ITR: Free-Boundary Problems in Precipitative Growth

0219411 Goldstein该项目解决了数学和计算的挑战，涉及新的和困难的自由边界问题的流体流动，沉淀/结晶和蒸发的增长现象。 这些出现在各种各样的背景下，如海底的热液喷口、陆地洞穴和电化学模式的形成，人们发现复杂结构的生长是通过沉淀。 从中空的钠杆钟乳石到奇异的弯曲的螺旋岩和石灰岩洞穴中起伏的片状帷幕，再到海底几十米高的硫化铁烟囱。 尽管有多年的实证研究，这些迷人的增长形态在很大程度上是无法解释的任何定量方式。 我们将发展计算方法来研究沉淀生长现象，主要是基于边界积分和微分几何方法在表面演化的研究。 许多这些结构形成的巨大地质时间尺度造成了实验结果的匮乏，几乎没有任何实验室类似物被创造出来。 我们还将开发和探索实验模型系统，可以在可访问的时间尺度上显示这种模式的形成。在我们的实验室中发现的一个这样的系统涉及通过电沉积进行的管状生长，其中宏观管状沉积物在数十分钟内围绕从阴极逸出的氢气泡生长。理论方法将包括在大的Peclet数和耗尽层修改由于洛伦兹力的基础电动力学的研究，所有作为理解表面生长的几何规律，可以产生丰富和迷人的形态在自然界中看到的一种手段，和计算技术来研究这些法律。

0219411GoldsteinThis project addresses mathematical and computational challenges posed by growth phenomena involving novel and difficult free-boundary problems in fluid flow, precipitation/crystallization and evaporation. These appear in contexts as diverse as hydrothermal vents in the ocean floor, terrestrial caves, and electrochemical pattern formation, where one finds growth of complex structures by precipitation. These range from hollow soda-straw stalactites to fantastic curved helictites and undulating sheet-like draperies in limestone caves, to iron-sulfide chimneys tens of meters high on the ocean floor. Despite years of empirical study, these fascinating growth morphologies are largely unexplained in any quantitative manner. We will develop computational methods to study precipitative growth phenomena, based primarily on boundary-integral and differential geometric methods in the study of surface evolution. The enormous geological time scales on which many of these structures form has created a paucity of experimental results, and few if any laboratory analogs have been created. We will also develop and explore experimentally model systems that can display such pattern formation on accessible time scales. One such system, discovered in our laboratory, involves tubular growth by electrodeposition, in which macroscopic tubular deposits grow in tens of minutes around bubbles of hydrogen gas evolving off a cathode. Theoretical approaches will include the study of the underlying electrokinetics at large Peclet number and depletion layer modifications due to Lorentz forces, all as a means of understanding the geometrical laws of surface growth that can produce the rich and fascinating morphologies seen in nature, and the computational techniques to study such laws.