Continuum modelling of particulate flows in nature and industry

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So much of the natural and man-made world is composed of collections of discrete solid grains. However, there is currently no completely satisfactory theory to describe their motion, en masse, in the many complex flow scenarios which are important across industry and geophysics. Despite the challenges, a promising paradigm has been building over the last 20 years. Based around key experimental, mathematical and physical insights, continuum models for both the flow of dry grains and for particles suspended in a background fluid are beginning to mature.In this project, the driving goal will be to develop a unified rheology spanning the many flow regimes that particulate materials can exhibit. Once this model begins to take shape, novel numerical methods will be developed to solve the resultant dynamical equations. This in-house code will then be applied to various test cases inspired by flows in nature, such as debris avalanches and subsea landslides, and in industry, such as hopper flows and drum mixers.The work will be framed and motivated by key open questions such as "Is it useful in modelling to categorise particle flow dynamics into gas-like, liquid-like and solid-like behaviour?", "What is the most appropriate numerical method to solve multi-regime particulate flow equations?" and "How does the presence of liquid water modify the severity of natural hazards and the efficiency of industrial processes?".