New numerical techniques for non-Newtonian flow simulations and their application to modelling of complex flows

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The research of the investigator is on the timely study of thefluid dynamics of non-Newtonian fluid flows. The investigatorwill examine systematically the design and development of an efficientcomputational modelling package that can handle variousmacroscopic models of complex fluids and also a wide spectrum ofphysical parameters that have been elusive for conventionalnumerical methods. In addition to general algorithmic developmentsincluding the fast solution method like the multigrid methods, theinvestigator aims to study and understand proper mathematicalmodels for a great variety of new physical phenomena arising inthe area of experimental rheology. In particular, the investigatorwill tackle an important challenge of modelling a continualoscillation of falling sphere in worm-like micellar fluid flows.In contrast to the Newtonian fluid or the polymeric fluids, thefalling sphere in a worm-like micellar fluid undergoes a continualand sustained oscillation as it falls. This part of the projectwill involve testing various macroscopic models that are relevant forthe worm-like micellar fluids and will lead to identification of the rightmathematical models for a falling sphere experiment. Theinvestigator will also address a mathematical foundation forthe so-called high Weissenberg number problem. Despite recentsignificant progress, the successful computations are stillconfined to very restrictive size of the Weissenberg number for alarge class of non-Newtonian fluid models including the well-knownOldroyd-B model. The investigator will implement the new numericalmethods for the computer simulations of highly elastic fluidflows, namely, models with high Weissenberg number to simulate andunderstand another newly observed intriguing physical phenomenon,the elastic turbulence.Fluids comprised of large macromolecules, known as non-Newtonianfluids or complex fluids, can generate many new physicalphenomenon. Examples of non-Newtonian fluids can be foundthroughout our daily lives, including molten plastics,engine oils with polymeric additives, paints, and many biologicalfluids such as egg white and blood. The design, implementation,and the use of numerical methods for the computer simulation ofsuch physical phenomena requires full grasp of non-Newtonianfluids and the results of the investigator's research areexpected to have significant applications, for example in industry.Namely, a polymer engineer could perform elaborateComputer Aided Design (CAD) studies in which the link between themolecular architecture of the raw material and the finalproperties of the product would be established, at leastqualitatively. Production problems would be predicted andpartially overcome through improved design. One could also thinkof using an on-line computational rheology model in concert withappropriate control algorithms to provide for intelligent,physics-based process control techniques. There are many moreopportunities that the investigator's research resultscould generate.