Interface-driven fluid dynamics exists all around us and presents very interesting and challenging fluid dynamic problems. In this work, we investigate three such phenomena: self-propulsion of bubbles and the related corner flow, coalescence of droplets, and evaporation of thin films with free surface temperature variations.;We begin by investigating the corner flows relevant to self-propulsion of bubbles. In Chapter 2, we experimentally investigate the pressure drop which occurs in a rectangular microchannel with and without surfactants. We find that, contrary to previous results, when surfactants are added to such systems, the pressure drop across bubbles becomes dependent on their lengths, and the average velocity of the liquid phase greatly exceeds the velocity of the bubble---we refer to this phenomenon as corner flow. In Chapter 3, we continue our investigation of the corner flow to create a physical model of the dynamics based on Marangoni-driven bubble migration and lubrication flows. In Chapter 4, we apply corner flow to generate self-propulsion of bubbles in closed wedge-shaped geometries.;Next, in Chapter 5, we study a different phenomenon of droplet coalescence in a converging geometry. When moving through converging channels, as droplets begin to separate, they are prone to coalesce. Through domain perturbation and lubrication analysis, we investigate the local deformations of the droplets that facilitate contact.;Finally, again through domain perturbation, in Chapter 6, we examine the dynamics within a thin film of liquid on a uniformly heated or cooled textured substrate as well as the evolution of the generated surface deformations due to evaporation.;We approach these problems through simple experiments and various approximation techniques to arrive at physical models. Nonetheless, our resultant physical models are generally in good agreement with previously known experimental or numerical results and present novel, simplified approaches to these complicated dynamical problems.
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