Most of us are familiar with granular materials from pouring our cereal into a bowl at breakfast! Yet despite their great abundance our understanding of their behaviour is still relatively basic and there are many exciting problems for applied mathematicians to tackle which have important applications in industry and the natural environment.
Research into granular materials in Manchester is focussed on the dense regime in which the grains behave either as a solid or a liquid. Most problems of practical interest involve regions of both behaviour. For example, in the rotating drum and the stratification pattern animations (see right hand sidebar) there is a large solid body of grains with a thin avalanche at the free-surface where the deformation is concentrated. The constitutive description of granular materials is still open and well-posed plasticity theories are being developed to describe slow flows in silos and hoppers.
The flow of avalanches over complex natural terrain is of importance for understanding the dynamics of hazardous geophysical flows (e.g. snow avalanches, debris-flows, pyroclastic flows and lahars) for planning and risk assessment in alpine, mountainous and volcanic regions. Recent work has focussed on how avalanches flow past deflecting dams and obstacles, which can be used to steer avalanches into less harmful areas and slow them down. These flows generate shock waves, expansion fans and particle free regions which can be readily observed in small scale experiments and require high resolution numerical methods to capture the discontinuous solutions. Hyperbolic problems of this kind also arise in two phase flows of grains and air, which are or importance in pneumatic conveying.
Avalanches are very effective at sorting particles by size. New theories for particle-size segregation are being developed which allow the evolving distribution within the avalanche to be computed. Large particles tend to rise to the surface and smaller grains percolate preferentially downwards to create inversely-graded layers. These are of fundamental importance in the formation of stratified layers, Catherine wheels and other complex patterns. In some situations the segregation can have a direct feedback on the bulk velocity of the avalanche, which gives rise to the spontaneous formation of coarse grained lateral levees that channelize the flow and enhance the run-out distance of hazardous geophysical mass flows.