Numerical Methods and Analysis for Interfacial Flow with Ionic Fluids and Surfactants

离子流体和表面活性剂界面流动的数值方法与分析

• 批准号: 1909407
• 负责人: Michael Siegel
• 金额: $ 40万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1909407&HistoricalAwards=false
• 关键词: Numerical; Methods; Analysis; Interfacial; Flow

This project is an investigation of fundamental problems in the dynamics of fluids, complex fluids, and deformable matter that occur in applications to biology and microtechnology. Its focus is on the development of new mathematical models and efficient numerical methods to study the morphology and control of drops, cells, and vesicles by electric fields in electrolytic fluids and by flow fields with surfactant. Electrokinetic techniques are among the most common methods for manipulating soft particles and ionic fluids in micro-scale and biological applications and can induce, for example, shape changes in cells and vesicles, from which membrane properties can be inferred. They can also induce membrane channel and pore formation for advanced cell treatment and therapy. Surfactants are used to enhance or control a wide range of complex fluid flows that occur in industries ranging from oil extraction to agriculture, food, and pharmaceutical processing. They are also important in microfluidic applications. Impacts of the proposed research include the development of new mathematical models and numerical methods that will be of benefit to scientists and engineers studying electrokinetic and surfactant phenomena in biology and engineering. An additional impact of this project is the education and involvement of graduate students. The interdisciplinary training they receive will be valuable preparation for a range of careers in mathematics and science.During the deformation of a fluid-fluid interface with surfactant, surfactant exchange between the interface and bulk occur in a thin layer adjacent to the interface, and the layer's dynamics control interfacial surface tension and shape. During the interfacial flow of an ionic fluid that is driven by an electric field, a thin screening cloud of ions develops at the interface to form an electrochemical double layer or 'Debye layer'. The electric field induces motion in the ion cloud, the interface, and the surrounding fluid. The influence of surfactants on interface and flow dynamics and the occurrence of 'induced-charge electrokinetic flow' in an ionic fluid are both important phenomena in a wide range of applications. This project addresses a difficulty in the numerical computation of such flows in the practically important limit of thin surfactant exchange layers and thin electrical double layers, by developing fast and accurate 'hybrid' or multiscale numerical methods that incorporate an asymptotic analysis of the layer dynamics into a boundary integral or similar formulation of the interfacial free boundary problem. Central themes of the current project are the development of a hybrid method for electrokinetic flow about a deformable membrane and the investigation of fast and accurate numerical methods for studying the influence of surfactant and ionic surfactant on interfacial flow. The algorithm for electrokinetic flow will incorporate an analysis of the high-wavenumber or small-scale component of the elastic and electrostatic stresses on a membrane into a nonstiff method that is capable of handling the multiple time and space scales inherent in the problem. The method will be used to study canonical problems in the deformation of drops, vesicles, and cells, and to explore the interaction between membrane and ionic fluid properties. In the context of surfactant-laden flows, the hybrid numerical method will be developed to accurately handle multiply connected domains with close interaction of interfaces, such as occurs with multiple drops, and the presence of surfactant in the interior fluid, both of which are associated with substantial numerical challenges. This project also involves the development of fast or accelerated algorithms, including for drops in 3D flow with soluble surfactant, as well a fundamental analysis of the stability and convergence of the boundary integral methods that are a cornerstone of this work.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.

该项目旨在研究生物学和微技术应用中出现的流体动力学、复杂流体和可变形物质的基本问题。其重点是开发新的数学模型和有效的数值方法，以研究电解液中的电场和表面活性剂流场对液滴、细胞和囊泡的形态和控制。动电技术是在微尺度和生物应用中操纵软颗粒和离子液体的最常见方法之一，并且可以诱导细胞和囊泡的形状变化，从中可以推断出膜特性。它们还可以诱导膜通道和孔的形成，以进行先进的细胞治疗和治疗。表面活性剂用于增强或控制从石油开采到农业、食品和制药加工等行业中发生的各种复杂流体流动。它们在微流体应用中也很重要。拟议研究的影响包括开发新的数学模型和数值方法，这将有利于科学家和工程师研究生物学和工程学中的动电和表面活性剂现象。该项目的另一个影响是研究生的教育和参与。他们接受的跨学科培训将为数学和科学领域的一系列职业做好有价值的准备。在表面活性剂的流体-流体界面变形过程中，界面和本体之间的表面活性剂交换发生在邻近界面的薄层​​中，并且该层的动力学控制界面的表面张力和形状。在电场驱动的离子流体的界面流动过程中，界面处会形成一层薄薄的离子屏蔽云，形成电化学双层或“德拜层”。电场引起离子云、界面和周围流体的运动。表面活性剂对界面和流动动力学的影响以及离子流体中“感应电荷动电流”的发生都是广泛应用中的重要现象。该项目通过开发快速准确的“混合”或多尺度数值方法，将层动力学的渐近分析纳入边界积分或界面自由边界问题的类似公式中，解决了在薄表面活性剂交换层和薄双电层的实际重要限制中对此类流动进行数值计算的困难。当前项目的中心主题是开发可变形膜电动流动的混合方法，以及研究表面活性剂和离子表面活性剂对界面流动影响的快速准确的数值方法。动电流算法将对膜上弹性应力和静电应力的高波数或小尺度分量的分析纳入非刚性方法，该方法能够处理问题中固有的多个时间和空间尺度。该方法将用于研究液滴、囊泡和细胞变形的典型问题，并探索膜和离子液体特性之间的相互作用。在充满表面活性剂的流动的背景下，将开发混合数值方法，以准确处理具有界面密切相互作用的多重连通域，例如在多个液滴中发生的情况，以及内部流体中存在表面活性剂的情况，这两者都与大量的数值挑战相关。该项目还涉及快速或加速算法的开发，包括使用可溶性表面活性剂进行 3D 流滴，以及对边界积分方法的稳定性和收敛性进行基本分析，这是这项工作的基石。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Jeffery’s paradox for the rotation of a single ‘stick–slip’ cylinder

单个“粘滑”圆柱体旋转的杰弗里悖论

• DOI: 10.1016/j.mechrescom.2023.104154
• 发表时间: 2023
• 期刊: Mechanics Research Communications
• 影响因子: 2.4
• 作者: Siegel, Michael;Yariv, Ehud
• 通讯作者: Yariv, Ehud

A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions

• DOI: 10.1017/jfm.2022.469
• 发表时间: 2022-06-20
• 期刊: JOURNAL OF FLUID MECHANICS
• 影响因子: 3.7
• 作者: Ma, Manman;Booty, Michael R.;Siegel, Michael
• 通讯作者: Siegel, Michael

Deformation and stability of a viscous electrolyte drop in a uniform electric field

均匀电场中粘性电解质滴的变形与稳定性

• DOI: 10.1103/physrevfluids.4.053702
• 发表时间: 2018-07
• 期刊: Physical Review Fluids
• 影响因子: 2.7
• 作者: Wang Qiming;Ma Manman;Siegel Michael
• 通讯作者: Siegel Michael

Rotation of a superhydrophobic cylinder in a viscous liquid

超疏水圆柱体在粘性液体中的旋转

• DOI: 10.1017/jfm.2019.776
• 发表时间: 2019
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Yariv, Ehud;Siegel, Michael
• 通讯作者: Siegel, Michael

Convergence of the boundary integral method for interfacial Stokes flow

界面斯托克斯流边界积分法的收敛性

• DOI: 10.1090/mcom/3787
• 发表时间: 2023
• 期刊: Mathematics of Computation
• 影响因子: 2
• 作者: Ambrose, David;Siegel, Michael;Zhang, Keyang
• 通讯作者: Zhang, Keyang