Elastic Effects in Granular Flows
Dr. Charles S. Campbell
University of Southern California
Los Angeles, CA 90089-1453 USA
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 behavior 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 neighbors. 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 subdivided into two subregimes, the Inertial-non-Collisional regime, in which the particle interact in clusters that do not quite become force chains, and the Inertial-Collisional regime (the old Rapid Flow regime) for which kinetic theory models are appropriate.
Through a coordination of wave Elastic effects have also been show to control the convection in deep vertically vibrated vibrated boxes, and are the key to understanding the convection processes. Furthermore the Elastic-Inertial regime may help explain a controversy in the fluidized bed community in which there is experimental evidence of an unexplained viscous-like behavior that may reflect the linear behavior in the elastic inertial regime.
This talk will reflect the current state of the elastic flow theory and include recent work on non-round particle effects.
Dr. Campbell holds a BA (1977) in Mathematics from Vassar College and an MS (1978) and PhD (1982) in Mechanical Engineering from Caltech. He spent a year as a Project Engineer at Hughes Aircraft's Space and Communications group, before his current position at the University of Southern California. He was chosen in the first round of Presidential Young Investigators in 1984 and the premier recipient of the Kona (Japanese for "Powder") presented in Japan in 1991.