Research Highlights

Our work was originally motivated by the need to understand granular flow in the core of the proposed MIT Modular Pebble-Bed Reactor. The flow is extremely slow (less than one pebble per minute) and dense (near jamming), so it is beyond the realm of classical statistical mechanics and hydrodynamics. Still, it is necessary to understand the random trajectories of fuel and moderator pebbles as they pass though the core. We started by working with MIT Nuclear Engineering on pebble-flow experiments in scaled-down reactor models, while at the same time building our own lab for experiments and large-scale computer simulations.

A major scientific goal of our research is to understand the microscopic dynamics of random packings in granular flow (and more generally, relaxation in dense amorphous materials). Our first step in this direction has been the Spot Model, which postulates a mechanism for grains to rearrange collectively in response to diffusing "spots" of free volume, extended across several grain diameters. The model allows for global shear and diffusion while constraining each grain to mostly move cooperatively with its "cage" of nearest neighbors. We have tested the model in many ways against drainage experiments and simulations and it seems consistent with much of the data. For now, however, it is just a "kinematic model" in the sense that it can reproduce the packing dynamics of drainage only after fitting some parameters (spot size, volume, and diffusivity), which we hope to eventually derive from mechanical considerations.

Motivated by these ideas, we have performed state-of-the-art particle-tracking experiments on diffusion and mixing in slow drainage by processing images from a high-speed digital video camera. Our experiments revealed that statistical fluctuations depend primarily on geometry, not flow rate (or classical notations of "temperature"). In particular, there is a universal crossover from superdiffusion to normal diffusion at roughly one particle diameter, as a function of the distance dropped, not time, for a wide range of flow rates. We also showed that cage breaking occurs over surprisingly long distances, at the scale of the entire silo. We also observed direct evidence for spot-like cooperative motion in spatial correlations in velocity fluctuations at the scale of 3-5 particle diameters.

We have also done extensive experiments on the mean-velocity profile and flow rate in silos of different shapes to test various theoretical models. We conclude that a satisfactory theory of granular drainage is still lacking, so we are pursuing some new ideas (see below).

In addition to real experiments, we have collaborated with Sandia National Laboratories to perform large-scale paralle computer simulations of the experiments. The Sandia code, which now also runs on our Beowulf cluster, uses the discrete-element method to track the motion of hundreds of thousands of frictional, visco-elastic spheres, with remarkable realism. The simulations allow us to "look inside" the experiments and study the collective motion of grains in great detail. In this way, we have studied the dynamics of random packings in granular flow and directly tested the Spot Model. We found that simulations with the Spot Model produce remarkably realistic flowing random packings without explicitly describing frictional mechanics, aside from some fitting of parameters to independent measurements, although more study is needed to assess the model as a method of multiscale simulation.

Current Projects

  1. Chris Rycroft and Gary Grest are performing extensive parallel DEM simulations of pebble-flow in realistic full-scale models of pebble-bed reactors, to study the effects of core shape, a dynamic central column of moderator pebbles, and the concept of a bidisperse core with smaller moderator pebbles and larger fuel pebbles. We are also beginning to combine these simulations with modeling of the reactor physics or core neutronics, gas flow, and heat transfer.
  2. Jeremie Palacci and Chris Rycroft are studying the stability and convergence characteristics of the Spot Model, and its sensitivity to various parameters.
  3. Ken Kamrin is developing a stochastic flow rule for Mohr-Coulomb plasticity, as a means of connecting classical concepts of friction and incipient failure with more recent ideas of cooperative, random motion (e.g. spots) and partial fluidization. The stochastic plasticity theory seems to predict various features of our drainage experiments and simulations from mechanical first principles, such as the kinematic parameter and the spot shape (correlation function). It also seems like a promising route toward a unified theory of different shear flows (not just gravity-riven drainage, but also granular Couette cells).
  4. We are also doing further silo-drainage experiments and DEM simulations to test existing continuum models of granular flow, as well as our new theories.