Hydrodynamics of bubble motion and oscillatory flows

这项工作涉及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表面活性剂的流体中的运动。实验表明，即使微量的表面活性剂也能显著增加运动气泡的阻力。通过对Navier-Stokes方程和界面上的表面活性剂方程的精细建模、渐近分析和直接数值模拟，我们解决了定常和非定常问题，特别是评价了表面活性剂对尾迹尺寸和控制的影响。这种控制在增强型相间传质系统中是可取的。同时，我们还将研究在润滑轴承流动模型中出现的一类精确的Navier-Stokes解。我们发现，这样的精确解可以描述当两个板中的一个或两个垂直于自身运动时，两个板之间的粘性流动。当这种边界运动是周期运动时，混沌解可以出现在足够高的一阶雷诺数。这些流动是底层流动，其对波动扰动的稳定性非常复杂，因为基流一开始就是混沌的。当它们嵌入到有限几何中时，我们考虑这种局部流。直接的Navier-Stokes计算将在许多几何结构中进行，并对高频极限进行渐近分析，以预测向混沌的转变。这项工作研究流体力学中的数学问题，导致科学计算和分析问题。这些模型来自于与增强技术过程有关的应用，如微重力中的材料处理、环境和化学过程、生物医学应用和润滑技术。我们结合使用数学和计算工具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，我们使用模拟来确定挤压轴承中的流动可以保持层流而不是变得混乱的情况。混乱的流动可能会导致设备发生故障，对机器造成灾难性影响。与实验相比，建模和仿真的优势在于允许进行广泛的参数研究，从而有助于确定关键实验和设计策略。这项研究在对大规模模拟进行基准测试以及提供与实验的直接比较方面都很有价值。

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.