skip to content

Elastic effects in granular flows

Presented by: 
CS Campbell [Southern California]
Thursday 8th January 2009 - 10:30 to 10:55
INI Seminar Room 1
Previously, granular flows had been divided into (1) the slow, quasistatic regime using models born of metal plasticity theory and (2) the fast, rapid-flow regime using models born of the kinetic theory of gases. However it was clear that even collectively, the models were incomplete. In addition, there was evidence that many flows operate in an intermediate regime where the rheological behaviour was not understood. Furthermore, the parameter space in which either model was valid were entirely unknown. Recently. it was discovered that adding the interparticle stiffness as an additional rheological parameter allowed the entire flowmap of granular flow to be drawn. This allows one to put practical limits on the quasistatic and rapid regimes and to understand the physics of the intermediate regime. The flows could be divided into two broad regimes, Elastic and Inertial. The Elastic regime are dominated by force chains with particles in intimate contact with their neighbours. The internal forces are generated by the compression of the interparticle contacts and thus scale with the interparticle stiffness. This is divided into two subregimes, the Elastic-Quasistatic, the old quasistatic regime, and the Elastic-Inertial regime, the previously understood intermediate regime. In the Elastic-Quasistatic regime, the stresses are generated by the process of the formation, compression, rotation, and destruction of force chains. The process is shear rate independent because the formation is proportional to the shear rate, while the destruction is inversely proportional to the shear rate and the compression is largely geometrically controlled and shear rate. However, some degree of the chain's compression reflects the particle inertia and at large enough shear rates this becomes noticeable and the material enters the Elastic-Inertial regime, where, reflecting the increased inertia, the stresses increase linearly with the shear rate. This is the new "flow" regime referred to above. Inertial flows are free of force chains and demonstrate the famous Bagnold scaling where the stresses vary as the square of the shear rate. However, it too can be divided into two subregimes, the Inertial-non-Collisional regime, in which the particles interact in clusters that do not quite become force chains, and the Inertial-Collisional regime (old Rapid Flow regime) for which kinetic theory models are appropriate. Through a coordination of wave Elastic effects have also been shown to control the convection in deep vertically vibrated boxes, and are the key to understanding the convection processes. Furthermore the Elastic-Inertial regime may help explain a controversy in the fluidised bed community in which there is experimental evidence of an unexplained viscous-like behaviour that may reflect the linear behaviour in the Elastic-Inertial regime. This talk will refect the current state of the elastic flow theory and include recent work on non-round particles.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons