Fast high-order methods for electrohydrodynamics of vesicle suspensions

该项目的目标是开发新的计算工具来模拟囊泡悬浮液的电流体动力学（EHD）。囊泡包裹着粘性流体，它们具有生物细胞的相同结构成分——脂质膜。因此，他们的EHD已经成为理解一般生物细胞在电场下如何行为的范例。该系统的动力学特征是单个膜上的粘性、弹性和电应力之间的竞争以及非局部流体动力学相互作用。许多技术应用需要更好地了解EHD，包括靶向药物递送、基因转染和芯片实验室设计。提出的工作将使研究人员能够了解微观尺度的物理（例如，单粒子变形）如何改变致密悬浮液的宏观尺度行为（例如，电流变学）。此外，该项目还将开展预计会产生广泛影响的教育、指导和外联活动。多囊泡EHD的数学模型由膜周围流体的不可压缩Stokes方程、远场边界条件和流体-囊泡界面的运动学条件组成。经典的Taylor- Melcher漏介质框架模型是单个囊泡的电响应模型，helrich能量结合局部不可拓性模型是它们的弹性响应模型。所提出的数值方法将基于边界积分方程公式，避免了体积离散化。快速、高阶的方法将用于求解囊泡位置及其跨膜电势的耦合边界积分方程。囊泡EHD面临的计算挑战与其他颗粒流（如滴流、气泡流和胶囊流）相同。因此，这里提出的方法可以更普遍地应用于其他几个具有实际重要性的问题。该奖项由数学科学部的计算数学项目颁发，由英国工程技术局CBET部门的微粒和多相过程项目共同资助。

The objective of this project is to develop novel computational tools for simulating the electrohydrodynamics (EHD) of vesicle suspensions. Vesicles enclose a viscous fluid and they share the same structural component of a biological cell, the bilipid membrane. Hence, their EHD has been a paradigm for understanding how general biological cells behave under an electric field. The dynamics of this system is characterized by a competition between viscous, elastic, and electric stresses on the individual membranes and the nonlocal hydrodynamic interactions. A number of technological applications call for better understanding of EHD including targeted drug delivery, gene transfection and lab-on-a-chip design. The proposed work will enable researchers to learn how the physics at micro-scale (e.g., single particle deformation) alters the macro-scale behavior of dense suspensions (e.g., electrorheology). In addition, this project will undertake educational, mentoring, and outreach activities that are expected to have a broad impact. The mathematical model for multiple-vesicle EHD consists of the incompressible Stokes equation for the fluid surrounding the membranes combined with a far-field boundary condition and a kinematic condition at the fluid-vesicle interfaces. The classical Taylor- Melcher leaky-dielectric framework models the electric response of individual vesicles and the Helfrich energy combined with local inextensibility models their elastic response. The proposed numerical methods will be based on boundary integral equation formulations, which avoid volume discretizations. Fast, high-order methods will be developed for solving the coupled boundary integral equations for the vesicle positions and their trans-membrane electric potentials. Computational challenges faced by the vesicle EHD are shared by other particulate flows such as drop, bubble and capsule flows. Therefore, the methods proposed here could more generally be applied to several other problems of practical importance. This award by the Computational Mathematics Program of the Division of Mathematical Sciences is co-funded by the Particulate and Multiphase Processes program in the CBET Division of the ENG Directorate.