FRG: Collaborative Research: Physical, Mathematical and Engineering Problems in Slow Granular Flow

North Carolina State University, Raleigh NC

Investigators

Abstract

Proposal: DMS-0244488 PI: Michael Shearer Institution: North Carolina State University Title: FRG: Collaborative Research: Physical, Mathematical and Engineering Problems in Slow Granular Flows ABSTRACT This proposal addresses a spectrum of fundamental and applied problems in the slow flow of granular materials. It includes coordinated efforts in experiment, mathematical analysis, modeling, and numerical simulation, supported by a long-standing industrial collaboration. Continuum models of granular materials are desirable from several points of view, but the associated partial differential equations are typically ill-posed, a mathematical difficulty that has severely hampered progress, especially for multidimensional flow. This ill-posedness reflects a real instability, the tendency of the deformation in granular flow to localize into shear bands. Fundamental issues surrounding the continuum description will be addressed through inter-related projects that investigate: (i) the role of discreteness and nonlinearity in regularizing the ill-posed continuum description, (ii) the formulation from micromechanical considerations, based on experiments and MD simulations, of a continuum model that accounts for microscopic velocity fluctuations, (iii) mathematical predictions and experimental tests of multidimensional steady-state hopper flows, and (iv) the settling of powders, an industrially significant prototype two-phase flow problem. The research program attacks different aspects of a basic question: What behavior of slowly flowing granular material can be understood by modeling the material as a continuum? This is particularly an issue for industrial settings such as the flow of agricultural grains in a converging hopper: When a silo is discharged, the granular material flows somewhat like a continuous fluid, but the forces on the hopper walls are unlike those exerted by a fluid due to the solid-like properties of the material and its discreteness. Scientifically, we wish to understand these properties, especially the role that the discreteness of the material plays in the models. Among other contributions, this research is expected to improve predictive capabilities in the materials-handling industry and thereby increase efficiency in manufacturing. The group will create a research environment that integrates research with the training of students and post-docs, through weekly group meetings, participation in conferences and a new course on granular materials. Collaboration across fields will be facilitated by the proximity of the mathematics and physics departments at Duke University, and by the existing collaborations between PIs at NC State and Duke Universities.