Dry shear flows
Abstract: Granular materials have been modeled as a continuum in many engineering fields such as agricultural, geotechnical, hydraulic and pharmaceutical. The laws that govern their mechanical behaviors follow that of the Newtonian mechanics at the particulate level. However, because of the relative size of the individual grains with respect to the containing vessels and/or with respect to the observation scales, the aggregate behavior has been found to challenge the continuum assumption. In this talk, we will briefly review the continuum approach to the physical behavior of flowing granular materials. This theoretical development parallels that of the kinetic theory for gases. The underlying assumption is that there is a stationary and homogeneous statistical distribution of both particle concentration and its velocity probability field. Many useful results that provide insight into granular flows can be derived from this approach. However, both physical and numerical experiments reveal that granular flows are in general non-homogeneous and often transient. Both time scale and length scale violate the basic assumption behind the kinetic theory of gases. For instance, in shearing granular materials, particles form intermittent clusters. The size and lifetime of these clusters depend not only on the grain properties, but also on the shearing rate. The fact that these clusters exist shows that homogeneity and stationary statistics of the particle distribution are no longer valid. While no formal theory now exist to deal with a general granular flow in which multiple length and time scales may co-exist, some conceptual arguments may be made to explain the physical processes at various stages of granular flows.