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

该项目是对生物学和微技术中出现的流体动力学基本问题的研究。 其重点是开发新的数学模型和有效的数值方法，以研究电场对电解液中细胞、囊泡和液滴的形状和位置的操纵。 这些所谓的“动电技术”是微型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，施加电场来诱导细胞和囊泡的形状变化，这用于推断膜特性。电场还用于在膜上形成瞬时孔，这是一种用分子装载细胞以进行药物输送或基因治疗的重要技术。 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现象。 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生涯做好宝贵的准备。在电场驱动的离子流体的界面流动过程中，离子屏蔽云在界面处形成，并形成电化学双层或“德拜层”。电场既作用于它引起的离子云，又驱动它和周围的流体运动。这被称为“感应电荷动电流”，是应用中的一个重要现象。我们通过开发一种快速而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界面自由边界问题的新型边界积分公式中，解决了薄双层实际重要限制中此类流动数值计算的重大困难。 当前项目的中心主题是开发一种用于膜周围动电流的混合方法。该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、囊泡和细胞的电形成中的典型问题，并通过电形成和电融合来检查囊泡的制造。数值研究将得到分析研究的补充，分析研究将用于证明现有的电流体动力流简化或“集总参数”模型的合理性，并导出新模型。 研究人员还建议开发一种解决离子表面活性剂问题的混合方法，该方法结合了动电流和可溶性表面活性剂的特征。

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.