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Consequences of the ?(I) constitutive law

Presented by: 
CJ Cawthorn & EJ Hinch & JN McElwaine [Cambridge]
Thursday 8th January 2009 - 11:45 to 12:00
INI Seminar Room 1
Following the proposal of a three-dimensional constitutive law for dense granular flows by Jop, Forterre & Pouliquen, a wide range of researchers have begun to apply this so-called p(I) law to a wide range of granular flows. In this presentation, I shall highlight some of the many applications of the p(I) law, describe its strengths and weaknesses (most of which are mentioned in a recent review paper) and suggest some possible modifications that may extend its range of validity. The p(I) law was developed with free surface flows in mind. Indeed it was constructed from a friction law for granular flow down a rough inclined plane. Since its proposal, the mu(I) law has been used to successfully model a range of free surface flows, and has produced good quantitive results. As well as describing some past successes, we will discuss some new stability calculations predicting the formation of longitudinal vortices in flow down an inclined plane, lending more support to the use of the p(I) law. For confined flows, such as Coutte or Taylor-Coutte shear, it has been n0ted that the p(I) law makes predictions that are quantatively poor. We shall discuss some possible reasons for this, and propose a simple modification that should extend the contitutive law's predictive powers to encompass such confined geometrics. Finally we shall highlight the need for a proper understanding of how flowing regions can interact with static of plug regions, either by erosion or accretion. We will discuss some progress in this direction, and consider its application to experimental geometrics, such as split-walled shear cells, rotating drums, and the collapse of a granular column.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons