Many thousands of tons of granular material are handled daily in industries ranging from mining to chemical to pharmaceutical. Their values range from cents per ton to thousands of dollars per gram. Handling massive amounts of small-value material can be expensive if done inefficiently and potentially make a project uneconomical. At the same time, high-valued products must be handled carefully to avoid damage with consequently large economic losses. Yet the mechanical behavior of granular materials is not well understood. Classically granular flow have been studied in two limiting flow regimes - the fast-flow or "rapid flow" regime and the slow-flow or quasistatic flow regime. There has been little understanding as to what occurs in between, and without that information, it has been impossible to even quantify the conditions under which each flow regime is valid. Recently, the P.I. has been able to fill in this intervening space and create unified flowmaps covering all regimes of granular flow behavior - at least for simple materials. The key was including as a rheological parameter, the stiffness of the interparticle contacts, the property that links the elastic properties of individual particles to the elastic properties of the bulk material - and thus to bring solid properties back into the rheology of granular solids. He divided granular flows into two broad regimes. In the Elastic regime, particles are locked in force chains in persistent contact with their neighbors; the stresses are generated by the deformation of those contacts and are thus proportional to the contact stiffness. In the Inertial regime flows become independent of the stiffness. These were further subdivided into four sub-regimes, Elastic-Quasistatic, the old quasistatic regime, the Elastic-Inertial when inertial effects have comparable order, the Inertial-non-Collisional regime, which behave inertially, but the particle interact in cluster, and the Inertial- Collisional regime, where binary contacts dominate (the old Rapid-flow regime). The goal of the project will be to extend this work through coupled experiments and computer simulations to further flesh out the rheological behavior. The coupling between simulation and experiment will occur in several ways. First, as these are new and not-well understood flow regimes, simulations will be used to guide the design of an annular simple shear rheometer. Also, simulations of the experiments themselves will yield insight into what is happening inside the shear cell and aid in the interpretation of the results. In turn, the experiments will guide future simulation development. A particular goal will be to determine adequate contact models that allow the simulations to replicate the experiments. Finally, the simulations will be extended to further probe elastic granular rheology.
Intellectual Merit: The elastic theory is transformative in being the first unified theory of granular flow and fills out the entire flowmap, connecting the rapid and quasistatic regions and all the intervening regimes. While at the moment, like most granular theories, it is limited to monodisperse spheres with simple contact models, it nonetheless demonstrates the fundamental scaling laws that must in some form apply to more complex systems and thus provides the key to future expansion of granular flow theories. The proposed work involves experimental verification of the elastic model as well as a start on its extension to more complicated systems.
Broader Impact: Quasistatic and rapid flow models are being incorporated in a large variety of computer models used in design applications for the chemical, pharmaceutical, mining, construction, agriculture, petroleum, geo-technical, as well as hazard assessment. Until the flowmaps that were generated from the elastic theory, there was no way to determine the conditions under which the models were valid. Thus this work will finally begin to put into perspective, the last 40 years of granular flow theory. At the same time, it will prevent costly errors resulting from the misapplication of the wrong model to an industrial problem.
Educational Impact: Courses taught at USC receive wide distribution over the school DEN network, now available worldwide and on demand by streaming video on the internet. In particular, granular flow theory makes up a large portion of the P.I.'s course, AME533 Multiphase Flows. In addition, USC is located in a low-income, largely African-American, area, South Central Los Angeles, and has many community outreach programs to connect with local residents and students. In the past the P.I. has supported three female PhD students. Finally the P.I. is partnering with another professor to bring in underrepresented summer interns, many from the University of Puerto Rico, to give hands on experience and to educate in simulation techniques. Particular emphasis will be put on the simulation techniques as most rheological scale simulations can now be performed on home PC's. This will permit the intern to continue the collaboration when he or she has returned home at the end of the summer.
