Granular Media: Mesoscopic Physics on a Laboratory Scale

Granular materials, complex nonlinear pattern formation, and control of complex patterns are at the forefront of our understanding of collective behavior. The study of granular materials provides insight into poorly understood and vitally important industrial problems, and an unprecedented opportunity to investigate experimentally the theoretical underpinnings of statistical physics. In granular systems, collective behavior and pattern formation can occur with a small number of macroscopic particles. This property creates a unique opportunity to gain a fundamental understanding of mesoscopic systems, such as colloids, lubrication, and nanoscale porous media. Pattern formation in granular systems illustrates the profound link between granular flows and ordinary fluids and is a cornerstone of our research.

Experimental tests of granular kinetic theory: We conduct experiments to directly test granular kinetic theory in the laboratory. Using high speed digital photography, we track the position a velocity of individual grains in a 2D rotating drum. At moderate rotation rates three flow regimes are formed --- a dilute gas at the top, a dense gas in the middle, and a elasto-plastic solid at the bottom. In earlier work, we have confirmed that continuum equations of motion derived using kinetic theory of dense inelastic gases give quantitative results for the dilute phase. We are now exploring their applicability to the dense phase, where we may encounter visco-elastic behavior, which is not currently included in the theory. Finally we are exploring ways of extending kinetic theory and connecting with elasto-plastic solid models to bring the entire flow regime under a unified theory.
Experimental granular rheology: By uniformly exciting a granular media using a random sum of its container's elastic vibrational modes, we can directly measure the speed of sound, thermal conductivity, and viscosity as a function of density and granular temperature in this uniformly heated steady-state. Using a sinusoidally varying forcing we can measure the frequency dependence of the transport properties.
Granular media as an analog for collective systems in extreme conditions: We will study the flow of uniformly heated granular media in a small channel as an analog for mesoscopic systems. We can explore phase transitions in systems of rods, in mixtures of rods and spheres, and in mixtures of different sized spheres. These studies will add to the understanding of both granular media and ordinary condensed matter under extreme situations including confined geometries, gradients which are large on the scale of the mean free path, and flow in which intrinsic mechanical stress can induce phase transitions.
Granular pattern formation: A vertically oscillated and uniformly heated granular layer provides a strong analogy with ordinary fluids. By varying the amount of external heating a continuous range of behavior, from fluid-like at high temperature, to granular at zero external heat flux, can be studied. In the unheated, vibrated granular layer extremely large scale patterns can be produced with up to 500 wavelengths.

Biologically-Inspired Micro-robotics

Organisms adapted for motion on beaches and in deserts show amazing mobility in a variety of surface conditions. Long term adaptation of these animals to shifting sand provides a great opportunity to understand the optimal general principles of legged locomotion. Nature has not developed wheeled motion, and legged animals like spiders, crabs, and lizards provide an existence proof that rapid locomotion in flowing environments is possible. There is increasing evidence that motion on complex terrain rely on both active and passive control. To that end we are developing micro-robots with legs that are based on principles of real organisms to leverage the passive mechanical aspects of real organisms. The long term goal is to produce autonomous robots of 1-10cm in size, that can run on general terrain at speed up to 10 body-lengths-per-second. We are currently working on anatomically accurate leg design using 3D printing, for rapid prototyping, and nitinol memory wire as muscles.

Patterns: Competition and Control

The study of pattern formation has produced an understanding of simple bifurcations to single-patterned states in spatially extended systems. Patterns in nature, however, display a complexity which defies this basic understanding. We will push the study of pattern formation to a new level of complexity using novel experimental techniques to study systems which combine large numbers of spatial modes with pattern competition and spatiotemporal inhomogeneous forcing. Further, we will use spatiotemporal perturbations to control patterns and stabilize them beyond their normal range of stability. This is a prerequisite step for control of complex pattern formation in industrial processes, and control of natural systems such as weather, evolution, and thought.

Complex nonlinear pattern formation and control: We will explore complex nonlinear pattern formation in binary mixture Rayleigh-Benard convection. We can measure the density and concentration fields using a novel visualization technique based on the preferential absorption of infrared laser-light by one component of the mixture. We can systematically add complexity to this system by increasing the number of spatial modes through changes in aspect ratio and inclusion of pattern competition. We will combine visualization and arbitrary spatiotemporal perturbations using a high-powered laser rastering system to form a closed loop control system. Previously, control of simple pattern forming systems with a small number of spatial modes has been achieved in the laboratory using both linear and nonlinear control, but we will extend both methods to control complex pattern formation.

Specific Projects for 2012

We need students to work on the experimental projects listed below, which are planned for 2012. In addition we have a number of molecular dynamics and continuum simulation project which could be explored. If you are interested please contact Mark Shattuck.

Bio-Inspired Micro-Robot Leg Design and Testing: We will use commercially available 3D printing services to produce small 1-5cm articulating robot legs based on desert spiders and crabs. Nitinol memory wire will be used for antagonistic muscles.
Experimental determination of the Speed of Sound in granular materials: If sufficient energy is injected into granular materials then they can flow like a Newtonian fluid. However, due to the energy loss during collisions between grains the granular temperature can be quite low leading to a very low speed of sound in the material. We will measure the speed of sound in a 2D horizontal granular layer excited from two sides by creation of standing waves perpendicular to the excitation.
Granular pattern formation with extremely large aspect ratio: A vertically oscillated granular layer can produce a wide range of patterns. We will explore the effect of container size on the pattern formation by vibrating extremely large granular layers, which can creating patterns with up to 500 wavelengths.
Effect of tool angle on fracture pattern in polymer sheets: Pulling a tool through a cellulose sheet creats a distinctive pattern which depends on the size of the tool but is independent of the rate of pulling. We will explore the dependence of the pattern on the angle of the tool using an existing experimental setup.