Polymer Dynamics and Rheology (Polymers and Industrial Mathematics)
Polymers are long, chain-like molecules made from joining together lots of small molecules (or monomers). Sometimes polymer molecules are linear, but very often, notably in the case of Low Density Polyethylene (LDPE) used to make plastic bottles, they include many branches. During the manufacture of polymeric (or plastic) materials and commodities, liquids containing polymers are subjected to flow. Polymer molecules behave like springs, and become stretched by the flow, giving rise to the strongly elastic behaviour of polymeric fluids. The study of the dynamics of polymer molecules, and how this depends on their size and shape, is crucial for the understanding of flow of polymeric fluids. If polymer molecules overlap sufficiently, then they get tangled up (like spaghetti) so that they are constrained in their movement. The 'tube model' for entangled polymers provides a conceptual framework for understanding the constrained motion, and for making mathematical predictions about the polymers' response to flow. Branch points in the polymer molecules provide additional obstacles to the motion of entangled polymers, so that the distribution of branch points in polymer molecules is a critical factor in determining flow properties.
Current and future research in this area spans a number of topics, including:
(i) examining how commercial reactions affect the distribution of sizes and shapes of branched polymers,
(ii) fundamental studies of the tube model, in relation to computational schemes such as atomistic simulation,
(iii) multiple time and spatial scales for diffusion in branched polymer melts,
(iv) constitutive equations for flow of polymer melts, in relation to the molecular architectures,
(v) other direct measurements of polymer motion, such as radiation scattering, and
(vi) processing flows of polymer melts.
Polymers and Industrial Mathematics
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.