Assistant Professor
Physics Department & James Franck Institute,
Teaching Physics 185
Unfortunately the U of C bookstore dropped the required textbook from its
order list. It is
Required textbook: Classical Mechanics (Hardcover) by John R. Taylor
(Author)
Publisher: University Science Books (January 1, 2005)
ISBN-10: 189138922X ISBN-13:
978-1891389221
The textbook is expected to arrive on January 12th. In the mean time handouts on the
materials covered will be available in class.
Computations
in Science Seminar
Publications
CV postscript
/pdf
last updated January 2005
(site under construction)
I am
a theoretical physicist working largely in classical physics. Many of my
research projects deal with dynamic topological transitions involving fluid
interfaces. Some simple examples are the breakup
of a liquid drop, the splash of a liquid drop falling
onto a solid substrate and the formation of a thin filament across the viscous entrainment transition. Understanding how the
kinematics of these dynamic transitions arise from general, fundamentally
geometric constraints may give insights relevant for out-of –equilibrium
phenomena in general. They are also relevant to technologies, e.g. ink-jet
printing, catalysis in combustin engines, coating of biological cells and
formation of micron- and nano-scale fibers and composite fibers. Scientists
working on these questions come from a variety of fields, mostly engineering,
particularly chemical engineering & transport, soft condense matter physics
and nonlinear dynamics.
Members of my research group are: Francois Blanchette, a James
Franck Institute theory postdoc jointly supported by Tom Witten, Todd Dupont,
Mary Silber and the Materials Science & Engineering Research Center at U.
Chicago; and three graduate students: Marko
Kleine Berkenbusch (joint with Leo Kadanoff), Laura Schmidt, and Robert Schroll.
I often collaborate with Sidney
R. Nagel and members of his experimental physics group. I also have ongoing
collaborations with Jean-Pierre Delville’s
nonlinear optics group at Bordeaux I, France, and with Douglas
N. Robinson’s cell biology group at Johns Hopkins University.
Below is a more detailed list of the research questions I am working on:
(Most recent first. A longer discussion follows when you click underlined
phrases. A list of older research projects are here.
Notation: student names are in red. Experimentalists are in bold italics. Theorists/Simulators
are in bold. )
1. What is the physical mechanism underlying
the unusual breakup of an air bubble in water? Is the breakup scale-invariant, or does it retain a memory of initial and boundary conditions?
(With Peder Moller, Nathan Keim,
Francois Blanchette, Vakhtang Putkaradze & Sidney R. Nagel.)
We have all seen large air bubbles break apart in water. Surprisingly the
dynamics of this familiar phenomena is in fact rather mysterious. Recent
experiments by the Nagel group at U. Chicago, the Taborek group at UC Irvine
and the Lohse group at U. Twente in
Enschede, Netherlands suggest the thinning of the bubble neck does not
correspond to surface-tension-driven, scale-invariant breakup, but instead
resemble an inertial collapse driven by energy focusing, a mechanism previously
observed in implosion of a spherical air bubble, such as occurs in sonoluminescence,
the creation of a high-speed jet due to a concentration of Faraday waves and granular jetting
after a high-speed projectile impacts a layer of fine sand. More intriguingly,
recent works by Jaeger group
at U. Chicago show air can dramatically change the dynamics of granular
jetting. Using analytics and numerics, we are working to understand the
transients leading towards bubble breakup and the structure of the asymptotic
dynamics.
2. Why does a liquid drop stop splashing when we
remove a fraction of the ambient air? (With Lei
Xu & Sidney R. Nagel.
See movie.)
When a liquid drop hits a dry solid substrate at 4 m/s, we expect a splash.
Recent experiments by Lei Xu & Sidney R. Nagel showed that, surprisingly,
when the ambient air pressure is reduced to roughly a third of atmospheric pressure,
the splash is suppressed. Reducing the air pressure to that comparable with
pressure on a high mountain such as the Everest ENTIRELY suppresses the splash.
In a Phys. Rev. Lett., we proposed that the dramatic
effect of air in splash formation should be attributed to compressible effects
that provide an upwards lift to the radially expanding liquid sheet that forms
after drop impact. While a scaling argument based
on this idea satisfactorily collapses splash threshold data for 4 different
gases (Helium to SF6) and 3 different liquids, it was not possible to directly
observe the proposed mechanism in action because the time-window of the
high-speed photography was limited to 10 microsecond or longer after impact.
3. What mechanism is responsible for the jetting and bridge-formation
dynamics when an interface near a second-order phase transition is deformed by
radiation pressure from an intense laser source? (With Robert D. Schroll , Jean-Pierre Delville & Regis Wunenberg)
Surprisingly, there appears to be a net transport of fluid across the
interface when the laser power is sufficiently high. Preliminary experimental
measurements and calculations suggest this flow is driven by light scattering
off the density fluctuations that exist near a second-order phase transition.
4. What anchors the thin steady-state thin liquid
spout observed in thermal convection of stratified layers? (With Laura E.
Schmidt)
Experiments on stratified thermo-chemical convection designed to mimic
mantle convection showed that thermal convection of two fluid layers with
disparate material parameters have a very different nature than thermal
convection of a single layer, i.e. Rayleigh-Benard convection. At a large
temperature difference across the layer, a single layer system becomes
turbulent, driven by random release of warmer, buoyant fluid blobs from the
bottom surface. In contrast, a double-layer system remains largely
steady-state. The experimentalists hypothesize that the overall convection
pattern is stabilized because the warmer, lower fluid layer is entrained via
steady-state thin spouts. Using a long-wavelength model for the thin liquid
spout formed in thermo-chemical convection, Laura Schmidt and I showed that a
entrained spout can only be stabilized by a severely deformed bottom layer. In
particular, the bottom layer topography must assume the form of a power-law
cusp. Here is a powerpoint talk Laura gave on an
earlier version of her work at the APS division of fluid dynamics meeting at
Seattle, WA (2004).
5. What determines the sharpest cusp / thinnest
spout that can be created by a viscous entrainment transition? (With Marko Kleine
Berkenbusch)
In 1934, in a classic study of emulsification dynamics, G. I. Taylor showed
that how severely a liquid drop can be deformed by an exterior flow depends
crucially on the viscosity contrast and the precise type of flow. When the drop
viscosity is comparable with the exterior liquid viscosity and the drop is
immersed in an extensional flow, the drop can deform only slightly before
bursting (see picture here). When the drop is far
less viscous than the surrounding, the drop can deform severely, with an aspect
ratio that scales as a square root of the viscosity contrast, before bursting.
In contrast, a selective withdrawal experiment (see
picture here) in which a lower layer of viscous liquid is deformed by an
imposed flow in an upper layer, showed that the interface can be signficantly
deformed before the lower layer “bursts”, i.e. becomes entrained into the flow
in the upper fluid. Near the transition, a hump with a small radius of
curvature develops on the interface. In this Phys. Rev.
Lett. and ,Phys. Rev. E. the experimentalists
suggest the sharp feature forms because, as the entrainment transition
approaches, the interface approaches a steady-state singularity, only to be
cut-off at a 50 micron cross-over lengthscale. Puzzlingly, the observed cutoff
lengthscale has little dependence on the viscosity contrast, but instead varies
most dramatically when the capillary lengthscale, the O(cm) lengthscale over
which the interface flattens out away from the hump.
The selective withdrawal experiments suggest that small-scale features on
the interface can be created either by tuning the viscosity contrast, as done
by Taylor, or by tuning the flow geometry by changing the reservoir conditions.
In a recent Phys. Rev. Lett. we tested this idea
quantitatively. We analyzed a simplified, long-wavelength model of viscous
entrainment and showed that, in this limit, different kinds of transitions can
be created by only changing the reservoir condition, without changing the
material parameters. Three kinds of transitions are observed: a generic saddle
bifurcation, a continuous transition where the small lengthscale vanishes, and
a weakly discontinuous transition. Here is a
powerpoint talk I gave at the Dynamical Systems Conference at Snowmass,
Colorado on the long-wavelength model.
Marko Kleine Berkenbusch and I are working to extend this idea of changing
the nature of the entrainment transition by controlling the reservoir condition
which influences the flow geometry. We have a developed a simple numerical
model of the selective withdrawal experiment, where a flat interface seperating
two fluids of equal viscosity is deformed by an flow due to a point sink
located in the upper fluid above the interface. As the sink strength is
increased, the interface deforms and forms a sharp cusp. Unlike the experiment,
the simulation results show a saddlenode bifurcation at the entrainment
transition and a weak, logarithmic coupling between the small and large-scale
deformation Marko’s web page or
from a talk on an earlier version (pdf) of the
work Marko gave at the APS Division of Fluids Dynamics Meeting in Seattle, WA
(2004).
Results from the viscous entrainment work are relevant to ongoing
experiments by Jason Wyman,
M. Mrkish, Marc Garfinkel, Sidney R. Nagel & group to engineer a novel biomedical therapy
for diabetes by coating and transplanting
insulin-producing Islet cells into patients, and experiments by Sarah Case & Sidney R.
Nagel on spout
formation when the entraining fluid is less viscous than the entrained fluid.
6. What is the distribution of forces and
resistances that a living cell uses to achieve shape change? (With Laura E. Schmidt, Douglas
N. Robinson & the Robinson group)
Cytokinesis, the division of a mother cell into two daughter cells, is a
striking and geometrically simple cell shape change. The dividing cell
marshalls molecules to actively generate forces and also regulates the
mechanical resistance. Together with Douglas
Robinson and his group at Johns Hopkins University, we hav examined the
dynamics of cytokinesis in Dictyostelium by measuring the shape change
dynamics, creating a rescaling scheme that is robust and reliably collapses
data from wild-type, and mutant cells. A writeup of our key results can be found
in this PNAS article.
7. How does the breakup dynamics of a water
drop immersed in a viscous oil retain a complete imprint of its initial shape?
(With Peter
Howell &Mike Siegel )
Previous studies of surface-tension driven breakup of a liquid drop show that, near breakup, the
dynamics becomes scale-invariant, governed
solely by the proximity to the singularity. In particular, the dynamics forgets
all depdence of initial and boundary conditions so that the breakup dynamics at
different times prior to breakup can be collapsed onto a single dynamics via an
appropriate dynamic rescaling of the coordinate axes. Recently, via a
combination of experiments (Itai Cohen
& Sidney R. Nagel),
simulation (Pankaj Doshi
& Osman Basaran
Purdue) and theory (with Peter
Howell & Mike Siegel), we showed that
scale-invariat dynamics is NOT THE ONLY POSSIBLE DYNAMICS NEAR BREAKUP. The
breakup of a water drop in viscous oil proceeds via a very different process
because the interior of the water drop is essentially static. During breakup,
the neck of the drop simply collapes uniformly inward, with a complete imprint
of initial conditions. Here is a Science article on
this exceptional breakup dynamics. Uncovering this exception motivated a search
for other possible exceptions to the
scale-invariant breakup dynamics.
More recently, we also analyzed a long-wavelength model of such a static
interior breakup and obtained complete, analytic expression for the breakup as
a function of the initial shape. Surprisingly our analysis showed that
long-wavelength modes along cannot create a minimum on the drop surface. Other
effects, either nonlocal coupling of induced flow or axial curvature effects on
surface tension pressure, are required to create a minimum on the interface. A preprint of our work can be found here.
messages:
Help save the tapirs. They are
handsome, little-known and endangered.
On October 27, 2004, the Boston
Red Sox WON the World
Series. What curse?
Last
modified: Thu June 22 14:55:03 CST 2005