| Summary: | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018. === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 211-262). === Immiscible fluid flows are ubiquitous in nature and industry, from multiphase-flow phenomena on geologic scales such as CO2 sequestration and methane venting from seafloor sediments to bubble/drop/emulsion generation in microfluidic techniques. All these flows are inherently multi-scale, from the intermolecular interactions on the nanometer scale in the vicinity of contact lines, where fluid phases meet the surrounding solid surface, to the micrometer scale of the confinement in a pore or microfluidic device, and finally to kilometer scale of the natural geologic phenomena. The multi-scale nature of immiscible fluid flows combined with the inherent disorder present in many natural or industrial systems renders description of these flows a formidable task. Here, using a combination of experimental observations and theoretical modeling we show that the interplay between confinement and contact line motion leads to novel and non-trivial consequences on the dynamics and instability of immiscible fluid fronts. We first present a theoretical model for thin-film flows on solid surfaces in the partial wetting regime and show that a self-consistent description of free energy of this system at equilibrium leads to a Cahn-Hilliard form with an effective height-dependent surface tension due to the interniolecular forces in the vicinity of the contact line. Within the framework of non-equilibrium thermodynamics, we then study the consequences of this new form of free energy on the spreading of drops and dewetting of thin films in the partial wetting regime. We show that on macroscopic scales, our model recovers the classic hydrodynamic Cox-Voinov description of moving contact lines and is consistent with experimental observations. We further show that on the microscopic scale our model is consistent with the molecular kinetic theory, therefore bridging the gap between the two descriptions across the scales. We finally show that our model captures the dynamics of nanometric dewetting thin films in spinodal and nucleation regimes as well as their long-time coarsening behavior and brings the theoretical predictions closer to the previous experimental observations. We then revisit the classic Taylor-Bretherton problem in the partial wetting regime, where air displaces a highly viscous liquid in a capillary tube. In contrast with the classic results for complete wetting, we show that the presence of a moving contact line induces a wetting transition at a critical capillary number that is contact angle dependent. Beyond wetting transition, a film of the defending liquid coats the tube walls. The entrained liquid film immediately starts receding along the tube wall, forming a growing dewetting rim behind the contact line, which finally leads to the breakup of the bubble. The bubble pinch-off is an example of singularity formation, where separation of length scales close to the point of singularity are expected to lead to self-similar and universal dynamics. We show that the breakup of a bubble confined in a capillary tube undergoes a sequence of two distinct self-similar regimes even though the balance remains between viscous and surface-tension forces. While the breakup of a bubble in an unbounded reservoir is known to be non-universal, we demonstrate that the presence of the early-time self-similar regime in a confined system effectively erases the system's memory and restores universality to bubble breakup. We then revisit the classic Saffinan-Taylor instability in the imbibition regime, where a more wetting and less viscous liquid displaces a less wetting and more viscous liquid in a radial Hele-Shaw cell (two plates separated by a small gap). We show that the wetting liquid invades the cell in the form of a thin-film front, which becomes unstable and leads to a viscous fingering pattern. To gain an understanding of the front dynamics, we develop a thin-film model, which predicts the base state of the invading thin films to be an undercompressive shock, which has previously been shown to lead to stable fronts. Using linear stability analysis and nonlinear simulations, we show that consistent with our experimental observations the thin film front in a Hele-Shaw cell is unstable. The instability here is due to the pressure coupling between the two fluid flows in a confined domain. We further show that the scaling of the wavelength of instability in thin-film front is different from the Saffman-Taylor instability, suggesting that it belongs to a new pattern formation class. In the final part of this thesis, we explore how the interplay between wetting and disorder influences the pattern formation. We introduce disorder into the Hele-Shaw system by making one of the surfaces randomly rough. In particular, we show that in the imbibition regime aside from the primary thin films that we observed in smooth cells, secondary thin films of the scale of roughness appear. These secondary films wick into the crevices of the rough surface with a diffusive dynamics and change the effective wettability of the medium. We therefore show that disorder on the micro-scale affects the macroscopic morphology of unstable fluid fronts. === by Amir Alizadeh Pahlavan. === Ph. D.
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