UC Santa Barbara

Surfactants —molecules with a tendency to adsorb to interfaces between fluids— have been known to critically affect the behavior of multiphase flows for decades. They slow the rise of air bubbles in water, increase the thickness of liquid coating films, and trigger the motion of the so-called “tears” in a glass of wine, to name a few examples. In recent years, it has been shown that these substances also play a central role in the performance of superhydrophobic surfaces (SHS), textures designed to reduce friction by retaining a layer of air while immersed in water. Indeed, the presence of even small traces of surfactants, unavoidable not only in the environment but also in nominally clean conditions, inevitably leads to adverse Marangoni forces that substantially inhibit drag reduction. Quantifying and predicting these effects would have far-reaching technological implications in energy efficiency, yet it is extremely challenging due to the underlying mathematical complexity and the difficulty in the detection and control of surfactants in experiments.

The first part of this dissertation introduces two numerical methods: one is designed for the surfactant transport problem in deforming geometries, while the other solves the incompressible Navier-Stokes equations for the fluid flow in parallel multi-processor environments. The computational framework is based on a level-set representation of moving interfaces and the utilization of adaptive Cartesian grids, providing a unique tool to efficiently tackle the full problem in relatively general scenarios. We then describe the first theoretical model for laminar flows over superhydrophobic surfaces inclusive of surfactant, based on simplifying physical assumptions that apply in the specific case of two-dimensional SHS gratings. In practice, however, flows over realistic SHS textures have key three-dimensional features. To overcome this limitation, a new model for three-dimensional gratings is presented, allowing for the first time to compare theoretical predictions with experimental measurements, which we perform using confocal microscopy in microfluidic devices. Additionally, this thesis presents (i) a striking experimental demonstration of maze-solving by surfactants in the context of free-surface flows, and (ii) a concise theoretical study on the sunlight inactivation of the SARS-CoV-2 virus, with potential applications in UV disinfection technology.