Numerical Studies of Droplets on Superhydrophobic Surfaces

The work presented here explores and utilizes numerical methods to study the phenomenon of superhydrophobic surfaces. Interest in superhydrophobic surfaces has been the source of much research over the past decade due to new applications and better techniques for theoretical and computational research. Numerical simulations have been very helpful in elucidating and understanding roughness-induced superhydrophobicity and droplet behavior. In this thesis, we first explore superhydrophobic surfaces using a Gibbs free energy model. Advancing work that has been done on the metastable Cassie and Wenzel states identified by this approach, we apply the string method to identify saddle point states and associated energy barriers. Furthermore, this model is extended to include surfaces with a hierarchical microstructure that can further increase the superhydrophobicity of the surface. Next, we present and discuss a phase field model that has been used to study wetting. We then present an analysis of the shifting parameters in the model when numerically implemented and find that a near uniform shift in the phase field results in a change in the droplet size and contact angle. We also present an analysis of spontaneous droplet shrinkage and derive values for the critical droplet size in two and three dimensions such that larger droplets will not shrink. We then present results obtained using this model to study droplets on topographically and chemically patterned surfaces. We study the associated energy landscape of a pillared surface. Additionally, we discuss the different modes of transition for each surface and examine energy barrier dependence on different problem parameters. Finally, we propose a novel, proof-of-concept surface optimization problem that evolves towards an optimal surface geometry such that droplet rolling is more energetically probable than collapsing. This is achieved by minimizing an objective functional that is constructed to minimize favorable energy barriers and increase unfavorable barriers. We present a thorough development of the numerical implementation of this method and present the results from several test cases. This work introduces a new approach to the search for optimized superhydrophobic surfaces