This exploratory research will focus on using three-dimensional phase-contrast magnetic resonance imaging (PCMRI) velocimetry data to determine fluid mechanical properties in realistic flow geometries. PCMRI can measure the full three-dimensional flow field with 20 micron accuracy, giving a rich supply of information. Previous studies have used simple flows and have performed one-dimensional analysis, but no three-dimensional calculations have been attempted. The key to the extension to three dimensions is to replace the analytical methods suitable for one dimension with a computational fluid dynamics approach. A finite-element least-squares approach will be used to determine the viscosity as a function of position by solving the inverse problem associated with Stokes flow of a general viscous fluid. Since the model system contains three equations (corresponding to three momentum balances) and two unknowns (viscosity and pressure), it is over determined and will be solved in a least-squares sense. Once the viscosity-position relation is known, it will be possible to relate viscosity to the invariants of the rate-of-strain tensor without preselection of a constitutive equation. This will represent a significant advance in the ability to study flow behavior in complex environments. The project is highly exploratory in that the computational analysis method is novel, and the use of PCMRI is still relatively new. The exploratory project will focus on getting a good set of PCMRI data and classical rheological data for the same fluids for comparison. If successful, more complex systems and transient effects will be investigated. The project has significant broader impact since rheology is highly relevant to physiology (e.g. blood flow) and since better rheological methods will improve the infrastructure for engineering research and design.
