Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

Solid-State Compatibilization of Immiscible Polymer Blends: Cryogenic Milling and Solid-State Shear Pulverization

The blending of common polymers allows for the rapid and facile synthesis of new materials with highly tunable properties at a fraction of the costs of new monomer development and synthesis. Most blends of polymers, however, are completely immiscible and separate into distinct phases with minimal phase interaction, severelydegrading the performance of the material. Cross-phase interactions and property enhancement can be achieved with these blends through reactive processing or compatibilizer addition. A new class of blend compatibilization relies on the mechanochemical reactions between polymer chains via solid-state, high energy processing. Two contrasting mechanochemical processing techniques are explored in this thesis: cryogenic milling and solid-state shear pulverization (SSSP). Cryogenic milling is a batch process where a milling rod rapidly impacts the blend sample while submerged within a bath of liquid nitrogen. In contrast, SSSP is a continuous process where blend components are subjected to high shear and compressive forces while progressing down a chilled twin-screw barrel. In the cryogenic milling study, through the application of a synthesized labeledpolymer, in situ formation of copolymers was observed for the first time. The microstructures of polystyrene/high-density polyethylene (PS/HDPE) blends fabricated via cryomilling followed by intimate melt-state mixing and static annealing were found to be morphologically stable over time. PS/HDPE blends fabricated via SSSP also showed compatibilization by way of ideal blend morphology through growth mechanisms with slightly different behavior compared to the cryomilled blends. The new Bucknell University SSSP instrument was carefully analyzed and optimized to produce compatibilized polymer blends through a full-factorial experiment. Finally, blends of varying levels of compatibilization were subjected to common material tests to determine alternative means of measuring and quantifying compatibilization,