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Physics of Granular MaterialsWhy are Brazil nuts found near the top of a can of mixed nuts? What causes an avalanche of rocks or snow? We may think of these systems as a collection of grains. The behavior of a single grain is easily understood, but the properties of a collection of grains is very complex. Granular materials when poured or shaken display a surprising range of collective behavior such as convection, size separation and pattern formation.
Granular materials are important constituents in many industrial processes and geophysical phenomena. However, no fundamental statistical theory is currently available to describe their properties. A major factor is the lack of quantitative experiments that can be used to develop models. Therefore, we have performed a series of experiments to investigate their properties in my laboratory. Some recent examples and their motivation are discussed below.
Granular gases: Correlations and distributionsWe investigated the velocity distributions of steel spheres rolling on a tilted rectangular two dimensional surface using high speed imaging imaging. This is one of the simplest model systems to investigate the application of hydrodynamic approaches to granular matter. The particles are excited by periodic forcing of one of the side walls. We observe strongly non-Gaussian velocity component distributions even in the dilute regime (Kudrolli 2000) unlike what has been assumed in developing theory of rapid granular flow. The particle velocities are observed to be correlated over large distances comparable to the system size (Blair 2001). We implemented long time particle tracking of all the particles in the system. This enabled us to obtain collision properties including the inelasticity parameter. The path length and collision time distributions of the particles were found to deviate from formulas calculated from the kinetic theory of elastic gases (Blair 2003). We propose a new function for the distributions which has not yet been explained by theory. The radial correlation function was measured and found to deviate from the Carnahan and Starling formula normally used in theory. These results form the context for new experiments that we are performing on the equation of state of excited granular matter.
Magnetized granular materialsWe studied the effects of long range interactions on the phases observed in cohesive granular materials. Our system consists of magnetized steel particles inside a container which is vibrated vertically (Blair 2003, 2004). At high vibration amplitudes, a gas of magnetized particles is observed with velocity distributions similar to non-magnetized particles. Below a transition temperature compact clusters are observed to form and coexist with single particles. The cluster growth rate is consistent with a classical nucleation process. However, the temperature of the particles in the clusters is significantly lower than the surrounding gas, indicating a breakdown of equipartition. If the system is quenched to low temperatures, a meta-stable network of connected chains self-assemble due to the anisotropic nature of magnetic interactions between particles [see figure above]. This is a rich model system which can be used to study complex cohesive granular materials.
Dynamics of anisotropic grainsWe investigated the effect of anisotropy of the constituent particles on the packing and dynamics of granular matter. These experiments were inspired by Seth Fraden. An important question is whether orientational order due to the principle of entropy maximization observed in anisotropic thermal systems carries over to dissipative granular systems. We find that not only do the particles self-organize to form ordered domains from an initial random state but also observe novel motion [see movie]. Vortex patterns are observed when a container filled with rods is vertically vibrated (Blair 2003).
Above a critical packing fraction, moving domains of nearly vertical rods spontaneously form and coexist with horizontal rods. We show that the motion is generated due to the inclination of the rods by doing experiments with a row of rods in an annulus. In collaboration with L. Tsimring's group at UCSD, we showed that the motion occurs due to the frictional collision of the rod with the driving plate (Volfson 2004). This is a novel example of a granular rachet formed due to spontaneous symmetry breaking. More recently we have studying the dynamics of a single dimer on an osciallted plate. This is a simple generalization of the classic bouncing ball paradigm for period doubling and transition to chaos. We observe several novel modes including a drift mode in which uphill drift motion can be induced by suitable choice of parameters (Dorbolo 2004).
Diffusion and surface flow instabilities inside silosWe examined the gravity driven flow of granular materials inside a silo in collaboration with M. Bazant's group at MIT. By tracking individual particles over long periods of time we showed that while the mean flow was reasonably described by kinematic and diffusing void models, the actual amount of particle diffusion was very small (Choi 2004). A sub-ballistic to diffusive crossover was observed. A new model which takes into account the observed correlations has been developed and is being currently tested.
Effect of liquids on the cohesive and segregation properties of granular matterWe studied the effect of adding small amounts of liquids to granular matter. This is a topic in which little quantitative work has been done even though humidity or liquids are almost always present in natural situations where granular matter occurs. Two different experimental setups were used. First, our experiments were conducted with mixtures poured into a quasi-two dimensional silo which allows visualization through the transparent side walls. Our data for the increase in the angle of repose and subsequent saturation appears to be inconsistent with some of the models of wet granular matter. Our experiments showed the importance of viscosity of the liquid in determining the angle of repose of the pile formed after pouring the granular mixture (Samadani 2001). We also reported one of the first systematic studies of segregation transition of bidisperse granular mixtures in the presence of liquids (Samadani 2000).
Then, the maximum angle of stability of a cohesive pile was investigated using a rotating drum apparatus to understand the discrepancies noted in previous studies. We first showed the effect of the side walls by varying the width of the drum. The maximum angle of stability was then measured in the limit where side walls are unimportant. We developed a new liquid bridge model which takes into account the nature of the grain contacts and the cohesive force due to liquid bridges to show the grain size, system size, and surface tension behavior (Nowak 2005). In this model, the friction between particles is considered less important compared to geometric stability of the particles. The experimental data is in excellent agreement with the prediction of our model.
See the publications home page for cited references.
Department of Physics
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Last updated November 17, 2005.