Many problems of environmental significance require the effective prediction of particulate (contaminant) transport in a fluid system (which constitutes a `two-phase' fluid/particle problem). The primary focus of this project is a suspension of solid particles (dust/ash) in a viscous incompressible fluid. Most practical cases of interest have particles that are typically fractions of a millimetre in size, but still occupy a non-small fraction of the total mixture mass and exist in large numbers. The simultaneous treatment of all individual particles (and the correspondingly complicated fluid domain) is computationally impractical, a state of affairs that will remain for the foreseeable future.
Furthermore, the behaviour of a single particle cannot be solved in isolation of the other particles, owing to particle-particle interactions through the motion of the interstitial fluid, or by direct particle collisions at high concentration levels. In such cases, both phases of the mixture exchange momentum with the other, so that the fluid motion and the particle motion remain coupled together. Furthermore, the presence of bounding surfaces for the fluid mixture can have crucial consequences for the structural and temporal development of the flow and the distribution of suspended material.
This project aims to continue the development of existing macro scale models, in which both phases are treated as co-existing (coupled) continua, through a combination of analytical and computational methods.