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

受限界面的非线性动力学：超越线性分析并走向控制

基本信息

批准号：
2029540
负责人：
Ivan Christov
金额：
$ 38.77万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2029540&HistoricalAwards=false
关键词：
Nonlinear Dynamics Confined Interfaces Beyond

项目摘要

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.

从响应磁场的流体的杂技到从地球上提取油，到消费设备电池中的电极操作，必须对接口的运动进行建模，分析和控制，以实现所需的流动模式，提高能量恢复的效率或确保安全性。该奖项将支持基本的科学研究，该科学研究将有助于新知识和对流体之间接口动态的理解。该研究计划的结果可能成为新方法的基础，以精确操纵散布和限制的流体层，这是推进添加剂制造（也称为3D打印）过程所需的，以及使用液滴运动（封闭液体富集界面）来执行化学诊断器的实验室芯片设备。因此，该奖项将促进科学领域的进步，并有可能为有益于美国经济和社会的新技术背后的科学做出贡献，从而促进了民族繁荣。此外，这项研究将吸引本科生，研究生和博士后研究人员，参与PI既定的指导和多样性努力文化，以支持卓越的科学卓越和扩大参与该研究领域的参与。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，并且它们的形状在系统的输入中可能是不可预测的。当前对这种不稳定性的研究集中在不可预测的行为的起始阶段，这称为线性制度。同时，动态受到多种物理效应的影响，其耦合影响仍然相对尚未探索。为了解决这些知识差距，基础研究将得出数学模型并构建数值方法，以了解接口的后期（称为非线性）时间演变，最终产生了操纵不稳定性的方法。具体而言，研究团队将：（i）得出非标准的Hele-shaw几何形状中的不混溶性流体流体界面动力学的尖锐数学模型，包括由于域边界运动和通过磁场通过磁场的非侵入性强迫而引起的多物理相互作用；（ii）基于涡旋方法的拉格朗日尖锐地面跟踪的构造有效的数值方法，以启用界面的非线性演化分析，包括它们维持永久性旅行激发（solitons）的能力；（iii）线束（i）和（ii）以及动态系统理论中的优化和控制策略，以更新限制系统的外部强迫，从而实现预定的界面形状和动作。该奖项颁发了NSF的法定任务，并反映了通过评估范围和众所周知的基础，这反映了对基础的支持，并得到了构成的影响。