Surface Tension Driven Flows

Papageorgiou 本项目将研究几个非线性问题，涉及自由表面分离不同性质的流体，其中表面张力是重要的。我们将研究非线性演化方程所模拟的流动，这些方程在界面接触和拓扑结构发生变化时遇到有限时间奇点。一个例子是液体射流分裂成液滴。一个典型的物理问题是复合射流的核心流体包围的第二个不混溶的环形流体。在毛细不稳定性下的破裂通常产生复合球形颗粒，并且局部奇异现象的分析在设计实验以及并入和测试混合大规模模拟中都是有价值的。此外，我们将研究表面活性剂溶液（含杂质的流体相）中气泡的运动和管理。 特别重要的理论是参数范围的预测，其中气泡的浮力或热毛细运动被逮捕后，或由表面活性剂建立在后端的球形气泡延迟再动员。在许多情况下，系统参数大，奇异摄动型的渐近解将被构造和分析。 我们研究了两个相关类的基本问题，在几个关键的技术和制造的情况下遇到的。一个共同的特征是存在分离流体的界面。这些对流体如何移动有重要影响，并且这种模型的数学和计算分析在不同的制造过程以及微重力环境中正在进行的实验（例如抛物线飞行以及航天飞机）中非常有用。使用数学分析工具和现代计算方法将使我们能够确定重要的物理机制，这些机制在实验室或空间中可能是昂贵的。此外，在极端情况下（在许多过程中，这是规则而不是例外-例如液体射流分裂成液滴），使用数学分析是必要的。除了其固有的有用性，这样的数学解决方案可以用来使大规模的计算更准确和有效，以及测试现有代码的准确性。 液体射流破碎除了打印和燃料喷射系统的更传统的应用之外，还具有许多现代应用。复合射流可用于制造用于缓慢药物释放的复合颗粒、制造用于增强机械或空气动力学部件的纤维以及用环境友好的油墨和染料进行彩色印刷。 我们对气泡动力学的研究将有助于确定大规模净化系统的有效操作方式（受污染的液体通常通过使大量气泡通过它们而被净化），为安全农业喷雾的设计提供理论指导，并产生理论，可以与在太空中进行的旨在无容器微重力下生产复杂材料的实验相媲美环境.

Papageorgiou This project will study several nonlinear problems involving free surfaces separating fluids with different properties and where surface tension is important. We will study flows modelled by nonlinear evolution equations which encounter finite-time singularities as interfaces touch and a change in topology takes place. An example is the breakup of a liquid jet into droplets. A paradigm problem of physical interest is the compound jet comprised of a core fluid surrounded by a second immiscible annular fluid. Breakup under the capillary instability usually produces compound spherical particles and analysis of the local singular phenomenon is of value in both designing experiments and incorporation into and testing of hybrid large scale simulations. In addition we will study the motion and management of bubbles in surfactant solutions (fluid phases with impurities). Of particular theoretical importance is the prediction of parameter ranges where the bubble is remobilized after its bouyant or thermocapillary motion is arrested or retarded by surfactant build-up at the back end of the spherical bubble. In many cases system parameters are large and asymptotic solutions of the singular perturbation type will be constructed and analyzed. We study two related classes of fundamental problems encountered in several key technological and manufacturing situations. A common feature is the presence of interfaces separating fluids. These have important effects on how the fluids move and the mathematical and computational analysis of such models is extremely useful in diverse manufacturing processes as well as on-going experiments in microgravity environments (for instance parabolic flights as well as in the space shuttle). Using tools of mathematical analysis and modern computational methods will enable us to identify important physical regimes which would perhaps be prohibitively expensive in the laboratory or in space. In addition, the use of mathematical analy sis is imperative in extreme situations (which are more the rule rather than the exception in many processes - for instance the breakup of a liquid jet into droplets). Besides their intrinsic usefulness, such mathematical solutions can be used to make large scale computations more accurate and efficient as well as test the accuracy of existing codes. Liquid jet breakup has many modern applications in addition to the more traditional ones of printing and fuel injection systems. Compound jets are useful in the manufacture of compound particles used for slow drug release, the manufacture of fibres used to reinforce mechanical or aerodynamic components, and color printing with environmentally friendly inks and dyes. Our studies of bubble dynamics should lead to identification of efficient operational regimes in large scale purification systems (contaminated liquids are often purified by passing large numbers of gas bubbles through them), provide theoretical guidelines for the design of safe agricultural sprays, and produce theories that can be compared to experiments done in space aiming at the production of sophisticated materials in containerless microgravity environments.