Nonlinear Dynamics of Confined Interfaces: Beyond Linear Analysis and Towards Control

从流体对磁场的反应，到从地球上提取石油，再到消费设备电池中的电极操作，必须对界面的运动进行建模、分析和控制，以实现所需的流动模式，提高能量回收的效率，或确保安全。该奖项将支持基础科学研究，这些研究将有助于对流体之间界面动力学的新知识和理解。这项研究计划的成果可能成为精确控制流体扩散和受限层的新方法的基石，这是推进增材制造（也称为3D打印）工艺所必需的，也是利用液滴运动（封闭流体-流体界面）进行化学诊断的芯片实验室设备所需要的。因此，该奖项将促进科学领域的进步，并有可能为有利于美国经济和社会的新技术背后的科学做出贡献，从而促进国家繁荣。此外，该研究将在PI建立的指导文化和多样性努力中吸引本科生，研究生和博士后研究人员，以倡导科学卓越并扩大该研究领域的参与。流体界面并不总是以有序的方式移动和变形。它们可能是不稳定的，它们的形状从系统的输入来看是不可预测的。目前对这种不稳定性的研究主要集中在不可预测行为的起始阶段，即所谓的线性状态。同时，动力学受到多种物理效应的影响，这些物理效应的耦合影响相对来说尚未被探索。为了解决这些知识差距，基础研究将推导数学模型并构建数值方法来理解界面的后期（称为非线性）时间演化，最终产生操纵不稳定性的方法。具体而言，研究团队将：(i)推导出非标准Hele-Shaw几何中非混相流体-流体界面动力学的尖锐界面数学模型，包括由于域边界运动和通过磁场的非侵入性作用力引起的多物理场相互作用；（ii）基于涡片法构建拉格朗日锐界面跟踪的有效数值方法，以分析界面的非线性演化，包括其承受永久行激励（孤子）的能力；（iii）利用(i)和（ii），结合动力系统理论的优化和控制策略，实时更新受限系统的外部作用力，从而实现预定的界面形状和运动。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。

From the acrobatics of fluids that respond to magnetic fields, to the extraction of oil from the Earth, to electrode operation in consumer device batteries, the motion of interfaces must be modeled, analyzed and controlled towards achieving a desired flow pattern, improving the efficiency of energy recovery, or assuring safety. This award will support fundamental scientific research that will contribute new knowledge and understanding of the dynamics of interfaces between fluids. The outcomes of this research program could become the building blocks for new approaches towards the precise manipulation of spreading and confined layers of fluids, which is needed to advance additive manufacturing (also called 3D printing) processes, as well as lab-on-a-chip devices that use motion of droplets (closed fluid-fluid interfaces) to perform chemical diagnostics. Therefore, this award will promote both the progress of a scientific field, as well as potentially contribute to the science behind new technologies that benefit the U.S. economy and society, thus advancing national prosperity. Furthermore, the research will engage undergraduate, graduate and postdoctoral researchers within the PI's established culture of mentorship and diversity efforts, towards championing scientific excellence and broadening participation in this research field.Fluid interfaces do not always move and deform in an orderly fashion. They can be unstable, and their shapes can be unpredictable from the inputs to the system. The current research on such instabilities has focused on the initiation stage of the unpredictable behavior, which is called the linear regime. At the same time, the dynamics are influenced by multiple physical effects, whose coupled influence remains relatively unexplored. To address these knowledge gaps, the fundamental research will derive mathematical models and construct numerical methods to understand the late stage (termed nonlinear) time evolution of interfaces, eventually yielding methods to manipulate instability. Specifically, the research team will: (i) derive sharp-interface mathematical models of the dynamics of immiscible fluid-fluid interfaces confined in nonstandard Hele-Shaw geometries, including multiphysics interactions due to domain boundary motion and non-invasive forcing via magnetic fields; (ii) construct efficient numerical methods for Lagrangian sharp-interface tracking, based on the vortex sheet method, to enable analysis of the nonlinear evolution of interfaces, including their ability to sustain permanent traveling excitations (solitons); and (iii) harness (i) and (ii), in conjunction with optimization and control strategies from dynamical systems theory, to update the external forcing of the confined system on-the-fly and, thus, achieve pre-determined interfacial shapes and motions.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.