Ellis, A.S.; (2007) Modelling chute delivery of grains in a food-sorting process. Doctoral thesis , University of London.

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Abstract

The whole of the thesis is motivated by a particular problem from the food-sorting industry in which grains of food, typically rice, flow down chutes. As they fall down the chute, the grains form a rapidly moving mono-layer. This project starts with a discrete model treating individual grains based on partcle dynamics without air resistance. Single grains and then many grains are addressed, and the methodology used includes large computations describing the particle paths, velocities and other key features accompanied by analysis. Much of the thesis thereafter is concerned with the development of a continuum model for the chute flow of grains, inspired by the clusters and voids seen in the above computations and based on analogies with the Lighthill-Whitham model of traffic flow. The crucial difference here is that the flow is not uni-directional and so a multi-valued flow-density relation is required. The introduction of such a law yields complex and rich flow behaviours. The mathematical interest is in solving hyperbolic and parabolic partial differential equations, incorporating shocks and fans into analytical and numerical solutions of the governing equation, in asymptotic methods used in analysis of particular limits, especially those relating to clashing or separation of grains, and in seeking steady state solutions for the density profile. Finally, air effects are studied. In particular, local viscous or inviscid effects in the gaps between grains are investigated, followed by the subsequent interaction effects on many grains.

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