Collaborative Research: Self-Assembly and Aggregate Formation in Stratified Fluids

我们世界的大气、湖泊和海洋通常涉及密度变化，较轻的流体层位于较重的流体层之上。在这个项目中，我们正在探索一种我们已经发现的新机制，通过这种机制，悬浮在这种分层系统中的粒子可以相互吸引并自组装，形成大的圆盘状簇。这种吸引的机制涉及到颗粒本身在层状流体中产生的流体流动。这种群集在湖泊和海洋中无处不在，它们可以为各种生物提供食物来源，或导致污染颗粒的浓度。这些星团的起源很可能就在这个奖项正在探索的新的聚集形成机制中。研究生将参与该项目。具体来说，该奖项将对分层环境中新发现的粒子之间的流体动力学相互作用进行理论、数值和实验研究。北卡罗来纳大学联合流体实验室的pi最近的实验工作表明，悬浮在密度分层环境中的被动颗粒通过自诱导流动相互作用，这种流动可能导致随着时间的推移彼此接近，直到接触。由于这种新发现的吸引机制，许多粒子的集合倾向于聚集和自组装成大规模的二维结构。该项目旨在通过新颖的渐近方法、数值模拟和仔细的实验，首次在自然界中表征这种新发现的相互作用效应。本研究将探索扩散、平流和几何（通过物理边界条件）之间复杂的相互作用，以诱导新的集体现象。这需要开发新的计算、渐近和实验方法，从通过粘性应力张量耦合到悬浮在分层环境中的粒子的母Navier-Stokes方程中提取定量预测。作为这一建议的一部分，新的渐近方法也将被证明对流体动力学和势理论中更广泛的问题有用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The atmospheres, lakes, and oceans of our world typically involve density variability, with layers of lighter fluid sitting on top of heavier fluid. In this project, we are exploring a novel mechanism we have discovered through which particles suspended within such layered systems are seen to attract each other and self-assemble, forming large disc like clusters. The mechanism for this attraction involves fluid flows which the particles themselves create from being in a layered fluid. Such clusters occur ubiquitously in lakes and oceans, where they can provide food sources for a variety of organisms, or result in concentrations of polluting particles. The origins of these clusters may well lie within this new aggregate formation mechanism under exploration within this award. Graduate students will be involved in the project. Specifically, the award will undertake a combined theoretical, numerical, and experimental investigation of a newly discovered hydrodynamic interaction between particles in a stratified ambient environment. Recent experimental work by the PIs at the UNC Joint Fluids Lab have demonstrated that passive particles suspended in a density-stratified environment interact through self-induced flows which can result in approaching one and another over time until coming into contact. Collections of many particles tend to aggregate and self-assemble into large-scale 2D structures due to this newly identified attraction mechanism. The project aims to characterize this newly-identified interaction effect in nature for the first time, through novel asymptotic methods, numerical simulations, and careful experimentation. The research will explore the complex interplay between diffusion, advection, and geometry (through physical boundary conditions) in inducing new collective phenomena. This requires developing novel computational, asymptotic, and experimental methods for extracting quantitative predictions from the parent Navier-Stokes equations coupled through the viscous stress tensor to particles suspended in stratified environments. The new asymptotic methods developed as part of this proposal will also prove useful for a wider range of problems in fluid dynamics and potential theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.