Rayleigh-Taylor Instability, Non-Newtonian Rheology, and Chain Of Bubbles in Polymer Solutions

摘要CTS-0325743I。瑞利-泰勒不稳定性、非牛顿流变学和聚合物溶液中的气泡链液体中气泡的运动是流体力学的主要领域之一。达芬奇已经对此进行了研究，他注意到了上升气泡的曲折运动，这在长长的柱子里相对容易观察到。现有的知识体系，甚至它的语言内涵，都只是将气泡视为一个离散的、彼此分离的单位。牛顿液体中空气的连续喷流通常通过射流的Rayleigh-Taylor不稳定性产生气泡。在PI最近的工作中发现，在浓缩的聚合物溶液中，气泡可以形成一种定性的新结构。聚合物溶液的弹性性质可以阻止Rayleigh-Taylor不稳定性的发展。结果，不是单个泡沫，而是形成了一条长链的气泡。链条上的气泡非常稳定，缓慢上升，由细颈连接；整个结构类似于珠子，或气泡式“香肠”；见下一页图1、2。聚合物溶液的流变性是非常有趣的，需要仔细研究。到目前为止，甚至对这种不寻常而有趣的现象的一般理解也是不完整的。提出了许多关于气泡链的基本问题，但还没有对这一现象进行建模。拟议的研究将致力于气泡链动力学的研究和建模，并将集中在几个主要问题上：形成气泡链所用聚合物的流变学，形成气泡链所需的条件的实验阐明，各种条件下空气射流的稳定性分析，以及现象的强非线性建模。

AbstractCTS-0325743I. Kliakhandler, Michigan Technological UniversityRayleigh-Tayler Instability, Non-Newtonian Rheology, and Chain of Bubbles in Polymer SolutionsThe motion of bubbles in a liquid is one of the major fields in hydrodynamics. It was studied already by Leonardo da Vinci, who noticed sinuous movement of rising bubbles, which is relatively easy to observe in long columns. The available body of knowledge and even its language connotation consider bubbles only as a discrete, detached from each other, units. The continuous jet of air in Newtonian liquids produces usual bubbling through Rayleigh-Taylor instability of the jet.In the recent work by PI it was found that in concentrated polymer solutions bubbles may form a qualitatively new structures. The development of Rayleigh-Taylor instability may be arrested by elastic properties of the polymer solutions. As a result, instead of individual bubbles, a long chain of bubbles is formed. The bubbles in the chain are very stable, slowly rising, connected by thin necks; the whole structure is similar to beads, or bubble "sausage"; see figures 1, 2 on the next pages. The rheological properties of polymeric solutions where it is possible to create the chain of bubble are quite interesting and call for their careful study.So far, even the general understanding of this unusual and interesting phenomenon is incomplete. Many basic questions about the chain of bubbles arise; no modeling of the phenomenon has yet been done.The proposed research will be devoted to the study and modeling of chain of bubbles dynamics, and will concentrate on the few main issues; rheology of polymers used in the formation of the chain, experimental elucidation of conditions necessary for the creation of chain of bubbles, analysis of stability of the air jet for various conditions, and strongly nonlinear modeling of the phenomenon.