Simulating the Dynamics of Electrowetting: Modeling, Numerics, and Validation

0754983 Shapiro电润湿是一种在微尺度上操纵流体的技术。通过在致动电极处施加电压，可以（有效地）改变表面张力性质，并且移动、分裂、合并和混合液体包。电润湿的应用包括可重新编程的芯片实验室系统、自动对焦手机镜头、笔记本电脑的彩色油像素和视频速度智能纸。PI将开发经过实验验证的模型，这些模型将首先在两个空间维度上预测电润湿动力学，然后在三个空间维度上预测，这将使下一代系统分析，设计和控制成为可能。这些模型将包括基本的整体流动物理学：表面张力、低雷诺流体动力学、静电学或电动力学，以及接触角饱和和滞后等临界损失现象。可以经历分裂和合并拓扑变化的移动的液体/气体或液体/液体界面将通过隐式有限元（FEM）方法的组合来跟踪，这将允许自然地、容易地和准确地计算界面曲率和所得的表面张力，并且通过仅在分裂/合并事件处局部应用的水平集方法，将自然地产生拓扑变化。这将结合联合收割机的FEM（它非常准确地处理曲率）和水平集方法（它自然地捕捉拓扑变化）的优势。有限元法也将用于解决低维沃尔德的Navier Stokes方程，静电（或电动）部分的麦克斯韦方程，并处理边界条件在移动固体/液体/气体三线在一个数字健全的方式。三线运动/钉扎模型将进行评估，并与电润湿实验进行比较-这将改善初始滞后模型，并将结合文献中的流体动力学和平均分子动力学描述。目前，还没有建模工具来理解和量化电润湿系统的动态行为。为了建立这样的模型，PI将：1）包含基本的物理现象; 2）正确表述整体偏微分方程（特别是电动效应和所产生的流体力之间的相互作用），3）使用变分方法来重铸这些方程，然后创建数值上可行的FEM算法来求解它们，4）跟踪可以经历拓扑变化的移动界面，通过FEM和水平集方法的组合，以数字上合理的方式，4）包括来自第一原理和文献（当可能时）或来自实验数据（当不可能时）的损失现象，例如饱和和滞后，以及5）通过隔离和确认每个新部分来验证电润湿实验。其优点在于实现并结合了这些组成部分。PI与两个领先的电润湿小组（一所大学和一家公司）合作，并即将开始与第三个小组（一家公司）合作。所有这三个小组都表示强烈需要这样一个物理第一原理，实验通知，动态电润湿建模工具。如果成功，结果将被电润湿社区用于理解，分析，设计和控制下一代电润湿系统。所开发的用于跟踪两相微流拓扑结构变化的方法将在许多其他微流体应用中使用。

0754983ShapiroElectrowetting is a technique for manipulating fluids on the micro-scale. By applying voltages at actuating electrodes, it is possible to (effectively) modify surface tension properties, and to move, split, merge, and mix liquid packets. Applications of electrowetting include re-programmable lab-on-a-chip systems, auto-focus cell phone lenses, and colored oil pixels for laptops and video-speed smart paper. The PIs will develop experimentally validated models that will predict electrowetting dynamics first in two, then in three, spatial dimensions, which will enable next-generation system analysis, design, and control. The models will include the essential bulk-flow physics: surface tension, low-Reynolds fluid dynamics, electrostatics or electrodynamics, as well as critical loss-phenomena such as contact angle saturation and hysteresis. Moving liquid/gas or liquid/liquid interfaces, that can undergo split and merge topology changes, will be tracked by a combination of an implicit finite element (FEM) method, which will allow computation of interface curvature and the resulting surface tension forces naturally, easily, and accurately, and by the level-set method applied only locally at split/merge events, will naturally yield topology changes. This will combine the strengths of FEM (it handles curvature extremely accurately) and the level-set approach (it naturally captures topology changes). FEM will also be used to solve the low-Reynold's Navier Stokes equations, the electrostatic (or electrodynamic) part of Maxwell's equations, and to handle boundary conditions at the moving solid/liquid/gas triple line in a numerically sound manner. Triple line motion/pinning models will be evaluated and compared against electrowetting experiments - this will improve the initial hysteresis model and will incorporate a combined hydrodynamic and averaged molecular-kinetic description from the literature. Intellectual Merit Currently, there are no modeling tools to understand and quantify the dynamic behavior of electrowetting systems. To build such models, the PIs will: 1) include the essential physical phenomena, 2) correctly state the bulk partial-differential-equations (especially the interplay between electrodynamic effects and the resulting fluid forces), 3) use the variational method to recast these equations and then create numerically viable FEM algorithms to solve them, 4) track moving interfaces, that can undergo topological changes, by a combination of the FEM and level-set methods, in a numerically sound manner, 4) include loss-phenomena such as saturation and hysteresis from first-principles and the literature (when possible) or from experimental data (when not), and 5) validate against electrowetting experiments, by isolating and confirming each new part. The merit is in achieving and combining these components. Broader Impact The PIs collaborate with two leading electrowetting groups (at a university and a company), and are about to begin a collaboration with a third (a company). All three groups have expressed a strong need for such a physical-first-principles, experimentally informed, dynamic electrowetting modeling tool. If successful, the results will be used by the electrowetting community to understand, analyze, design, and control next-generation electrowetting systems. The methods developed for tracking 2-phase micro-flow topology changes will be of use in many other micro-fluidic applications.