Chaotic mixing of viscous fluids in time-periodic cavity flows

Chaotic mixing of viscous fluids in slow flows is pervasive in the chemical and polymer industries but poorly understood. However, relatively simple experiments provide a wealth of information regarding mixing mechanisms and indicate the need for complementary theoretical developments in dynamical systems. In this thesis, we present a versatile cavity flow apparatus, capable of producing a variety of two-dimensional velocity fields, and use it to conduct a detailed experimental study of mixing of Newtonian and viscoelastic fluids in low Reynolds number flows. Since the goal is detailed understanding, only two time-periodic cavity flows induced by tangential wall motions are considered: one continuous and the other discontinuous. In the Newtonian case, the two flows produce exponential growth of intermaterial area, as expected from chaotic flows, and a mixture of islands and chaotic regions. A procedure for identifying periodic points and determining their movements is presented as well as how to make meaningful comparisons between periodic flows. We observe that periodic points move very much as a planetary system; planets (hyperbolic points) have moons (elliptic points) with twice the period of the planets; furthermore the spatial arrangement of periodic points becomes symmetric at regular time intervals. Detailed analyses reveal complex behavior: birth, bifurcation, and collapse of islands; formation and periodic motion of coherent structures, such as islands and large scale folds. Experimental results show that the viscoelastic systems also exhibit regular and chaotic regions, and the large scale structures--folds and symmetry--in the viscoelastic systems are remarkably similar to that of the Newtonian systems. But, the islands in the viscoelastic systems are significantly larger than the Newtonian\u27s, and the size of those islands increases monotonically with increasing Deborah number