Spreading Problems in Fluid Mechanics

流体力学中的传播问题

• 批准号: 0104935
• 负责人: Michael Miksis
• 金额: $ 26.88万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104935&HistoricalAwards=false
• 关键词: Spreading; Problems; Fluid; Mechanics

0104935MiksisIn this proposal, it is planned to investigate both the problem of the spreading of a liquid along a solid substrate and the spreading of a liquid along a liquid interface. The Navier-Stokes equations will govern the motion of the fluids. The investigation of the spreading of a liquid along a solid substrate is interesting and difficult because of the singularities that can occur at the contact line. Spreading along a liquid interface is a challenging problem where multiple free boundaries can exist. Here, in addition to the liquid/liquid and liquid/gas boundaries, a triple junction can exist at the liquid/liquid/gas line of intersection. Predicting the dynamics of these three phase lines is one of the aims of this proposal. We will be interested in situations where the interfaces are clean and situations where surfactants are present. Mathematically we are faced with problems having coupled moving interfaces along which singularities can exits. Both asymptotic and numerical methods will be used to study these complex free boundary problems. For example, we will consider the thin film limit where the complete three-dimensional system of equations can be reduced to a coupled system of nonlinear evolution equations. We will also apply the level-set numerical method to solve the complete nonlinear system of equations.When a liquid drop is resting on a solid surface, the free boundary of the drop is characterized by the gas/liquid interface, and the line of contact between the liquid/gas/solid phases. This three-phase line is usually referred to as the contact line. It occurs whenever three phases come into contact. It is a familiar phenomena of everyday life, and can be observed when one pours oil into a frying pan or in a partially filled wine glass. It also occurs in many areas of practical interest. Examples are industrial coating processes, the transport of gas/liquid mixtures in pipes, the spreading of droplets of medication in the lungs and the spreading of liquid wastes (e.g. oil or chemicals) on the sea. The latter problem is an example of a situation where the contact line (refereed to as the triple junction in this case) occurs at the intersection of a liquid/liquid/gas interface. Even though the contact line occurs in these many areas, our understanding of it is very limited. Models are still being developed and because of the mathematical singularities associated with the behavior of the solutions in the neighborhood of the contact line, solution techniques, both analytical and numerical, need to be identified.

在该提议中，计划研究液体沿着固体基底的扩散问题和液体沿着液体界面的扩散问题。Navier-Stokes方程将控制流体的运动。 液体沿着固体基底的铺展的研究是有趣的和困难的，因为在接触线处可能发生奇异性。沿液体界面沿着扩散是一个具有挑战性的问题，其中可能存在多个自由边界。 这里，除了液体/液体和液体/气体边界之外，在液体/液体/气体相交线处可以存在三重连接。 预测这三个相线的动态是本提案的目的之一。 我们将对界面清洁的情况和存在表面活性剂的情况感兴趣。在数学上，我们面临的问题有耦合运动界面沿着的奇点可以退出。 渐近和数值方法将被用来研究这些复杂的自由边界问题。 例如，我们将考虑薄膜极限，其中完整的三维方程组可以简化为非线性演化方程的耦合系统。 当液滴静止在固体表面上时，液滴的自由边界由气/液界面和液/气/固三相之间的接触线来表征。 这种三相线通常被称为接触线。 当三相接触时就会发生这种现象。 这是日常生活中常见的现象，当一个人把油倒进煎锅或半满的酒杯时，就可以观察到。它也发生在许多具有实际意义的领域。 例如，工业涂层过程、管道中气体/液体混合物的运输、药物液滴在肺中的扩散以及液体废物（如石油或化学品）在海上的扩散。 后一个问题是接触线（在这种情况下称为三重接合点）出现在液体/液体/气体界面的交叉点处的情况的示例。 即使接触线出现在这些许多领域，我们对它的理解是非常有限的。模型仍在开发中，由于数学奇点与接触线附近的解决方案的行为，解决方案的技术，分析和数值，需要确定。