## PhD Thesis – Multiscale Modeling in Granular Flow

**Abstract:**
Granular materials are common in everyday experience, but have long-resisted a
complete theoretical description. Here, we consider the regime of slow, dense
granular flow, for which there is no general model, representing a considerable
hurdle to industry, where grains and powders must frequently be manipulated.
Much of the complexity of modeling granular materials stems from the
discreteness of the constituent particles, and a key theme of this work has
been the connection of the microscopic particle motion to a bulk continuum
description. This led to development of the “spot model”, which
provides a microscopic mechanism for particle rearrangement in dense granular
flow, by breaking down the motion into correlated group displacements on a
mesoscopic length scale. The spot model can be used as the basis of a
multiscale simulation technique which can accurately reproduce the flow in a
large-scale discrete element simulation of granular drainage, at a fraction of
the computational cost. In addition, the simulation can also successfully track
microscopic packing signatures, making it one of the first models of a flowing
random packing. To extend to situations other than drainage ultimately requires
a treatment of material properties, such as stress and strain-rate, but these
quantities are difficult to define in a granular packing, due to strong
heterogeneities at the level of a single particle. However, they can be
successfully interpreted at the mesoscopic spot scale, and this information can
be used to directly test some commonly-used hypotheses in modeling granular
materials, providing insight into formulating a general theory.

**Thesis committee:** Martin Z. Bazant,
R. Ruben Rosales, Jean-Christophe Nave, Arshad Kudrolli.

## Download entire document or individual chapters

The individual chapters of the thesis can be downloaded here:

- Header pages – abstract; acknowledgments; contents; lists of figures and tables.
- Chapter 1: Introduction – motivation; previous work at MIT; the contribution of this thesis.
- Chapter 2: Diffusion and mixing in granular drainage – the void model; the spot model; DEM simulation; velocity correlations in simulation and experiment; the density problem.
- Chapter 3: Dynamics of Random Packings – spot model calibration and simulation; random packing statistics and stability.
- Chapter 4: Further studies of the spot model – computing packing fraction using the Voronoi tessellation; modeling a free surface using the spot model; 2D spot simulation; spot model parallelization.
- Chapter 5: Pebble-Bed Simulation – background; mean velocity profiles; comparison to the kinematic model; diffusion; volume fraction, porosity, and local ordering; pebble residence time; the bidisperse PBR concept; effect of wall friction.
- Chapter 6: Testing the Stochastic Flow Rule – continuum theories of two dimensional stress; the Stochastic Flow Rule; SFR solutions in the silo and Couette geometries; comparison of SFR solutions to DEM simulation.
- Chapter 7: Measuring a granular continuum element – computation of material parameters on the spot scale; stress, strain rate, and packing fraction; evolution of material parameters via Lagrangian tracking; the precise mechanism of shear dilation.
- Chapter 8: Conclusion – concluding remarks and future directions.
- Appendices – diffusion calculations for the spot and void model; numerical solution of the kinematic model in the cylindrical reactor geometry; the spot model simulation code.
- Bibliography

The entire document is available here (40 MB).