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调查。 其重点是发展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“电动技术”是在微尺度设备和生物应用中操纵粒子和流体的最常见方法之一。 例如，施加电场以诱导细胞和囊泡的形状变化，并且这用于推断膜性质。电场也用于在膜中形成瞬时孔，这是一种重要的技术，用于将分子装载到细胞中用于药物递送或基因治疗。 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电动现象。 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他们在数学和科学领域的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，在界面处形成屏蔽离子云，并形成电化学双层或“德拜层”。电场既作用于离子云，又诱导和驱动离子云和周围的流体运动。这被称为“感应电荷动电流”，并且它是应用中的重要现象。我们解决了一个显着的困难，在薄双层的实际重要的限制，通过开发一个快速，准确的混合或多尺度数值方法，将层的动态渐近分析到一个新的边界积分公式的界面自由边界问题的数值计算。 当前项目的一个中心主题是开发一种用于膜周围电动流的混合方法。该算法将结合到一个非刚性的方法，能够处理多个时间和空间尺度固有的问题的高波数或小尺度的组件上的弹性和静电应力的膜的分析。该方法将被用来研究典型的问题，在电变形的下降，囊泡，和细胞，并检查囊泡制造电形成和聚结电融合。数值调查将补充分析研究，将被用来证明现有的减少或“集总参数”模型的电流体动力学流，并得出新的模型。 研究人员还建议开发一种混合方法来解决离子表面活性剂的问题，该方法结合了电动流动和可溶性表面活性剂的特点。

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.