An important class of non-Newtonian fluids are those composed of two or more different phases. These include: suspensions of solid or deformable particles in either Newtonian or non-Newtonian fluids; polymer foams; and
phase separated polymer blends. For example, glass fibres are often added to injection moulded plastics to reduce cost and to improve the mechanical or thermal properties of the finished product. Small spheres are often suspended in a fluid in order to transport, for example, pharmaceutical powders around processing plants; and many food-stuffs and skin-care products are formed from oil-in-water emulsions. While the motion of single particles in Newtonian fluids is well understood, suspensions of large numbers of particles that interact through the fluid remain challenging, both analytically and numerically. A complicating factor is that in many application one or both of the phases may be a strongly viscoelastic fluid such as polymer melt.
Research in the Polymers and Industrial Mathematics group focuses on the mechanics of polymers and other complex fluids, free-surface flows and inverse problems. We are also concerned with the development and implementation of novel numerical and computational solution methods for both ordinary and partial differential equations, from fundamental aspects (the theoretical analysis of numerical methods) to problem-specific aspects (the design, development and practical implementation of novel algorithms). Within the polymer area, we conduct fundamental research into fluids that have a complex microstructure, such as polymer melts and solutions and colloidal dispersions. Our research combines methods from molecular physics and continuum mechanics to develop multiscale models that link together the microscale motion of individual molecules to the flow behaviour of the bulk material. An important class of industrial flow problems are those involving free surfaces, such as in inkjet printing, film coating and bubble growth in polymeric foams. We also work on a diverse range of inverse problems in heat transfer, porous media, fluid and solid mechanics, acoustics and medicine. This is a strongly interdisciplinary subject and much of our research involves collaborations with independent research groups in science and engineering departments both at Leeds and worldwide, as well as with industry.
The project is eligible for School of Mathematics Doctoral Training Grant funding - please contact us for more information.