Fronts and filaments : methods for tracking and predicting the dynamical effects of advection on excitable reactions

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2019.In advection-reaction-diffusion (ARD) systems, the spreading of a reactive scalar can be significantly influenced by the flow field in which it grows. These systems, which range from chemical reactions to ocean plankton populations, become very difficult to understand, predict, and control, because of the complex interaction between fluid flow and nonlinear chemical reactions. Greater understanding of these systems can be obtained through models that isolate the most important behaviors. I present results which model ARD systems as reaction fronts, or stretched laments carried by the flow. I perform experiments and analysis on the excitable BelousovZhabotinsky (BZ) reaction in a nearly two dimensional system with flows both steady and unsteady in time. I create and utilize a reaction front tracking tool, and use Lagrangian methods to understand the importance of the flow gradient to reaction growth. To start, I consider the motion of the reaction fronts that lie at boundaries between reacted and unreacted which can quantify spreading. I present an algorithm to measure local speed and thickness of reaction fronts. These quantities can in turn measure diffusivity and reaction rate. The algorithm is then expanded to measure front speed in the presence of flow, and test reaction front models. After identifying that the chemical speed appears to depend on flow, I show that this is due to depth shear through the thin experiment layer, and I suggest improvements to make future experiments more two dimensional. After that I investigate how BZ tends to gather at the same value of the Lagrangian stretching in both laminar and chaotic, time-varying flows. I hypothesize that the optimal stretching is due to moderate stretching promoting reaction, but large stretching causing blowout. This optimal stretching value is dependent on the reaction, but not fluid flow. I investigate the causes of this by considering three effects of the flow gradient: perimeter change, thickness change, and lament stretching. My results offer new avenues to research ARD systems, and new insights to allow models to more closely match ARD systems, especially in time dependent flows