Hydrodynamics of bubble motion and oscillatory flows

[00:22 . 28]本工作从计算和分析两类流体动力学问题。首先考虑气泡在含有可溶性表面活性剂的流体中的运动。实验表明，即使是微量的表面活性剂也能显著增加运动气泡的阻力。通过仔细的建模、渐近分析和直接数值模拟Navier-Stokes方程与表面活性剂方程在体和界面上的耦合，我们解决了定常和非定常问题，特别是评估了表面活性剂对尾迹大小和控制的影响。这种控制在增强的相间传质系统中是理想的。同时，我们还将研究润滑轴承流动模型中出现的一类精确Navier-Stokes解。我们发现，当一个或两个板块垂直运动时，这种精确解可以描述两个板块之间的粘性流动。当边界运动是周期性的，混沌解可以出现在足够高但一阶的雷诺数下。这些流是底层流，由于基流一开始就是混沌的，所以对波浪形扰动的稳定性非常复杂。当这些局部流嵌入有限几何中时，我们考虑它们。直接的Navier-Stokes计算将在许多几何形状中进行，并对高频极限进行渐近分析，以预测向混沌的过渡。这项工作研究流体动力学中的数学问题，导致科学计算和分析问题。这些模型来自与增强技术过程有关的应用，例如微重力材料加工、环境和化学过程、生物医学应用和润滑技术。我们使用数学和计算工具的组合以及密集的计算来阐明和确定可以提高上述应用程序效率的制度和机制。例如，我们通过模拟确定了挤压轴承中的流动可以保持层流而不是变得混乱的情况。混沌流动会导致设备故障，对机械造成灾难性的影响。与实验相比，建模和仿真具有允许广泛参数研究的优势，因此有助于确定关键的实验和设计策略。该研究对大规模模拟的基准测试以及与实验的直接比较都有价值。

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.