Research
Jamming and Granular Physics
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 Jammed Packing of Spheres |
In many natural systems, we can observe the flow and motion of a vast array of spatially disordered particles. We can also observe this flow suddenly stop and become "jammed". Whether it is the hardening of a glass upon reducing its temperature or the jamming of granular particles (e.g. sand) when the packing denisity is increased, this transition from the un-jammed to the jammed state bears striking resemblence to normal thermodynamic phase transitions. The proposed phase diagram (above) by Sidney Nagel (UChicago) and Andrea Liu (UPenn) illustrates a way in which many types of amorphous systems may experience a transition to the jammed state.
Understanding the physics of a crystalline solid relies on knowledge of the underlying crystal structure. For example, the low-temperature properties of a crystal, such as the heat capacity, depend on the long-wavelength vibrational modes of the lattice. Because of the symmetry of crystals, we can calculate these by hand, and make predictions about the low-temperature behavior (e.g. heat capacity being proportional to the cube of the temperature). However, glassy materials (like window glass) are amorphous, they have no crystalline symmetry to simplify calculations. Their vibrational modes are much more complicated, as is their low-temperature behavior. I am investigating the extent to which a model of an amorphous, jammed solid can be used to describe the vibrational modes of granular and glassy systems. Most of the results are generated by computer simulation, such as the jammed granular packing pictured above. This work is being done in the Nagel lab at the University of Chicago.
Acoustic Echoes in Jammed Solids
A series of acoustic pulses in a glass at low temperatures will
generate coherent echoes at time intervals equal to the pulse spacing
(Graebner and Golding, Physical Review E, 1979). This phenomenon was
interpreted as analogous to spin echoes in NMR( http://en.wikipedia.org/wiki/Spin_echo).
This supported the idea of the origin of low-temperature excitations in
glasses as two-level tunneling states (P. W. Anderson, B. I.
Halperin, C. M. Varma,
1972; W. A. Phillips, 1972). Our recent simulations of model glasses
have provided an alternative, classical interpretation of the echoes.
The anharmonicity of the low-frequency normal modes in our glass
systems can also cause acoustic echoes. Currently I am studying these
echoes in simulations (image below) and experiments.
Drops, Bubbles, and
Singularities in Fluid Interfaces
Above
is a sequence of pictures from a high-speed video of
the dripping of a superfluid helium droplet at 1.34 Kelvin (1.34
degrees above absolute zero). The high-speed video was taken in an
optical cryostat. These images are representative of what
happens when
any low-viscosity fluid (such as water) undergoes a transition from one
fluid mass into two or more pieces. Although this process
occurs
around us all the time, it has only recently been studied due to the
availability of digital high-speed video.
The breakup of a drop or bubble into pieces is an example of a finite-time, topological singularity. The fluid's topology is changing because the shape begins as one piece and ends up as many pieces. Quantities such as the fluid velocity and pressure are becoming very large near the singularity, while the size of the connecting neck region shrinks to zero diameter. The exact manner in which these quantities diverge or shrink depends on the fluid parameters, which define universality classes for the singularities, just as in critical phenomena and thermodynamic phase transitions.
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From Bubbles to Droplets
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high-density
bubble low-density bubble |
In
order to understand the different singularities formed when a bubble
collapses and a droplets breaks apart, we
used gaseous xenon in a special cell designed for high pressures.
As the pressure was increased in the xenon bubble (black in the
images), the density of the gas increases and eventually becomes
comparable to the density of the surrounding water. The image
above shows what the pinch-off looks like as one increases the density
from (a) to (d). This work was featured
in Physics Today magazine in January 2009.
Dimensionality in Fluid
Pinch-off
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breakup of a decane liquid
lens on water coalescence of a dodecane lens on water |
Just like normal phase tranistions in thermodynamic systems, droplet
break-up can strongly depend on the dimension of the system. The above
pictures shows my
work on break-up in liquid lens systems, where a drop of
hydrocarbon oil is placed on the surface of water, and subsequently
spreads out into a thin puddle or "lens" (just like a drop of olive oil
on water). The lenses are subsequently deformed by an
underlying fluid flow and eventually break-up into striking patterns
with many generations of satellite lenses. I have also investigated
this problem using computer simulations, and have shown that
low-viscosity pinch-off in 2D is a form of self-similarity of the
second-kind, where the critical exponent is irrational and anomalous (see publication).
Coulombic Fission of Charge Droplets
Droplets can also
break apart when there is too much electric charge placed on them. This
can occur in natural settings such as thunderstorm clouds, but is also
the basis for industrial processes such as electorspraying. The
behavior of charged drops is part of a larger field known as
"electrohydrodynamics". Above is a simulation showing the evolution of
a zero-viscosity, critically-charged drop (one that has just enough
surface charge to be unstable). The drop is a perfect conductor, and
forms pointed tips that sharpen indefinitely.
 | In real situations, droplets have a finite conductivity, and receltly we have shown that this finite conductivity controls the size and dynamics of jets and progeny drops emitted from the tip. On the left you see four simulations where we change the bulk (blue) and surface (red) conductivities of the drops, and observe the sharp tips emit tiny droplets. The better the conductor, the smaller the droplets emitted. For more details about this fasicinating phenomena, check out our recent publication here. |
Leidenfrost Drops
 laser interference image from below of Leidenfrost drop  | When a drop of liquid is placed on a very hotsurface, an amazing phenonmeon
occurs. Above a certain temperature, instead of boiling rapidly, the
drop will levitate on a thin cushion of vapor. This effect is known as
the Leidenfrost effect, and can be easily visualized when small water
drops float across a hot frying pan. Pictured at left is a water drop floating above an aluminum surface at T = 285C. The reflection of the drop can be seen in the metal surface. Underneath the drop, there is a small vapor pocket created by the evaporation of the liquid (see the cartoon). We are currently studying this thin vapor layer using laser light interference coupled with high-speed video. On the bottom left is a laser interference image of the underneath interface of a water drop on a glass surface at 245 C. The water drop is ~99 C. Laser interference is the same phenomena that produces colorful patterns in pools of water with oil in them on the side of the road. Here we are only using one color of light, red laser light, so we see bright and dark fringes rather than different colors. We can clearly see the neck where the drop is closest to the interface, as well as many fluctuations and structure that is not visible in the images from the side or in the simple model of the vapor cushion (see cartoon at left). I can measure the fluctuations in time and space of the vapor cushion and provide a more complete picture of the physics of Leidenfrost drops. |
Collapse and Disintegration of Antarctic Ice-shelves
 | Recently scientists have puzzled over the remarkably fast disintegration of Antarctica's massive glacial ice shelves. The potential energy released during iceberg capsize has been proposed as a possible driver of this violent collapse that turns and enourmous stable ice shelf (white) into a "mosh pit" of capsized icebergs (blue) in a matter of days. The initial distribution of cracks in the shelf, as well as tsunamis generated by capsizing bergs should affect the dynamics of collaspse. We are interested in the mechanism of such a geologically "fast" event. This work is in collaboration with Prof. Douglas MacAyeal (geosciences) and Prof. Wendy Zhang (physics) at the University of Chicago. |
The above picture shows the disintegration of the Larsen B ice shelf in Antactica in early 2002 (also see this article).
It's breakup and subsequent other large and rapid breakup events are
rare in the glaciological world and poorly understood. We are currently
undergoing a series of laboratory experiments to determine how
capsizing icebergs may accelerate such events. Here are two movies showing turbulence generated during iceberg capsize and the effects on stratification in a salty sub-layer. You can find movies and
more information on this project here.
Synthetic Cooperation in
Micro-Organisms
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In 2009 I spent one year studying the evolution of
cooperation in
Prof. Wenying Shou's lab at the Fred Hutchinson Cancer Research Center.
Our model system consisted of two syntheically-cooperating
yeast
strains (Shou
et. al., PNAS, 2007).
In
evolutionary biology, it is still an open question how the details of
cooperation, which is ubiquitous in our world, evolved on many scales
of life (genes cooperate to form genomes, organelles cooperate to form
cells, cells cooperate to form organisms...) |
This fluorescent image shows growth of two distinct yeast (s. cerevisiae) strains on a dextrose-rich agar pad. The picture is about 1 mm wide,while the typical yeast cell is 4 microns wide. They are metabolically marked (ADH1 promoter) with red (DsRed) and yellow (YFP) fluorescent proteins in order to distinguish them. The red cells are genetically altered so that they can not produce the nucleotide adenine, but they over-produce the amino acid lysine. The yellowish green cells can not produce lysine, but they over-produce adenine. In order for each strain to survive, obligitory cooperation is required (Shou et. al., PNAS, 2007). In the picture to the right, bright "pods" of "yellow" and "red" cells develop due to the need for cooperation. If cooperation was not required for growth, then the distribution of the active (bright) cells would be more uniform and homogenous. This type of "synthetic ecology" gives us a quantitative method for studying the basic components of a cooperative biological system and the necessary features for a system-wide sustainable existence. I am currently developing a mathematical model that describes the dynamics of growth and metabolite release of these cells, in conjunction with ongoing experiments in the Shou lab. One fascinating aspect of this system is how "cheaters" (those who do not over-produce) affect the dynamics, and how the spatially structued growth (agar pad) is different than growth in a homogenous liquid culture. These issues are currently being explored.
Justin C. Burton • James Franck Institute • University of Chicago
929 E. 57th St,
Chicago, IL 60637 • (773) 702-7204 • jcburton_at_uchicago.edu