This dissertation is the amalgam of several projects that I have undertaken over the course of my PhD, wherein I aim to elucidate different aspects of the complex interplay between fluid mechanics, solid mechanics, materials science, and manufacturing.

First, I will discuss how confined capillary flows interact with flexible obstacles. We food a Hele-Shaw cell textured with an array of elastic posts with oil and subsequently displace the defending fluid with an immiscible water phase. As water invades the cell and displaces the oil, the presence of a mobile contact line deforms the elastic medium due to the strength of interfacial tension relative to bending stiffness. We couple the elastic and fluid mechanical problems to predict the total drainage across a textured channel as a function of flow rate, geometry, and elastocapillary effects, all of which lead to entrapped volumes of oil between beams.

I then leverage capillarity as a fabrication tool in the discussion of a method for designing multi-functional thin films. In this system, fluid is spontaneously drawn into a Hele-Shaw cell due to surface tension-driven suction. On larger scales, the interaction between neighboring flows lead to tessellations and, more generally, designs that directly correspond to a graphical transform of the initial inlet configuration. Upon freezing the trapped fluid, typically via a curing agent, the film can be then removed from the cell for use. We introduce several modes of complexity, including methods for the fabrication of composite materials with localized mechanical properties.

Lastly, I discuss the mechanics of flexible chains impacting a rigid body. To do so, we leverage Kirchhoff theory for elastic rods to simulate a free-falling string’s impact onto and subsequent wrapping around a cylinder. When the impact point of the chain is offset from the center, we find that a major criterion for success is the synchrony in dynamics between the two strands straddling the pole. By extracting the long-time parameters of both numerical simulations and experiments, we construct a state diagram to predict a successful “catch” based on the initial conditions of the system