The investigators will develop robust, accurate, and cost-effective methods for simulating the dynamics of suspensions of flexible fibers in a Stokesian fluid. Flexible fibers make up the micro-structure of suspensions that show strongly non-Newtonian bulk behavior, such as elasticity, shear-thinning, and normal stresses differences in shear flows. By taking a nonstandard approach to this problem, and designing a numerical algorithm based on a nonlocal slender-body approximation to hydrodynamical interactions, it is possible to simulate problems not feasible with standard methods. As this numerical method has a firm mathematical foundation, method design can be approached as a numerical analysis problem, carefully treating issues of accuracy and stability in algorithm design. Technical obstacles to be addressed are the accurate inclusion of lubrication forces when filaments approach each other, and the development and application of fast summation strategies for evalluating filament-filament interactions. The investigators will also develop especially efficient methods for the special case of rigid filaments. They will apply these methods to a set of current theoretical issues, such as the development of normal stress differences in flexible fiber suspensions, the effect on fluid mixing of storing and releasing elastic stress in the fluidic microstructure, and the large-scale dynamics of rod-like self-locomoting elements (as arises in modeling bacterial baths)
The dynamics of microscopic flexible fibers immersed in a fluid are essential to understanding many current problems arising in biology, engineering, and physics. Examples range from manufacturing processes in the pulp and paper industries to new proposed methods for mixing fluids in small devices to the locomotion of micro-organisms. These are all complicated systems whose dynamics are not well understood, in part because the large-scale dynamics of the flow can depend on the detailed nonlinear dynamics of the microscopic fibers. To help increase our understanding of such problems, the investigators are developing efficient and accurate methods for numerically simulating the dynamics of such systems with many interacting fibers. They will apply these methods to a set of current applications, drawn from the basic physics of fluids, engineering, and biology.
