Chaotic mixing of non-Newtonian fluids in time-periodic flow

The objective of this dissertation is to determine the effect of non-Newtonian fluid behavior on chaotic mixing when the kinematics first begin to deviate from Newtonian flow. This study is important in the context of industrial applications since it is likely that most mixing equipment will possess chaotic fluid element trajectories, and Newtonian kinematics are often assumed in the design of mixing processes. Computations are done for a power-law viscosity fluid, and a comparative computational and experimental study is performed for a constant viscosity elastic fluid. The non-Newtonian effects are investigated in a two-dimensional, time-periodic flow between eccentric cylinders. The mixing in the chaotic flow is analyzed by examining the asymptotic coverage of a passive tracer, character and location of periodic points, and the rate of stretching of fluid elements.; Small variations in the velocity field associated with non-Newtonian kinematics produce large effects in the chaotic advection of a passive tracer. The rate of stretching remains exponential since the flow is chaotic, but with a longer time constant as the non-Newtonian effect increases. In many cases, the non-Newtonian kinematics result in the birth of new periodic islands causing a decrease in the asymptotic coverage of the tracer and a decrease in the rate of stretching in the neighborhood of the island. Exceptions to these observations are also present: in one case the rate of stretching increases, and in some cases the asymptotic coverage of the tracer is not affected or even increases. More importantly, suitable manipulation of operating conditions can produce non-Newtonian flows which mix as well as Newtonian flows. The agreement between the experimental and computed dye-structures indicates that investigation of chaotic advection using a solution based on a discretized velocity field is possible with an acceptable amount of error. Since significant effects are observed with less than a five percent difference in the kinematics, the assumption of Newtonian kinematics can lead to large errors in the design and operation of process mixing equipment.