Research
IRG I
IRG 1. Fluid Flows- Singularities and Microscales
Faculty (* = coordinators): I. Gruzberg, R. Ismagilov, H. Jaeger, L.
Kadanoff*, W. Kang, K.Y.C. Lee*, S. Nagel, P. Wiegmann, T. Witten, W. Zhang
Affiliates: T. Dupont, M. Silber
IRG1 is the direct descendant of the program that first introduced fluid flow and its accompanying singularities as topics for investigation in a materials laboratory. It is also among the first to bring out the connections between fluid and particulate flows (granular fluids). Our results have proven the aptness and importance of these investigations for the materials science community. The study of singularities provides an appropriate paradigm not only because they are mathematically deep and physically robust, but more especially because they offer a method of understanding and controlling small-scale flows which prove to be practically important. Many of the technologically interesting flow effects are also the most intellectually challenging. Our reported and proposed work is directed at the robust effects of singularities, aimed at studying the effects of microscales upon flows and of flows upon microscale phenomena.
Thin Necks, Slender Bridges, Close Approaches: Zhang, Nagel
and Kadanoff are investigat-ing topological changes in fluids related to
small structures produced when two different masses of fluids are pulled
apart or pushed together. These small-scale structures are likely to have
technological implications. One outgrowth of this project points to the
kinds of successes we are aiming at. Nagel, Mrksich (IRG4), and M. Garfinkel,
M.D. in surgery at U of C, are using the very thin spouts formed by ‘selective
withdrawal’ to ‘shrink-wrap’ irregularly shaped cells
with a uniform coating. This coating keeps pig pancreatic cells within a
human body but separated from human immunological response. This approach
seems to be promising for the treatment of type I diabetes. The collaboration
has demonstrated that the encapsulated coat is indeed permeable to glucose
and insulin but impermeable to larger molecules responsible for immune reactions.
The basic research underpinning this kind of work is being continued as
well. The Zhang & Nagel groups have made fundamental advances in understanding
the flow-driven topological transition that underlies the formation of the
thin liquid spout. A simplified numerical model capturing the key ingredients
in the selective withdrawal processes identified the transition as a discontinuous
saddle-node bifurcation. In particular, the original interpretation of an
approach towards a singular shape is shown to result from an unusual, approximately
logarithmic coupling between the smallest and the largest lengthscales that
persist until transition. Viscous entrainment experiments have identified
multiple distinctive spout states. Simulation and theoretical analysis to
characterize the dynamics of these spout states are underway.
Bouncing Droplets: Blanchette and Bigioni, two postdocs in the
Zhang & Jaeger groups, collaborated to uncover the mechanism for the
unusual cascade of coalescences observed when a liquid drop impacts a deep
layer of the same liquid at very small speeds. Using simulation and experiment,
they showed that coalescence initiates capillary waves that propagate along
the interface and collapse at the top of the liquid drop. This wave pulls
the drop away from the interface so violently that the drop pinches into
two pieces instead of coalescing in one step. [Nature Physics,
2, 254-257, (2006)]
Two-Dimensional Flow and Growth: Gruzberg, Wiegmann, and
Kadanoff have been co-mentoring a group including a postdoc and five graduate
students who are using a new approach to explore singular growth and flow
processes in 2D. The physical processes under study include the spread of
an almost inviscid fluid in a viscous fluid (Hele-Shaw flow), diffusion-limited
aggregation (DLA), dielectric breakdown, electrodeposition, mineral dendrites,
and droplets of electronic fluid in the quantum Hall effect (QHE). The new
theoretical approach is based on Laplacian Growth, SLE (Schramm-Loewner
evolution), and a special case of Schwarz-Christoffel (SC) transformations.
In the Laplacian growth part, an essential role is played by the integrable
structure of the growth. It was shown that singularities of the growth are
related to the genus of transitions associated with the Whitham universal
hierarchy. This connection allowed us to classify singularities and analyze
singularities occurring at droplet break-up, during the creation of new
droplets, and shock-wave-type singularities. A variant of SLE where the
driving function is a combination of a continuous Brownian motion and stochastic
process with jumps has been considered, and this work involves the formation
of line defects in 2D materials. Kadanoff and Gruzberg are working on the
mathematical theory of such line defects using "Toeplitz matrices”
and have developed a new application to the 2D Ising model and discovered
new information about the eigenvalues of these matrices. The SC transformation
has been applied to describe lattice DLA using polygons diffusing on a lattice.
The elementary polygons assemble into more complicated ones, but at any
stage of the aggregation one can use SC conformal mapping to describe the
growing cluster. The parameters of this mapping evolve during growth and
also influence it. This stochastic motion of the parameters has been described
analytically and also simulated numerically using SC-tools set of routines
designed for MatLab. Connections of these findings are now being made with
QHE experiments by Kang and granular flow experiments by Nagel and Jaeger.
Feasibility for kilometer-scale liquid films in space. The Witten
group showed that appropriate fluid design can surmount most of the obstacles
to achieving a fluid film of kilometer diameter outside Earth's atmosphere
and gravity [PRE 74, 051602 (2006)]. They identified
the chief impediment to creating such a film as puncture by micrometeoroids,
and suggested a way of curing this impediment via physico-chemical means.
If puncture damage can be prevented, Reynolds numbers of the order of 107
appear feasible. Witten, Jaeger and Lee will identify a suitable surfactant
system to test the stability under vacuum at small scale.
Chiral sedimentation. A principal means of characterizing
chiral molecules is optical rotatory dispersion. The rotatory power of a
molecule is a known spatial moment of its polarizability tensor. Chiral
sedimentation is an analogous property of a chiral object: the object rotates
as it sinks, at a rate characteristic of its chirality.The Witten group
has shown that objects consisting of as few as three Stokeslet drag centers
can show chiral sedimentation and that the chiral effect requires hydrodynamic
interaction among the Stokeslets. They are developing a formalism and numerical
procedure for predicting the chiral sedimentation of arbitrary configurations
of Stokeslets. The Witten, Cluzel and Scherer groups will explore the feasibility
of measuring chiral sedimentation for self-complexed RNA in solution.
Flow in Microfluidic Channels: Using multiphase flows within
microfluidic channels, Ismagilov has shown that nanoliter-sized droplets
(plugs) of aqueous reagents can be formed within flows of immiscible oil.
Together with Witten, Nagel, Zhang, and Kadanoff, the group has developed
a better understanding of mixing by chaotic advection in fluid plugs traveling
through winding channels. As slow chaotic mixing is most efficient at inducing
nucleation due to the long lifetime of interfaces generated, they have applied
this technique to investigate the effect of mixing on nucleation of protein
crystals. This system was first extended to three-phase liquid-liquid-gas
flow, and stable regimes of flow were identified and shown to correlate
with the capillary number. Most recently, this system has been extended
to three-phase liquid-liquid-liquid flow and criteria for identifying immiscible
liquids for use as effective spacers to prevent droplet coalescence were
identified. This system eliminates the undesirable drop merger effect as
it does not suffer from the problem of gas bubble compressibility. Theory
describing the flow of such fluids and stability criteria was initially
derived by an exchange student from Chile under the joint mentorship of
Ismagilov and Witten. Furthermore, this three-phase liquid-liquid-liquid
flow system was shown to be compatible with protein crystallization in plugs.
This work has enabled the development of cartridge-based screening tools
for protein crystallization and enzymatic assays in IRG4. Future work will
involve the continued development of experimental systems for protein crystallization
based on these systems and testing and refining these theories with support
from Kadanoff, Silber, Witten and Zhang.
Lipid Membranes. The collaboration between the Lee, Nagel
and Witten groups has made further progress in understanding the structure
of lipid mono- and multilayers. Extending earlier work on monolayer collapse,
the Lee group has shown that fluid monolayers undergo collapse at lower
pressures, and give rise to a variety of 3D collapse structures that are
distinct from the folds observed in solid-like monolayers (IRG3). The spontaneous
curvature of lipid molecules and their dipole density are found to dictate
the final collapse structure, and theoretical understanding of this structural
formation is provided by the Witten group. While membrane fluidity can be
systematically tuned by adding a varied amount of a secondary lipid to the
primary one, the Lee group has recently discovered that ganglioside GM1,
a glycosphingolipid containing sialic acid, can be both a rigidifier and
a fluidizer for the same lipid system. At low concentrations, GM1 has a
condensing effect while at higher concentrations, it acts to fluidize, with
a switch-over point between the two given by a stoichiometric ratio. To
pinpoint the structural aspect of GM1 that gives rise to the observed effect,
experiments with other gangiosides, ceramides, and PEGylated lipids are
underway.
The Nagel and Witten groups made further progress in exploring the multilamellar
surfactant cylinders known as myelins [PRL 96,
138301 (2006); Eur. Phys. J. E 18, 279
(2005)]. L. N. Zou in the Nagel group demonstrated an indentation-triggered
mechanism for creating single myelins with unprecedented control. J. R.
Huang in the Witten group [Eur. Phys. J. E 19,
399 (2006)] extended his theory of myelin formation to explain the twisted
structure often observed in myelins. Future work will test the predicted
scaling of minimal myelin diameter with degree of dehydration of the parent
smectic phase.
Splashes in Fluids and Granular Matter. Nagel and Zhang
have been collaborating on studying the dynamics of splashing. Their dramatic
discovery [PRL 94, 184505 (2005)] that the presence
of surrounding air was important in creating the splash has led to a number
of different projects. The experimental data support a model by Zhang in
which compressible effects in the gas are responsible for splashing in liquid/solid
impacts. Thus they found that for a smooth substrate splashing can be completely
suppressed by decreasing the pressure of the surrounding gas. They have
now also found that a drop can produce a “prompt” splash even
in the absence of air if the substrate is sufficiently rough. Simulations
by Zhang’s group including the effect of air are being compared with
experiments in Nagel’s lab. Experiments show that there are several
different regimes for splashing. Zhang’s and Nagel’s groups
are jointly attempting to establish the causes for the different regimes.
Their collaborative work is shedding light on the mechanisms for how the
energy, originally distributed uniformly as kinetic energy throughout the
drop, becomes partitioned into small regions as the liquid disintegrates
into thousands of disconnected pieces.
In a complementary system, Jaeger has been investigating the disintegration
of a granular “liquid”. A liquid-like granular jet was formed
by the impact of a solid body onto a volume of fine granular matter. In
fluids, impact-induced jets are held together by surface tension. The granular
jet exists in the absence of both surface tension and cohesion. Using high-speed
x-ray radiography at Argonne and digital video, jet formation both inside
and above the bed was tracked [Nature Physics 1,
164 (2005)]. Intriguingly, the jet breaks up into smaller “droplets”
similar to what would be expected from a slender column of ordinary liquid
(Rayleigh-Plateau instability). This breaking-up for fine-grained powders
also occurs in a different experimental geometry: gravity-driven flow out
of a vertical funnel [PRE 74, 051304, (2006)].
As in the liquid case, the gas appears to play a significant role in determining
the evolution of the droplets.
From annual report to the NSF, March 2007