Numerical Methods and Analysis for Induced-Charge Electrokinetic Flow with Deformable Interfaces

可变形界面感应电荷动电流的数值方法与分析

基本信息

批准号：
1412789
负责人：
Michael Siegel
金额：
$ 37.4万
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：
2014
资助国家：
美国
起止时间：
2014-08-01 至 2019-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1412789&HistoricalAwards=false
关键词：
Numerical Methods Analysis Induced Charge

项目摘要

This project is an investigation of fundamental problems from fluid dynamics that arise in biology and microtechnology. Its focus is on the development of new mathematical models and efficient numerical methods to study the manipulation by electric fields of the shape and position of cells, vesicles, and drops in electrolytic fluids. These so-called 'electrokinetic techniques' are among the most common methods for manipulating particles and fluids in micro-scale devices and biological applications. For example, electric fields are applied to induce shape changes in cells and vesicles, and this is used to infer membrane properties. Electric fields are also used to form transient pores in membranes, which is an important technique to load cells with molecules for drug delivery or gene therapy. 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 phenomena in biology and engineering. An additional impact of this project will be 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 interfacial flow of an ionic fluid that is driven by an electric field, a screening cloud of ions develops at the interface and forms an electrochemical double layer or 'Debye layer'. The electric field both acts on the ion cloud it induces and drives both it and the surrounding fluid into motion. This is known as 'induced-charge electrokinetic flow', and it is an important phenomenon in applications. We address a significant difficulty in the numerical computation of such flows in the practically important limit of thin double layers, by developing a fast and accurate hybrid or multiscale numerical method that incorporates an asymptotic analysis of the layer's dynamics into a novel boundary integral formulation of the interfacial free boundary problem. A central theme of the current project is the development of a hybrid method for electrokinetic flow about a membrane. The algorithm 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 electrodeformation of drops, vesicles, and cells, and to examine vesicle manufacture by electroformation and coalescence by electrofusion. The numerical investigations will be complemented by analytical studies that will be used to justify existing reduced or 'lumped parameter' models for electrohydrodynamic flow, and to derive new models. The investigators also propose to develop a hybrid method for problems with ionic surfactant, which combines features of both electrokinetic flow and soluble surfactant.

该项目是对生物学和微技术产生的流体动力学基本问题的研究。它的重点是开发新的数学模型和有效的数值方法，以研究电池，囊泡和电解液中细胞形状和位置的电场操作。这些所谓的“电动技术”是在微观设备和生物应用中操纵颗粒和流体的最常见方法之一。例如，电场用于诱导细胞和囊泡的形状变化，这用于推断膜性质。电场还用于在膜上形成瞬态孔，这是将细胞用药物递送或基因治疗分子加载细胞的重要技术。拟议的研究的影响包括开发新的数学模型和数值方法，这对研究生物学和工程学中电动现象的科学家和工程师有益。该项目的另一个影响将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提供宝贵的准备。在由电场驱动的离子流体的界面流中，离子的筛选云在界面上发展并形成电化学双层或“ Debye层”。电场两者都作用于离子云上，它引起并将其驱动和周围的流体运动。这被称为“诱导电动电动流动流”，它是应用中的重要现象。我们通过开发快速准确的混合或多尺度数值方法来解决此类流量的数值计算，从而解决此类流的数值计算，该方法将层动力学的渐近分析纳入了界面自由边界问题的新型边界积分公式中。当前项目的一个核心主题是开发围绕膜的电动流量的混合方法。该算法将结合膜上的弹性和静电应力的高波或小规模分量的分析，中的非固定方法，该方法能够处理问题中固有的多个时间和空间量表。该方法将用于研究液滴，囊泡和细胞的电去构造中的规范问题，并通过电渗封来检查囊泡制造囊泡。分析研究将补充数值研究，这些研究将用于证明现有的减少或“集结参数”模型，用于电水力流动流，并得出新模型。研究人员还建议为离子表面活性剂问题开发一种混合方法，该方法结合了电动流和可溶性表面活性剂的特征。