane flows. In this geometry we can easier test the systems response at higher inertial numbers (compared to simple shear). Our discrete element simulations and laboratory experiments revealed that density and friction are well-defined functions of the effective inertial number. The effective friction clearly increases with grain elongation. Phys. Rev. Fluids 3, 074301 (2018) (download pdf)

The stationary flow field in a quasi-two-dimensional hopper was investigated experimentally. The behavior of materials consisting of beads and elongated particles with different aspect ratio was compared. We show, that while the vertical velocity in the flowing region can be fitted with a Gaussian function for beads, in the case of elongated grains the flowing channel is narrower and is bordered with sharper velocity gradient. For this case, we quantify deviations from the Gaussian velocity profile. Relative velocity fluctuations are considerably larger and slower for elongated grains. Phys. Rev. E 96, 062903 (2018) (download pdf)

We studied the packing of spheres experimentally and numerically in 2 + e dimensions, realized by a container which is in one dimension slightly wider than the spheres. The particles organize themselves in a triangular lattice, while touching either the front or rear side of the container. This system appears to be similar to a frustrated spin-glass, but it has a well defined ground state built up from isosceles triangles. When the system is agitated, it evolves very slowly towards the potential energy minimum through metastable states. We show that the dynamics is local and is driven by the optimization of the volumes of 7-particle configurations and by the vertical interaction between touching spheres. Soft Matter. 13, 415-420 (2018) (download pdf)

We studied the outflow of soft, practically frictionless hydrogel spheres from a quasi-2D bin experimentally. Prominent features are intermittent clogs, peculiar flow fields in the container, and a pronounced dependence of the flow rate and clogging statistics on the container fill height. The latter is a consequence of the ineffectiveness of Janssen’s law: the pressure at the bottom of a bin containing hydrogel spheres grows linearly with the fill height. Phys. Rev. Fluids 2, 132302 (2017)2222, 123302 (2018) (download pdf) Phys. Rev. E 96, 062903 (2017)

The rheology of dense granular flows for frictionless spherocylinders was investigated by means of 3D numerical simulations in simple shear. This configuration is especially suitable for testing the case of slow shearing (quasistatic limit). geometry we can. The effective friction is non-monotonic, but predominantly decreasing when the aspect ratio Q is increased: it first sharply increases, reaches a maximum around Q=1.05, and then gently decreases until Q = 3, passing its initial value at Q=2. Phys. Rev. E 96, 062903 (2017) (download pdf)

We report the first experimental demonstration of bulk segregation in a shear-driven dry granular mixture, where the particles only differ in their surface friction coefficients. The smoother particles tend to sink to the bottom of the shear zone, while rough particles migrate to the top of the sample. This phenomenon is similar to the well known kinetic sieving in particle mixtures with size heterogeneity. In the present case the smooth particles have a higher probability to penetrate into voids created by the shearing than the rough ones. Discrete element simulations were carried out and
reproduced the experimentally observed segregation patterns. Moreover, simulations performed in the absence of gravity revealed that rough particles tend to remain in the shear zone, while the smooth particles are being expelled from it. We propose a mechanism in which the smooth particles are driven towards regions of lower shear rate. Soft Matter. 13, 415-420 (2017) (download pdf)

We studied the outflow and clogging of shape-anisotropic grains in 3D hoppers with small apertures. We show that an increasing aspect ratio Q of the grains leads to lower flow rates and higher clogging probabilities compared to spherical grains. On the other hand, the number of grains forming the clog is larger for elongated grains of comparable volumes, and the long axis of these blocking grains is preferentially aligned towards the center of the orifice. Soft Matter 13, 402-412 (2017) (download pdf)

When a granular material composed of shape-anisotropic grains is sheared in a cylindrical split bottom container, a secondary flow is generated that leads to the formation of a considerable heap of material near the rotation center. We demonstrate that this effect can be found not only with prolate grains, as shown in a previous study, but also for oblate particle shapes. Numerical (DEM) simulations reproduce this secondary flow effect. New J. Phys. 18, 113006 (2016) (download pdf)

We investigated the packing fraction, grain alignment, orientational order parameter, and flow field in a 3D hopper based on X-ray CT measurements. We analyzed subsequent clogged states for 6 materials including elongated particles (pegs), lentils, and nearly spherical grains (peas). We have shown that for elongated particles the grains get ordered in the flowing parts of the silo. Similarly to the case of simple shear flows the average orientation of the rods is not parallel to the streamlines but encloses a small angle with it. The order parameter increases as the grains travel downwards the silo and the local shear deformation grows. In most parts of the hopper the orientational distribution of the grains did not reach the stationary orientational distribution observed for simple shear. New J. Phys. 18, 093017 (2016) (download pdf)

Axial segregation of bidisperse granular mixtures of glass beads was investigated in a spherical container, rotating about its horizontal axis. Depending on the filling fraction of the mixer and on the composition of the mixture, qualitatively different spontaneously formed patterns are observed. For technical applications, the well-localized segregated bands allow a convenient separation of individual components of the mixtures. It is particularly surprising that the initial compositions of the granular mixtures have a fundamental influence on the location of the segregated bands. This evidences a collective pattern forming mechanism. The spontaneous formation of these bands cannot simply be traced back to individual particle dynamics. [Phys. Rev. E 93, 032903 (2016)] (download pdf)

Secondary flow and heaping has been observed in sheared granular rods in a cylindrical split bottom geometry. Flow reversal transiently reverses the secondary flow, leading to a quick collapse and slower regeneration of the heap. We present a symmetry argument and experimental data that show that the generation of the secondary flow is driven by a misalignment of the mean particle orientation with the streamlines of the flow. This general mechanism is expected to be important in all flows of sufficiently anisometric grains. [Soft Matter 11, 2570 (2015)] (download pdf)

The evolution of wide shear zones was investigated experimentally and numerically for quasistatic granular flows in split bottom shear cells. Shearing an initially random sample, the zone width (w) was found to significantly decrease in the first stage of the process. The characteristic shear strain associated with this decrease is about unity and it is systematically increasing with shape anisotropy, i.e. when the grain shape changes from spherical to irregular (e.g. sand) and becomes elongated (pegs). The strongly decreasing tendency of the zone width is followed by a slight increase which is more pronounced for rod like particles than for grains with smaller anisotropy (beads or irregular particles). [Phys. Rev. E 90, 032205 (2014)] (download pdf)

The packing fraction of a sheared granular material has been studied by X-ray Computed Tomography. We quantified the shear induced (Reynolds) dilation of an initially random sample. We also show, that for elongated grains the dilation is partially compensated by a compaction due to the shear alignment. The deformation scale corresponding to the dilation is considerably smaller than that of the alignment process. Shearing identical spheres results in a strong positional ordering of the grains. [Soft Matter 10, 5157 (2014)] (download pdf)

Granular physics has made considerable progress during the past decades in the understanding of static and dynamic properties of large ensembles of interacting macroscopic particles, including the modeling of phenomena like jamming, segregation and pattern formation, the development of related industrial applications or traffic flow control. The specific properties of systems composed of shape-anisotropic (elongated or flattened) particles have attracted increasing interest in recent years. Orientational order and self-organization are among the characteristic phenomena that add to the special features of granular matter of spherical or irregularly shaped particles. An overview of this research field is given. [Soft Matter 9, 7401 (2013)] (Review paper) (download pdf)

We report shear experiments with macroscopic shape-anisotropic particles and discuss induced orientational order and alignment. Optical observations of the top layer are accompanied by X-ray computed tomography, where positions and orientations of each individual grain in the bulk can be resolved. The induced orientational order influences local packing and other macroscopic properties like the shear resistance. A comparison is drawn with molecular liquid crystals (LC). Many observations are qualitatively and even quantitatively comparable to the well-understood nematic phase of rodlike molecules, even though the types of interactions are completely different. [Powders and Grains, AIP Conf. Proc. 1542, pp. 74-77 (2013)] (download pdf)

Shear induced alignment of elongated particles was studied experimentally and numerically. We show that shear alignment of ensembles of macroscopic particles is comparable even on a quantitative level to simple molecular systems, despite the completely different types of particle interactions. We demonstrate that for dry elongated grains the preferred orientation forms a small angle with the streamlines (see example image for rice), independent of shear rate across three decades. For a given particle shape, this angle decreases with increasing aspect ratio of the particles. The shear-induced alignment results in a considerable reduction of the effective friction of the granular material. [Phys. Rev. Lett. 108, 228302 (2012)] (download pdf)

We used X-ray computed tomography (CT) to obtain three-dimensional images of the particle orientations in sheared systems (reconstructed CT image shown here). All individual particle positions and orientations were extracted, the orientational distribution functions and the complete order tensor were determined. The evolution of these quantities was monitored as the shear induced alignment developed starting from an initially random configuration. [Soft Matter 8, 10950 (2012)] (download pdf)

The alignment, ordering, and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and X-ray computed tomography. At the grain level the steady state is characterized by a net rotation of the particles, as dictated by the shear flow. The distribution of particle rotational velocities was measured both in the steady state and also during the initial transients. The average rotation speed as a function of particle orientation is seen on the image. The rotation speed for particles with their long axis perpendicular to the shear alignment angle is larger, while shear aligned particles rotate slower. The ratio of this fast/slow rotation increases with particle aspect ratio. During the initial transient starting from an unaligned initial condition, particles having an orientation just beyond the shear alignment angle rotate opposite to the direction dictated by the shear flow. [Phys. Rev. E 86, 051304 (2012)] (download pdf)

The geometry of shear zones was investigated in layered granular materials. The presence of the material interface can lead to a special type of “total internal reflection” of the shear zone. In a wide range of configurations the reflection is characterized by a fixed angle which is analogous to the critical angle of refraction in optics. The zone leaves and reenters the high friction region at this critical angle and in between it stays near the interface in the low friction region. [Soft Matter 7, 8330 (2011)] (download pdf)

The nature of the grain motion was investigated during resonant silo discharge (called silo music). The grains do not oscillate in phase at neighboring vertical locations (see Fig.a), but information propagates upward in this system in the form of sound waves. We show that the wave velocity U is not constant throughout the silo (see Fig.b), but considerably increases toward the lower end of the system, suggesting increased pressure in this region, where the flow changes from cylindrical to converging flow. In the upper part of the silo the wave velocity matches the sound velocity measured in the same material when standing (in the absence of flow). Grain oscillations show a stick-slip character only in the upper part of the silo. [Phys. Rev. E 83, 032301 (2011)] (download pdf)
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Refraction and deflection of shear zones in layered granular materials was studied experimentally and numerically. We show, that (i) according to a recent theoretical prediction [T. Unger, Phys. Rev. Lett. 98, 018301 (2007)] shear zones refract in layered systems in analogy with light refraction, (ii) zone refraction obeys Snell's law known from geometric optics and (iii) under natural pressure conditions (i.e. in the presence of gravity) the zone can also be deflected by the interface so that the deformation of the high friction material is avoided. [Phys. Rev. E 80, 060302(R) (2009)] (download pdf)
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We present experimental and numerical results that show the formation of longitudinal stripes that arise from instability of the uniform flowing state of granular media on a rough inclined plane. For reltively dense flows we find a robust form of stripes that consists of fast sliding plug like regions (stripes) on top of highly agitated boiling material (see image a) - a configuration reminiscent of the Leidenfrost effect when a droplet of liquid lifted by its vapor is hovering above a hot surface. We determine the effective friction as function of the inertial number I and find, that the increasing trend known for dense flows breaks down at about I=0.7 and further increasing the inertial number leads to decreasing effective friction (see image b). [Phys. Rev. Lett. 103, 178302 (2009)] (download pdf)
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We show that the properties of avalanches in a gravitationally-forced granular layer on a rough inclined plane - a model system for rock avalanches on a hillside - depend dramatically but in a predictable manner on the shape (angularity) of the grains. Measuring major characteristics of avalanches as the the typical height, the ratio of the particle and front velocities and the growth rate of avalanche speed with increasing avalanche size we find that they correlate well with the most basic property of the material - the angle of repose. For rough non-spherical grains (i.e. materials with a high angle of repose), avalanches are faster, bigger and overturning in the sense that individual particles have downslope speeds that exceed the front speed as compared with avalanches of rather spherical particles that are quantitatively slower, smaller and where particles always travel slower than the front speed. [Phys.Rev.E. 78, 011306 (2008)] (download pdf)
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The flow rule of dense flows on an incline was tested for 14 samples of granular materials. We find, that the Pouliquen flow rule (PFR) provides reasonable but not perfect collapse of the u(h) curves measured for various plane inclinations and mean particle diameter d. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling referred to as Pouliquen-Jenkins flow rule (PJFR). Measuring the slope \beta of the PJFR for ten different sizes of sand and glass beads, we find a systematic, strong increase of \beta with the divergence angle \theta_1 of h_s. The copper materials with different shapes are not well described by either flow rule. [Phys.Rev.E. 76, 031301 (2007)] (download pdf)
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The overall phase diagram of granular flows on an incline with emphasis on high inclination angles was determined. A new method was developed for the measurement of the density of the flow for a wide range of the plane inclination. For low volume flow rates, a transition was detected between dense and very dilute (gas) flow regimes. We show using a vacuum flow channel that air did not effect the flow properties except for small changes in the very dilute gas-like phase. [Phys.Rev.E. 74, 061301 (2006)] (download pdf)
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The dynamical properties of avalanches depended strongly on the shape anisotropy of the particles used. For rough non-spherical grains, avalanches are faster, bigger and overturning. Individual grains have down-slope speeds that exceed the front speed as compared with avalanches of spherical glass beads that are quantitatively slower, smaller and where particles always travel slower than the front speed. [Phys.Rev.Lett. 94, 208001 (2005)] (download pdf)
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