Daniels Nonlinear Lab

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	Gels :: Granular Materials :: Thin Films

Overview

Most physical systems are not in equilibrium, but rather are subject to driving and/or dissipation. Far from equilibrium, where nonlinear effects become important, these systems display a rich array of complex behaviors. Systems can be dynamic, chaotic, or turbulent, and more remarkably can produce static patterns or exhibit persistent dynamics while remaining statistically stationary. Although there is typically no free-energy-like functional to minimize in a nonequilibrium system, quantities analogous to those used in equilibrium statistical mechanics can often elucidate the mean behavior.

Current experiments address:

granular materials
surfactant-driven gel fracture
instabilities in thin fluid flows
laboratory models of geophysical processes

Support

Our research is supported by North Carolina State University and the National Science Foundation (DMS-0604047 and DMR-0644743).

Surfactant-Driven Gel Fracture

The image at left was taken of a droplet of food coloring spreading within self-generated fractures at the surface of gel agar in a Petri dish. This is quite different from the circular way which surfactant-laden droplets spread on either solid or liquid surfaces, and is related to the fact that the gel substrate is a viscoelastic material which can fracture. We are studying how this instability arises from competition between the surface tension of the droplet and the elastic properties of the substrate. Such instabilities are important to understand in order to reliably work with non-Newtonian fluids in industrial and biomedical settings.

Publications

K. E. Daniels, S. Mukhopadhyay, P. J. Houseworth, and R. P. Behringer. Instabilities in droplets spreading on gels. Physical Review Letters 99 124501 (2007) [ Link ]

Gel Heterogeneity

We study the heterogeneity of gels near the sol-gel transition through the spatial variations in gel strength. The correlated motion of fluorescent polystyrene microspheres suspended in gels (see image at right) is measured via two-point microrheology. Analysis of this correlated motion provides a local measure of gel heterogeneity.

Granular Materials

From avalanches and erosion to the transport of grain or pharmaceuticals, granular materials are all around us. When working with them, it rapidly becomes clear that these "simple" systems produce complex behavior: networks of force chains (see image below) support the material, flowing motion is localized in shear bands, and particles segregate by size or shape when you try to mix them.

The dynamics of granular materials depend strongly on whether they are loosely or closely packed. In this movie we show the braiding trajectories in a 2D granular system, with the less dense system shown at the left.

Statistical Mechanics

With their ability to act as solids, liquids, or gases, the behavior of granular materials begs analogy with much of what we first learned about conventional molecules, but there are imporant differences. For example, the image at right shows a phenomenon known as "force chains". Forces are not carried uniformly in the material, but instead through long chain-like strucutres whose density and orientation depend on the state and history of the sample. We are able to visualize these forces using a photoelastic disks and a polariscope.

Research projects in the group address visualizing sound wave propagation, effects of order and anisotropy on material properties, phase transitions, and developing and testing statistical mechanical models.

Sound and Force Propagation

Sound propagation in granular materials has many unexplained features related to its speed of propagation, damping, and dispersion. We have developed a way to simultaneously image sound propagation and record acoustic signals on the single-particle scale to study the effects of the force chain networks on the sound.

In the animation to the left, the lower left frame shows the static force chain structure initially present in the pack. A square pulse begins at the driver (yellow) and propagates to the left to accelerometers (red and blue). The graph to the right shows the driver pulse (black) and the corresponding accelerometer responses. The upper left image shows a frame-differenced movie of the stress wave as it moves through the pack.

Mixing & Segregation

Granular materials of mixed sizes can segregate under shear, as seen in the image at right. We are working with Michael Shearer and Lindsay May in the NCSU Mathematics Department to develop models of how segregation happens in mixed samples and how mixing happens when the system is unstably stratified.

Publications

M. Shearer, J. M. N. T. Gray and A. R. Thornton, "Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches." European Journal of Applied Mathematics, 19, p. 61-86 (2008). [ Link ]

Geophysics: Natural Faults as Granular Systems

Geologic faults and granular materials have several key features in common:

stick-slip behavior
localized slip planes (see micrograph, courtesy Nick Hayman, at right)

Since real faults have granular textures on many scales, from microscopic grains to macroscopic rocks, we seek to understand the extent to which granular interactions (interparticle, frictional slip) account for the range of geological observations & the inferred dynamic fault histories.

Together with Nick Hayman (Univ. of Texas, Austin) we are conducting laboratory experiments using birefringent (photoelastic) particles in a simulated strike-slip fault. This movie of our laboratory fault experiment shows events in which the abrupt localization of the shear strain to the center of apparatus corresponds to little change in the force chain geometry away from the "fault." Bright particles are experiencing greater force than dark particles.

Publications

K. E. Daniels and N. W. Hayman. "Force chains in seismogenic faults visualized with photoelastic granular shear experiments." Journal of Geophysical Research. 2008. (In Press). Link to PDF

Thin Fluid Flows

[thin film schematic] In collaboration with applied mathematicians, we are investigating instabilities in surfactant- and gravity-driven liquid films.

Publications

R. Levy, M. Shearer, and T. P. Witelski, "Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves." Submitted to European Journal of Applied Mathematics. [ PDF ]