Scaling of granular flow processes: From surface flows to design rules

Scale-up of granular processes is notoriously difficult and there is little guidance at the present time. This is true even in the simplest case of noncohesive powders consisting of spherical grains, the scenario considered here. However, flows in granular materials are often restricted to thin regions of rapid surface flow with the rest of the material suffering only slow plastic rearrangements. This seemingly trivial observation leads to understanding of the entire system and to the concept that an understanding of surface flows constitutes the key element for scale-up of granular flow processes. A surface flow is characterized primarily by its thickness and the shear rate. For large particles, both are controlled primarily by the Froude number and the particle-size ratio (particle diameter to cylinder radius), whereas material properties have a secondary effect. Modem experimental techniques are yielding further insight into the physics of shear flows and theoretical analysis is providing guidance and scaling insights. The assembly of experimental and theoretical components opens the class of problems dominated by surface flows to serious engineering analysis and predictability. Current understanding is extended and integrated, the governing scaling laws are made explicit, and the results obtained in terms of rules are summarized. The use of the integrated knowledge by means of an example is exemplified.