Hydrodynamics of bubble motion and oscillatory flows

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0072228PapageorgiouThis work addresses computationally and analytically two classes of fluid dynamics problems. The motion of bubbles through fluids containing soluble surfactants is considered first. Experiments show that even trace amounts of surfactants can increase the drag on moving bubbles significantly. Through careful modeling, asymptotic analysis and direct numerical simulations of the Navier-Stokes equations coupled with the surfactant equations in the bulk and on the interface, we address both the steady and unsteady problems and in particular evaluate the effect of surfactants on wake size and control. Such controls are desirable in enhanced interphase mass transfer systems. In parallel, we will also study a class of exact Navier-Stokes solutions which emerges in models of lubrication bearing flows. We have found that such exact solutions can describe the viscous flow between two plates when one or both of the plates move normal to themselves. When this boundary motion is periodic, chaotic solutions can emerge at sufficiently high but order one Reynolds numbers. These flows are underlying flows whose stability to wavelike disturbances is highly complicated since the baseflow is chaotic to begin with. We consider such local flows when they are embedded into finite geometries. Direct Navier-Stokes computations will be performed in many geometries and high frequency limits analyzed asymptotically, in order to predict transitions to chaos.This work studies mathematical problems in fluid dynamics leading to scientific computations and analytical problems. The models arise from applications concerned with enhancing technological processes such as materials processing in microgravity, environmental and chemical processes, biomedical applications and lubrication technologies. We use a combination of mathematical and computational tools and intensive computations to elucidate and identify regimes and mechanisms that can enhance the efficiency of the applications mentioned above. For example, we identify, using simulations, situations where flow in squeeze bearings can stay laminar rather than become chaotic. Chaotic flows can cause the equipment to fail with disastrous effects on machinery. Modeling and simulations have the advantage, over experiments, of allowing wide parameter studies and hence help identify critical experiments and design strategies. The research is valuable in both benchmarking large scale simulations as well as providing direct comparisons with experiments.