Novel Model for Precipitation Reactions in Microfluidic Devices or, a Unified Framework for Coupling Phase-Change Chemistry and Fluid-Structure Interaction in Low Reynolds Number Flows

Chemical processes within flows are ubiquitous. There exists an important class of reactions that result in a phase change from liquid to solid: precipitation reactions. Inspired by recent microfluidic experiments, this dissertation develops a unified mathematical framework for handling such reactions occurring within a slow-moving fluid flow. A key challenge for precipitate reactions is that, in general, the location of the developed solid is unknown \emph{a priori}. To model this situation, we use a multiphase framework with fluid and solid phases; the aqueous chemicals exist as scalar fields that react within the fluid to induce phase change. We conduct several analytic and numerical validation studies to verify that the model exhibits desired fluid–structure behaviors without requiring interface boundary conditions. To demonstrate the functionality of this framework, we conduct full-scale simulations of two scientific applications: a microfluidic reaction experiment as well as a geophysical study of sinkhole formation. The results of this dissertation are (1) a rigorous derivation of a model framework that conserves mass and incorporates fluid-structure interaction, and (2) numerical methods for solving the full PDE system, which have been implemented in open-source software. The framework can be applied to precipitate reactions where the precipitate greatly affects the surrounding flow, a situation appearing in many laboratory and geophysical contexts including the hydrothermal vent theory for the origin of life. More generally, this model can be used to address low Reynolds number fluid–structure interaction problems that feature the dynamic generation of structures.