The research of the investigator is on the timely study of the fluid dynamics of non-Newtonian fluid flows. The investigator will examine systematically the design and development of an efficient computational modelling package that can handle various macroscopic models of complex fluids and also a wide spectrum of physical parameters that have been elusive for conventional numerical methods. In addition to general algorithmic developments including the fast solution method like the multigrid methods, the investigator aims to study and understand proper mathematical models for a great variety of new physical phenomena arising in the area of experimental rheology. In particular, the investigator will tackle an important challenge of modelling a continual oscillation of falling sphere in worm-like micellar fluid flows. In contrast to the Newtonian fluid or the polymeric fluids, the falling sphere in a worm-like micellar fluid undergoes a continual and sustained oscillation as it falls. This part of the project will involve testing various macroscopic models that are relevant for the worm-like micellar fluids and will lead to identification of the right mathematical models for a falling sphere experiment. The investigator will also address a mathematical foundation for the so-called high Weissenberg number problem. Despite recent significant progress, the successful computations are still confined to very restrictive size of the Weissenberg number for a large class of non-Newtonian fluid models including the well-known Oldroyd-B model. The investigator will implement the new numerical methods for the computer simulations of highly elastic fluid flows, namely, models with high Weissenberg number to simulate and understand another newly observed intriguing physical phenomenon, the elastic turbulence.
Fluids comprised of large macromolecules, known as non-Newtonian fluids or complex fluids, can generate many new physical phenomenon. Examples of non-Newtonian fluids can be found throughout our daily lives, including molten plastics, engine oils with polymeric additives, paints, and many biological fluids such as egg white and blood. The design, implementation, and the use of numerical methods for the computer simulation of such physical phenomena requires full grasp of non-Newtonian fluids and the results of the investigator's research are expected to have significant applications, for example in industry. Namely, a polymer engineer could perform elaborate Computer Aided Design (CAD) studies in which the link between the molecular architecture of the raw material and the final properties of the product would be established, at least qualitatively. Production problems would be predicted and partially overcome through improved design. One could also think of using an on-line computational rheology model in concert with appropriate control algorithms to provide for intelligent, physics-based process control techniques. There are many more opportunities that the investigator's research results could generate.
