Transactions between Granular Flow and Solidification: Merging Multiphase Transport with Statistical Mechanics

ABSTRACT - 0456420 Granular physics has undergone a renaissance of interest over the past decade, leading to new and exotic phenomena ranging from solitary oscillons. [Umbanhowar, 1996] to as yet unexplained traveling segregation waves [Choo, 1997]. These and other surprising behaviors continue to be discovered at a regular rate largely because we cannot predict outcomes in granular experiments in advance, as we can in the more analytically mature companion field of fluid dynamics. In restricted regimes, for example for rapid collisional flows, reliable granular models have been developed and proven, but few if any predictive models exist that capture multiple regimes ranging from the solid-like to the fluid-like. Therefore in this proposal, we seek to focus precisely on the interface between solid-like and fluid-like coexisting regions with the ultimate goal of producing an experimentally validated, quantitative, first principles model that spans the solidified-fluidized interface of granular beds. The proposed approach combines detailed experimental measurements of granular density and flow data with an existing analytic model. We will focus our investigations on cascading flow on a disk: a system that has not been extensively studied before, yet reveals a rich variety of states with complex interfaces that I believe can serve as a unique and useful testbed for the investigation of the features of interest. In addition to exhibiting numerous distinct patterned states, the disk system permits us to probe bed responses to centrifugal stress, which will provide unique insights into solidification and fluidization mechanisms. Intellectual Significance It is not currently possible to make generally applicable and practically useful predictions in granular systems where solid-like and fluid-like regions co-exist. Yet this state describes a considerable range arguably even a majority of industrial and geophysical granular systems (see below). The work proposed will generate significant improvements both in quantitative characterization of internal and surface states of such systems and in predictive modeling capabilities. The work will achieve this through the combination of a validated continuum model that permits the accurate simulation of solidified and fluidized regimes simultaneously with the best available experimental techniques including Particle Image Velocimetry of high speed video and X-ray Imaging. The experimental configuration that we will study is unique and permits the evaluation of how granular flow responds to changes in applied compressive stress and induced shear. The computational model has been demonstrated to correctly reproduce complex solid-fluid transitions in granular suspensions, and will be extended to dry grains in this work. This approach will lead to a detailed understanding of internal states within a complex granular bed, to significant advances in rheological modeling of transitional granular flows and, potentially, to a major improvement in predictive modeling capability to problems previously inaccessible to accurate simulation. Broader Implications One does not need to look hard to find broad implications of this research. On the industrial side, the implications are clearcut: as we describe in the proposal introduction, manufacturing efficiencies drop to 60% when granular materials are involved [Nelson, 1995], and taking the pharmaceutical industry as a case in point, entire manufacturing plants and product lines are not infrequently shut down entirely due an inability to scientifically predict outcomes and consequent failures in the reliable design of granular flow and mixing systems [USA, 1994; Muzzio, 2002]. The data that the proposed work will provide will be of direct benefit for the predictive design of industrial systems ranging from tumblers to chutes in which both solidified and fluidized states co-exist. Further afield, in geological systems the proposed work can be applied directly to landslide dynamics, but even within this field, there are broader implications than one might suspect. For example, there remains an unresolved paradox in Martian geophysics in which there is simultaneously strong geomorphological evidence for recent liquid surface water (e.g. sinuous channels) and definitive evidence that surface temperatures and pressures are far below values that could sustain this water [Christensen, 2003; Malin, 1999, 2000]. Into this controversy has been thrown the suggestion that many of the landforms associated with liquid water may in fact have been produced by dry Aeolian processes [Treiman, 2003; Leovy, 2003]. Yet there exists little in the way of fundamental predictive modeling that could definitively confirm or refute this suggestion [Shinbrot, 2004b]. Likewise, in terrestrial geophysics, the energy dissipated by long runout avalanches [Melosh, 1996] and by earthquakes [Scott, 1996] have been measured to be perplexingly small, and the work that we describe stands to shed light on frozen-fluidized granular interactions in these systems as well.