The flow of granular materials such as sand is ubiquitous in both industry and nature. The importance of understanding such flows is clear when it is estimated that a large fraction of the US gross domestic product is spent handling granular materials and that most facilities typically operate well below efficiency. Even a small improvement in our understanding of granular media behaviour could have a profound impact on EU industry. The research proposed here is concerned with improving our understanding of how granular materials respond to tangential boundary stresses. A recent experiment has revealed completely unexpected behaviour which we propose to interpret using a continuum model based upon conservation laws of mass, energy and momentum augmented by constitutive relations.
An efficient and general numerical solver using pseudo-spectral techniques will be developed to solve the resulting set of partial differential equations. The influence of incorporating or removing various physical effects will be assessed by comparing the model solution against the distinctive features of the data. Initially the response of a Newtonian fluid will be examined by solving the Navier-Stokes equations. Then non-Newtonian effects will be investigated by adopting a non-linear relationship between stress and strain in the material and finally constitutive laws, which incorporate the granular temperature, will be studied.
The objective is to isolate the simplest continuum theory, which predicts the key features of the data with the aim of then correctly predicting behaviour in other granular systems. Appreciating when a continuum description of a granular flow is valid is perhaps the fundamental question in the study of granular materials today. The proposed research will attempt to answer this question for one fascinating system, which shows truly novel behaviour and should provide insight into the physics of other sheared granular systems.
Call for proposal
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