All
of our work on granular matter is performed
in close collaboration with the group of Sidney
Nagel at UofC, and most graduate students
working in this area are co-mentored.
Droplet
and cluster formation in freely falling
granular streams
Particle beams are important tools for
probing atomic and molecular interactions.
Here we demonstrate that particle beams
also offer a unique opportunity to investigate
interactions in macroscopic systems, such
as granular media. Motivated by recent
experiments on streams of grains that exhibit
liquid-like breakup into droplets, we use
molecular dynamics simulations to investigate
the evolution of a dense stream of macroscopic
spheres accelerating out of an opening
at the bottom of a reservoir. We show how
nanoscale details associated with energy
dissipation during collisions modify the
stream’s
macroscopic behavior. We find that inelastic
collisions collimate the stream, while
the presence of short-range attractive
interactions drives structure formation.
Parameterizing the collision dynamics by
the coefficient of restitution (i.e., the
ratio of relative velocities before and
after impact) and the strength of the cohesive
interaction, we map out a spectrum of behaviors
that ranges from gaslike jets in which
all grains drift apart to liquid-like streams
that break into large droplets containing
hundreds of grains. We also find a new,
intermediate regime in which small aggregates
form by capture from the gas phase, similar
to what can be observed in molecular beams.
Our results show that nearly all aspects
of stream behavior are closely related
to the velocity gradient associated with
vertical free fall. Led by this observation,
we propose a simple energy balance model
to explain the droplet formation process.
The qualitative as well as many quantitative
features of the simulations and the model
compare well with available experimental
data and provide a first quantitative measure
of the role of attractions in freely cooling
granular streams. More on granular streams
incl. movies (both exp't
& simulation) can be found here.
Scott R. Waitukaitis,
Helge Grütjen, John R. Royer, and
Heinrich M. Jaeger, ”Droplet and
cluster formation in granular streams”,
Phys. Rev. E 83, 051302 (2011). pdf
The
role of interstitial gas in determining
the impact response of granular beds
We examine the impact of a solid sphere
into a fine-grained granular bed. Using
highspeed X-ray radiography we track both
the motion of the sphere and local changes
in the bed packing fraction. Varying the
initial packing density as well as the
ambient gas pressure, we find a complete
reversal in the effect of interstitial
gas on the impact response of the bed.
The dynamic coupling between gas and grains
allows for easier penetration in initially
loose beds but impedes penetration in more
densely packed beds. As a result, when
there is interstitial gas is present the
solid sphere sinks deeper into a loosely
packed bed
than when the gas is removed, but sinks
less deep into a more densely packed bed
than when the gas is removed! High-speed
imaging of the local packing density shows
that these seemingly incongruous effects
have a common origin in the resistance
to bed packing changes caused by interstitial
air. Effectively, interstitial gas (e.g.,
air) tends to oppose any change in packing
fraction, whether it is dilation or compaction.
This initially somewhat counter-intuitive
phenomenon is shown in the images on the
left, assembled from fast x-ray radiographs
of the interior of the granular bed, taken
at Argonne's APS. The colors correspond
to the bed packing density: yellow-green
= initial packing fraction before the impact,
orange to red = compaction, blue = dilation.
Time increases left to right, with the
far left image corresponding to the initial
impact of the sphere. Top row: loose bed,
with air (sphere drills deep hole into
bed). 2nd row: loose bed, no air (notice
the shock-like compaction front). 3rd row:
dense bed, with air (sphere dilates bed
but stops quickly); 4th row: dense bed,
no air (sphere dileates bed more, stops
later)
John R. Royer,
Bryan Conyers, Eric I. Corwin, Peter
J. Eng and Heinrich M. Jaeger, “The
Role of Interstitial Gas in Determining
the Impact Response of Granular Beds”,
Europhysics Letters 93, 28008 (2011).
pdf
Granular
Polymer Chains
It is an enduring puzzle why in a boxful
of ball bearings, even when compacted
by many taps, the particles never pack
denser than ~ 64% by volume. This is
much less dense than Kepler's stacking
of triangular layers, known to every
grocer as the optimal packing of oranges
(density ~74%). Yet despite their sub-optimal
density and lack of periodic order, jammed
packings are rigid and resist shear.
Replacing spheres with less symmetric
objects, such as rods or ellipsoids,
introduces new degrees of freedom that
alter the packing structure and create
new modes of response. In this paper
we describe the striking effects displayed
by the jammed packing of extended, flexibly-connected
granular chains. Although the density
and coordination number decrease dramatically
with increasing chain length, the packings
remain rigid. Using X-ray tomography
to examine the chain conformations, we
find long floppy chains effectively partition
into nearly-rigid segments that then
jam into a rigid structure. Just as the
packing of spheres is a basic structural
model for simple liquids and glasses,
we find the packing of chains parallels
the glass transition of molecular polymers
in its response to varying chain length,
topology, and stiffness. Read more about
this in a 2010 Argonne APS Science
Highlight (link).
Ling-Nan Zou, Xiang
Cheng, Mark L. Rivers, Heinrich M.
Jaeger, and Sidney R. Nagel, “The
Packing of Granular Polymer Chains,” Science 326,
408 (2009). link
to article
Granular
Streams: Clustering and Rupture into
"Grain Drops"
Thin
streams of liquid commonly break up
into characteristic droplet patterns
due to the surface tension driven Plateau-Rayleigh
instability. Remarkably, very
similar patterns are observed when
initially uniform streams of dry granular
material break up into clusters of
grains, even though flows of macroscopic
particles are considered to lack surface
tension. Using high-speed
video imaging in the co-moving frame
(i.e., by dropping an $80,000 high-speed
video camera alongside the stream),
measuring grain-grain interactions
with Atomic Force Microscopy, and controlling
the properties of the grain surfaces,
we demonstrate that cluster formation
is driven by minute, nanoNewton cohesive
forces due to a combination of van
der Waals interactions and capillary
bridges between nanoscale surface asperities. These
cohesive forces correspond to an equivalent
surface tension four to five orders
of magnitude below that of ordinary
liquids. As a result, gravitational
stretching of the stream dominates
and the stream ruptures into irregular
(but compact) clusters rather than
pinch off into smooth, spherical droplets.
Check out movies or
read more about these experiments: Nature
News&Views article (by Detlef
Lohse and Devaraj van der Meer from
the Physics
of Fluids Group at the University of
Twente), UofC
Press Release, NSF
News, MSNBC, Discover
Magazine, Scientific
American...
John R. Royer, Daniel
J. Evans, Loreto Oyarte, Qiti Guo,
Eliot Kapit, Matthias E. Möbius,
Scott R. Waitukaitis, and Heinrich
M. Jaeger, "High-Speed Tracking
of Rupture and Clustering in Freely
Falling Granular Streams", Nature 459,
1110-1113 (2009). pdf
of article / pdf
of supplemtary material / link
to News&Views piece about this
article
Granular Fingering
in a Hele-Shaw Cell
The
finger-like branching pattern that occurs
when a less viscous fluid displaces a
more viscous one confined between two
parallel plates, the so-called Hele-Shaw
geometry, has been studied widely and
with various normal fluids. We have investigated
the granular analogue of such Hele–Shaw
cell, where air (the low-viscosity fluid)
displaces glass beads (the high viscosity
granular "fluid"). Because
granular fluids composed of dry, non-cohesive
grains exhibit negligible surface tension,
this allows us to explore a regime not
accessible with ordinary fluids. We demonstrate
that the grain–gas interface exhibits
a fractal structure and sharp cusps,
which are associated with the hitherto-unrealizable
singular hydrodynamics predicted for
the zero-surface-tension limit of normal
fluid fingering. The scaling for the
finger width is distinct from that for
ordinary fluids, reflecting unique granular
properties such as friction-induced dissipation
as opposed to viscous damping. However,
the fractal dimension of the fingering
pattern and the shape of the singular
cusps on the interface agree with the
theories based on simple Laplacian growth
of conventional fluid fingering in the
zero-surface-tension limit. Read more
at Nature
News.
Xiang Cheng, Lei
Xu, Aaron Patterson, Heinrich M. Jaeger
and Sidney Nagel, "Towards the
zero-surface-tension limit in granular
fingering instability", Nature
Physics 4, 234 (2008). pdf
Impact
of a Granular Jet: Emergence of a Liquid
with Zero Surface Tension
When
one or two particles strike a smooth
wall at normal incidence, they rebound
in the direction whence they came.
Yet, as we show here, a dense stream
of non-cohesive particles hitting a
target retains its integrity and deforms
into a thin sheet with a shape resembling
the structures created by an impinging
liquid jet. However, with the granular
materials, this “liquid” has
special property of zero surface-tension.
Furthermore, by decreasing the number
of particles inside a jet, we can turn
the behavior of the granular jet from
the liquid-like behavior back to the
normal particle-like behavior. We believe
that this experiment is the classical
analog of the much more microscopic
and exotic experiment done at the Brookhaven
National Laboratory, where the quark-gluon
plasma produced by the high-energy
collisions of gold ions also shows
the liquid-like scattering pattern,
similar to what we observed with granular
materials. Read more in the press:UofC
Chronicle, AIP
Physics News, RHIC
News
Xiang Cheng, German
Varas, Daniel Citron, Heinrich M. Jaeger
and Sidney R. Nagel, “Collective
Behavior in a Granular Jet: Emergence
of a Liquid with Zero Surface Tension”,
Phys. Rev. Lett. 99, 188001 (2007). pdf
Fast
X-ray Imaging of Impact Dynamics in a
Granular Bed
The impact of solid objects
into a granular bed has been studied
since the 1800’s, yet many fundamental
questions remain unresolved. The
complex response of the bed to sudden
impact differs substantially from impact
in ordinary solids and liquids. We
investigate how this response is mediated
by the presence of interstitial gas between
the grains. Using high-speed x-ray
radiography we track the motion of a
steel sphere through the interior of
a bed of fine, loose granular material. We
find a crossover from nearly incompressible,
fluid-like behavior at atmospheric pressure
to a highly compressible, dissipative
response once most of the gas is evacuated. Read
more and see movies
John R. Royer,
Eric I. Corwin, Peter J. Eng, Heinrich
M. Jaeger, “Gas-Mediated Impact
Dynamics in Fine-Grained Granular
Materials”, Phys. Rev. Lett. 99,
038003 (2007). cond-mat/0702339
Tracking
the Flow Field Inside a Sheared Granular
System
Shear bands in dense granular
materials are localized regions of large
velocity gradients; they are the antithesis
of the broad uniform flows seen in slowly
sheared Newtonian fluids. Until recently
it was generally assumed that all granular
shear bands were narrow. However, in
2003 Fenistein et al. discovered that
in modified Couette cells granular shear
bands can be made arbitrarily broad.
In collaboration with Gary Grest's group
at Sandia, we have investigated the evolution
of granular shear flow as a function
of height in a split-bottom Couette cell.
Using particle tracking, magnetic-resonance
imaging, and large-scale simulations,
we find a transition in the nature of
the shear as a characteristic height
H* is exceeded. Below H* there is a central
stationary core; above H* we observe
the onset of additional axial shear associated
with torsional failure. Radial and axial
shear profiles are qualitatively different:
the radial extent is wide and increases
with height, while the axial width remains
narrow and fixed.
Xiang Cheng, Jeremy
B. Lechman, Antonio F. Barbero, Gary
S. Grest, Heinrich M. Jaeger, Greg
S. Karczmar, Matthias E. Möbius,
and Sidney R. Nagel, “Onset of
three-dimensional shear in granular
flow”, Phys. Rev. Lett. 96, 038001
(2006). pdf
Granular
Jets
When a heavy sphere is
dropped onto a bed of loose, fine sand,
a remarkable phenomenon occurs: a large,
focused jet of sand shoots upwards. Although
similar looking jets are observed on
impact in fluid systems, they are held
together by surface tension. Surprisingly,
the granular jet exists in the absence
of both surface tension and cohesion,
thus fluid jet models are of limited
use. Previous work by Shen and Thoroddson
(UIUC) and by Detlef Lohse's group at
Twente (The Netherlands) proposed that
the jet is created solely by the gravity-driven
collapse of a void left by the sphere’s
descent through the pack. We have found
experimental evidence that granular jets
are instead driven by a more complex
process involving the interaction between
the sand and interstitial air. Using
high-speed X-ray radiography, and high-speed
digital video, we observe the formation
of the jet both inside and above the
bed.We find that what previously was
thought of as a single jet in fact consists
of two components: a wispy, thin jet
that varies little with pressure followed
by a thick air-pressure-driven jet. This
is further evidence that qualitatively
new phenomena in granular systems can
emerge as a function of air pressure.
Our results highlight the importance
of the dynamic coupling between gas and
granule motion............More on granular
jets including movies and a demonstration
on how to produce
a jet in your kitchen (with a glass jar, a ball bearing and
a package of baking soda). Also....What
ended up in the press: UofC
Chronicle, NSF
press release, AIP
Physics News, new Feb '09:Jet
movie on NPR's Science Friday...also
shows very nice footage from Detlef Lohse's
group in Twente, The Netherlands.
John R. Royer, Eric
I. Corwin, Andrew Flior, Maria-Luisa
Cordero, Mark Rivers, Peter Eng, and
Heinrich M. Jaeger, “Formation
of Granular Jets Observed by High-Speed
X-ray Radiography”, Nature Physics
1, 164-167 (2005). pdf
John R. Royer, Eric
I. Corwin, Bryan Conyers, Andrew Flior,
Mark L. Rivers, Peter J. Eng, and Heinrich
M. Jaeger, “Birth and growth of
a granular jet”, Phys. Rev. E 78,
011305 (2008). pdf
How
do forces propagate through a granular
medium?
A "nugget" on
force propagation through a granular
sphere pack
D. M. Mueth, H. M.
Jaeger, and S. R. Nagel, “Force
Distribution in a Granular Medium,” Physical
Review E 57, 3164 (1998)
Daniel L. Blair, Nathan
W. Mueggenburg, Adam H. Marshall, Heinrich
M. Jaeger, and Sidney R. Nagel, “Force
distributions in 3D granular assemblies:
Effects of packing order and inter-particle
friction”, Phys. Rev. E 63, 041304
(2001). pdf
Nathan W. Mueggenburg,
Heinrich M. Jaeger, Sidney R. Nagel,
“Stress transmission through three-dimensional
ordered granular arrays”, Phys.
Rev. E 66, 031304 (2002)
J. Michael Erikson, Nathan
W. Mueggenburg, Heinrich M. Jaeger, Sidney
R. Nagel, “Force Distributions
in Three-Dimensional Compressible Granular
Packs”, Phys. Rev. E 66, 040301
(2002).
Using
force measurements as a "microscope"
to detect the onset of jamming
Glasses are rigid, but
flow when the temperature is increased.
Similarly, granular materials are rigid,
but become unjammed and flow if sufficient
shear stress is applied. The rigid and
flowing phases are strikingly different,
yet measurements reveal that the structures
of glass and liquid are virtually indistinguishable.
It is therefore natural to ask whether
there is a structural signature of the
jammed granular state that distinguishes
it from its flowing counterpart. Here
we find evidence for such a signature,
by measuring the contact-force distribution
between particles during shearing. Because
the forces are sensitive to minute variations
in particle position, the distribution
of forces can serve as a microscope with
which to observe correlations in the
positions of nearest neighbours. We find
a qualitative change in the force distribution
at the onset of jamming. If, as has been
proposed, the jamming and glass transitions
are related, our observation of a structural
signature associated with jamming hints
at the existence of a similar structural
difference at the glass transition —
presumably too subtle for conventional
scattering techniques to uncover. Our
measurements also provide a determination
of a granular temperature that is the
counterpart in granular systems to the
glass-transition temperature in liquids.Read
more... ..NSF
Press Release on this work and closely
related research by Bob Behringer's group
at Duke. Plus: a write-up in the UofC
Chronicle.
Eric Corwin, Heinrich
Jaeger, Sidney Nagel, “Structural
signature of jamming in granular media”,
Nature 435, 1075-1078 (2005). pdf
How
the interstitial gas affects size separation
in vibrated granular media
Vibrated granular materials
can appear very much like a fluid. Yet
there are important differences. A completely
counter-intuitive property is that if
a sufficiently heavy large object is
placed inside a vibrated container filled
with granular particles, it will rise
to the top. Even more confounding is
that a very light intruder can either
rise or sink. Using magnetic resonance
imaging and high-speed video techniques,
we have demonstrated that both the rising
and the sinking behavior is determined
by the interaction of the granular medium
with the air in its interstices: when
the system is evacuated, the intruder
follows the motion of the background
particles. These results suggest a new
model for understanding the role of the
interstitial air on the so-called "Brazil
Nut Effect", by which larger objects
typically rise to the top of a shaken
granular medium.......Here's more, including. movies demonstrating
the effect of interstitial gas (air)
on the rising or sinking of large granular
particles in a vibrated bed of smaller
particles
Matthias E. Möbius,
Benjamin E. Lauderdale, Sidney R. Nagel
and Heinrich M. Jaeger, “Size
Separation of Granular Particles”,
Nature 414, 270 (2001). pdf
Matthias E. Möbius,
Xiang Cheng, Peter G. Eshuis, Gregory
Karczmar, Sidney R. Nagel, and Heinrich
Jaeger, “The Effect of Air on Granular
Size Separation in a Vibrated Granular
Bed”, Phys. Rev. E 72, 011304 (2005)
Matthias E. Möbius,
Xiang Cheng, Peter G. Eshuis, Gregory
Karczmar, Sidney R. Nagel, and Heinrich
Jaeger, “The Effect of Air on Granular
Size Separation in a Vibrated Granular
Bed”, Phys. Rev. E 72, 011304 (2005).
Heinrich M. Jaeger
and Andrea J. Liu, “Far-From-Equilibrium
Physics: An Overview”, arXiv:1009.4874
(2010). pdf
Heinrich M. Jaeger,
“Sand, Jams and Jets”,
Physics World 18, 34-39 (2005). pdf
Heinrich M. Jaeger,
“Chicago Experiments on Convection,
Compaction, and Compression,”
in Physics of Dry Granular Media, NATO
ASI Series Vol. E 350, ed. H. J. Herrmann,
J.-P. Hovi and S. Luding (Kluwer Academic
Publishers, Dordrecht, The Netherlands,
1998) p. 553..
Heinrich M. Jaeger, Sidney
R. Nagel, and Robert P. Behringer,
"Granular Solids, Liquids and Gases",
Rev. Mod. Phys. 68, 1259 (1996). pdf
Heinrich M. Jaeger, Sidney
R. Nagel, and Robert P. Behringer,
"The Physics of Granular Materials",
Physics Today 49, 32 (1996).
H. M. Jaeger, J. B. Knight,
C.-h. Liu, and S. R. Nagel,
"What is shaking in the sand box?",
Mat. Res. Soc. Bull. 19 (5), 25 (1994).
Heinrich M. Jaeger and
Sidney R. Nagel, "La Fisica del
Estado Granular", Mundo Cientifico
132, 108 (1993).
Heinrich M. Jaeger and
Sidney R. Nagel, "La Physique de
l'Etat Granulaire", La Recherche
249, 1380 (1992).
H.M.
Jaeger and Sidney R. Nagel, "Physics of the
Granular State", Science 255,
1523 (1992).
What's
going on inside a granular shear band?
Granular materials react to shear stresses
differently than do ordinary fluids.
Rather than deforming uniformly, materials
such as dry sand or cohesionless powders
develop shear bands: narrow zones containing
large relative particle motion leaving
adjacent regions essentially rigid. Since
shear bands mark areas of flow, material
failure and energy dissipation, they
play a crucial role for many industrial,
civil engineering and geophysical processes.
They also appear in related contexts,
such as in lubricating fluids confined
to ultra-thin molecular layers. Detailed
information on motion within a
shear band in a three-dimensional geometry,
including the degree of particle rotation
and interparticle slip, is lacking. Similarly,
only little is known about how properties
of the individual grains - their microstructure
- affect movement in densely packed material.
Combining magnetic resonance imaging,
x-ray tomography, and high-speed video
particle tracking, we obtain the local
steady-state particle velocity, rotation
and packing density for shear flow in
a three-dimensional Couette geometry.
We find that key characteristics of the
granular microstructure determine the
shape of the velocity profile. ........Click
for a "nugget" on
investigating slow, dense shear flows
by a combination of high-speed video,
magnetic resonance imaging and x-ray
tomography.
Dan Mueth, Georges
Debregeas, Greg Karczmar, Peter Eng,
Sidney R. Nagel, and Heinrich M. Jaeger, “Signatures
of granular microstructure in dense
shear flows”, Nature 406 (6794)
385 (2000).
Avalanches
Chu-heng Liu, H.M.
Jaeger and Sidney R. Nagel, "Finite
Size Effects in a Sandpile", Phys.
Rev. A 43, 7091 (1991).
H.M. Jaeger, Chu-heng
Liu, Sidney R. Nagel and T.A. Witten,
"Friction in Granular Flows",
Europhysics Lett. 11, 619 (1990).
H. M. Jaeger, Chu-heng
Liu and Sidney R. Nagel, "Relaxation
at the Angle of Repose", Phys.
Rev. Lett. 62, 40 (1989).
Check out the
amazing exhibit module on granular materials
in the new Science
Storms exhibit at Chicago's Museum
of Science and Industry (Science Storms
opened March 2010)...within walking
distance of the campus. The
movie shows Ned Kahn's gorgeous large avalanche
wheel in the foreground. On
the big screen behind it you see H. Jaeger
talking and Scott Waitukaitis and John
Royer operating our freefalling video set-up
to capture images of the granular streams.
