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Flowing Granular Materials

 The Course Syllabus contains information about lectures and student expectations.

  Lecture 1 gives a brief overview of some of the many and varied places where granular materials show themselves. This lecture then introduces some of the concepts of continuum modeling of granular materials, as applied to the forces in a silo.

 Lecture 2 talks about constitutive relations and the equations of motion. We'll talk here about the classical Mohr-Coulomb theory, and basic application to hoppers and bins.

 Lecture 3 introduces some newer constitutive models - rate state ideas, the STZ theory, and a phenomenological model based on the Ginzburg-Landau theory.

 Lecture 4 presents the Broadwell model of particle interactions, a model wherein each particle has one of a finite number of velocities. The notes also illustrate the Chapman-Enskog expansion for a relaxation system.

 Homework 1 Due October 25.

 Lecture 5 gives a quick summary of the derivation of hydrodynamic equations from the Boltzmann equation. We will also spend a little time talking about granular dynamics simulations (see the websites at Stuttgart and Bar-Ilan).

 Lecture 6 gives a derivation of a model by Gray and Thornton of the segregation of 2 species of particles in an avalanche flow. The paper is here. We will also talk about work of Mullin on segregation experiments in a horizontally oscillating table - the paper and another.

We will also talk about the term paper. Papers to read are posted. This Summary may help you find something you are interested in.

 October 25 we will be taking a road trip, to visit the lab of Professor Karen Daniels at NCSU. More information in class. Read the paper and trace back the references.

 Lecture 7 gives a brief introduction to random walks and points you to an application by Bazant of flow out of a bin. The notes also contain material on SDEs.

 Lecture 8 is an expanded set of notes on SDEs. For those interested, I am also posting a tutorial by Desmond Higham on computing solutions to SDEs.

 Lecture 9 describes a model of granular avalanches as the depth-averaged mass and momentum balance laws with a frictional constitutive relation. To provide you with some of the physical intuition about avalanches and debris flows, I am posting a presentation showing some images, and illustrating the role uncertainty plays in the modeling.

 Lecture 10 is a statistical analysis of snow avalanches. These notes are based on a paper by Ancey and relies on earlier work by Holy that considers how to represent discrete observations as a continuous distribution.

 Lecture 11 addresses two features of models: the discrete to continuum expansion, and a meachanism to assess variation of an uncertain parameter in a model system.

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This page updated on September 15, 2006 12:26 PM