RUI: The effects of three-dimensional fluid flows on front propagation

流体在许多物理、化学、地质、天体物理和生物过程的行为中起着至关重要的作用。在过去的十年里，PI的研究小组在简单的二维（2D）流体流动中对反应锋的行为进行了大量的实验。这些实验的结果导致了一种理论的发展，该理论预测流动中存在“燃烧不变流形”（bim），这些流形就像阻挡反应锋面运动的无形屏障。由这笔拨款资助的实验将把这些研究扩展到三维（3D）流动。特别是，我们将探讨三维流动中的bim是否仍然作为阻碍反应锋运动的障碍。最终，这些实验可能会让我们更好地理解海洋中浮游生物的大量繁殖；更有效的化学反应器，特别是在微型装置中；等离子体流中的过程可能导致经济的核聚变发电；细胞尺度流动在生物过程中的作用，包括胚胎发育中的形态发生；超新星爆炸的爆炸；以及人口流动对疾病传播的影响。这是一项本科院校研究（RUI）资助；因此，所有这些研究都将由本科生完成，他们将在研究的各个方面发挥积极作用，包括实验设计，设备的构建和测试，数据收集和分析，以及结果的发表和展示。对于大多数学生来说，这将是他们第一次真正的研究经历，并将在他们作为科学家的发展中发挥重要作用。技术摘要：本基金将资助研究三维（3D）流体流动中反应前沿行为的实验。这是一个在物理、化学、生物和地质领域广泛应用的前沿生产系统的问题。PI在二维流体中做过类似的实验（都是本科生），经验丰富。这些实验的结果导致了一种理论的发展，该理论确定了流动中的“燃烧不变流形”（bim），这些流形充当了阻挡反应前沿的屏障。拟议的实验将把这些研究扩展到由嵌套的漩涡链组成的三维流动。反应前沿将由可激发的Belousov-Zhabotinsky化学反应产生，该化学反应已被证明具有与广泛的前沿产生系统相似的动力学。本研究解决的问题将包括：(a) BIM理论是否可以扩展到完整的3D问题；(b)在三维流动中是否仍然存在类似于二维流动中bim的障碍物阻碍锋面传播；(c)三维流动中的反应障碍能否被弱时间依赖性破坏。这是一项本科院校研究（RUI）资助；因此，所有这些研究都将由本科生完成，他们将在研究的各个方面发挥积极作用，包括实验设计，构建和测试仪器；数据收集和分析；以及结果的发表和展示。对于大多数学生来说，这将是他们第一次真正的研究经历，并将在他们作为科学家的发展中发挥重要作用。

Non-Technical abstractFluid flows play a crucial role in the behavior of many physical, chemical, geological, astrophysical and biological processes. During the past ten years, the PI's research group has done numerous experiments on the behavior of reaction fronts in simple, two-dimensional (2D) fluid flows. Results from those experiments have led to development of a theory that predicts the existence of "burning invariant manifolds" (BIMs) in the flow that act as invisible barriers that block the motion of reaction fronts. The experiments funded by this grant will extend those studies to three-dimensional (3D) flows. In particular, we will explore whether BIMs in 3D flows still act as barriers that impede the motion of reaction fronts. Ultimately, these experiments may lead to a better understanding of blooms of plankton in the oceans; more efficient chemical reactors, especially in micro-scale devices; processes in plasma flows that might lead to economical fusion-based electrical generation; the role of cellular-scale flows in biological processes including morphogenesis in a developing embryo; detonation of supernova explosions; and the effects of moving populations on the spreading of a disease. This is an RUI (Research at Undergraduate Institutions) grant; consequently, all of this research will be done with undergraduate students who will play an active role in all aspects of the studies, including experimental design, building and testing of the apparatus, data collection and analysis, and publication and presentation of the results. These will be the first real research experiences for most of these students, and will play an important role in their development as scientists.Technical AbstractThis grant will fund experiments that will study the behavior of reaction fronts in three-dimensional (3D) fluid flows. This is an issue with applications to a wide range of front-producing systems in physics, chemistry, biology and geology. The PI has extensive experience doing similar experiments (all with undergraduates) in 2D flows. Results from those experiments led to the development of a theory that identifies "burning invariant manifolds" (BIMs) in the flow that act as barriers that block reaction fronts. The proposed experiments will extend those studies to 3D flows composed of nested chains of vortices. Reaction fronts will be produced by the excitable Belousov-Zhabotinsky chemical reaction which has been shown to exhibit dynamics similar to those for a wide range of front-producing systems. Questions addressed by this research will include: (a) whether the BIM theory can be extended to the full 3D problem; (b) whether barriers similar to the BIMs in the 2D flows still exist to front propagation in 3D flows; and (c) whether reaction barriers in 3D flows can be destroyed by weak time dependence. This is an RUI (Research at Undergraduate Institutions) grant; consequently, all of this research will be done with undergraduate students who will play an active role in all aspects of the studies, including experimental design, building and testing of the apparatus; data collection and analysis; and publication and presentation of the results. These will be the first real research experiences for most of these students, and will play an important role in their development as scientists.