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Department of Mathematics

# Granular materials

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Granular materials are the second most abundant material on Earth after fluids, yet our scientific understanding of their behaviour is still open.

## Our research projects

Most of us are familiar with granular materials from pouring our cereal into a bowl at breakfast! Yet, despite thousands of years of using and handling granular materials, mathematically modelling their flow behaviour and the way disparate grains segregate is still a significant challenge. There are therefore many exciting problems for applied mathematicians to tackle which have important applications to both industry and the natural environment.

One of the major research challenges that is being addressed in Manchester, is how to formulate well-posed continuum models that can be used to calculate granular flows with evolving regions of liquid-like and solid-like behaviour. Such behaviour is extremely common, e.g. our breakfast cereal will remain solid-like as the box is rotated up until a critical angle, after which a liquid-like avalanche forms near the surface. This avalanche transports the cereal grains into the bowl, where they can come to rest again to form a static pile again.

Avalanches are actually very efficient at sorting particles by size and/or density, which causes problems in many industrial processes as well as generating beautiful structured patterns in deposits. In Manchester, we are world leaders in the development of new mathematical theories for particle-segregation as well as in investigating how this feeds back on the bulk flow dynamics. For instance, a combination of grain size and roughness differences is responsible for the segregation induced fingering (shown in the image at the top of the page) in which a bi-disperse mixture of large (brown) angular particles and small (white) spherical particles spontaneously forms a series of channels as they flow down a rough (turquoise) inclined plane.

Avalanches exhibit invariance over a very broad range of scales, so the mathematical models and small scale experiments that we develop in Manchester are of direct relevance to large scale natural hazards such as snow avalanches, mudslides/debris-flows and volcanic pyroclastic flows. These flows affect communities across the globe and our group is well-known for the development of depth-averaged models for understanding the flow of avalanches over/around defensive obstacles. More recently we have also been developing theories that combine frictional hysteresis and rheology to quantitatively model the formation of self-channelizing flows as well as waves that erode and deposit static material.

More information about our research, and some papers, can be found by browsing the webpages of academic staff members. Potential PhD students may email staff directly to discuss possible projects.

## Research seminars

Recommended research seminars: