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Item Numerical methods for simulating droplet dynamics in microfluidic devices(Montana State University - Bozeman, College of Engineering, 2016) Cauble, Eric Charles; Chairperson, Graduate Committee: Mark OwkesProton exchange membrane (PEM) fuel cells are of beneficial interest due to their capability of producing clean energy with zero emissions. An important design challenge hindering the performance of fuel cells is controlling water removal to maintain a hydrated membrane while avoiding excess water that may lead to channel blockage. Fuel cell water management requires a detailed knowledge of multiphase flow dynamics within microchannels. Direct observation of these gas-liquid flows is difficult due to the small scale and viewing obstructions of the channels within the fuel cell. Instead, this work uses a computational fluid dynamics (CFD) approach to compute the dynamics and formation of droplets in fuel cell channels by imposing contact angles and computing the curvature at the interface along the wall boundary. This thesis focuses on developing and implementing two methods to assist in computing the dynamical behavior of droplets in PEM fuel cells. The contact angle method leverages a conservative volume-of-fluid (VOF) formulation coupled with novel methodologies to impose and track dynamic contact angles. In particular, it is shown that variation of the contact hysteresis angle influences the wetting properties of the droplet and significantly impacts water transport throughout a fuel cell channel. The proposed curvature scheme employs the method of least squares to fit an implicit polynomial function to a cloud of points created at the interface. The points are constructed from the volume of fluid (VOF) representation of the phase interface and the curvature is computed explicitly from this best fit polynomial function. It is shown that the new curvature method is second-order accurate and can be used to compute the curvature of a droplet along a boundary with prescribed contact angles. This thesis presents details of the numerical approaches used to implement contact angles and to compute the curvature based on novel methods. The developed numerical methods are then used to simulate a droplet contained in a channel with an incoming gas flow and discuss the results relevant to water management in PEM fuel cells.