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

从响应磁场的流体的杂技，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操纵扩散层和受限层流体的新方法的基石，这是推进添加剂制造(也称为3D打印)工艺所需的，以及使用液滴运动(封闭的流体-流体界面)执行化学诊断的芯片实验室设备。因此，该奖项既将促进科学领域的进步，也可能为新技术背后的科学做出贡献，使美国经济和社会受益，从而促进国家繁荣。此外，这项研究将使本科生、研究生和博士后研究人员在PI既定的指导和多样化努力的文化中，朝着倡导科学卓越和扩大对这一研究领域的参与的方向发展。它们可能是不稳定的，它们的形状可能无法从系统的输入中预测。目前对这类不稳定性的研究主要集中在不可预测行为的初始阶段，即线性区域。同时，动力学受多种物理效应的影响，其耦合影响相对较少。为了解决这些知识空白，基础研究将建立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。具体地说，研究小组将：(I)推导出非标准Hele-Shaw几何结构中不混溶流体-流体界面动力学的尖锐界面数学模型，包括由区域边界运动引起的多物理相互作用和通过磁场的非侵入性强迫；(Ii)基于涡表方法，建立有效的拉格朗日尖锐界面跟踪的数值方法，以使能够分析界面的非线性演化，包括它们维持永久行进激励(孤子)的能力；以及(Iii)利用(I)和(Ii)结合动力系统理论的优化和控制策略，动态更新受限系统的外力，从而实现预先确定的界面形状和运动。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.