Leveraging Relationships Between Confined Flows and Deformable Media

Abstract

This dissertation is the amalgam of several projects that I have undertaken over the course of my PhD. These projects present unique systems within the diverse world of soft matter, each of which 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. Our approach consists of flooding a Hele-Shaw cell textured with an array of elastic posts with oil and subsequently displacing 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 first develop a model to predict the deformation of a beam loaded by capillary pressure. Then, we turn to fluid mechanics to study the drainage problem in which one phase is evacuated from the interstice between confined posts. Finally, 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 capillary suction. We study the resultant pattern formation when inlet ports are templated. On larger scales, the interactions between neighboring flows lead to tessellations and, more generally, designs that directly correspond to a graphical transform of the initial inlet configuration. Furthermore, we model the shape of droplets trapped within the fluid matrix as viscous forces resist surface tension-driven shape minimization. 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. While recent work has investigated the trapping of fibers when suspended in low Reynolds number flows, here we study the dynamic case in an inviscid fluid. To do so, we leverage Kirchhoff theory for elastic rods to simulate a free-falling string’s impact onto and subsequent wrapping around a cylindrical obstacle. These simulations enable us to explore the probability of the string being successfully “caught” as a function of its initial conditions, for example, the height of the drop, the length of the chain, and the symmetry of the impact. When the impact point of the chain is offset from the center, we find that a major criterion for success is the synchrony of snapping, or the point at which the wavefront of impact reaches the ends of the left and right ends of the falling strands. By extracting the long-time parameters of the system we construct a state diagram to predict chain catching. Lastly, we compare our model with an experimental study that drops ball chains on cylinders of varying radii.