Nonlinear Electrophoresis of Charged Colloidal Particles

该项目的目标是预测和测量电解质溶液中的带电粒子在强电压下的运动。这种运动被称为电泳，在芯片实验室设备、电子墨水显示器、颜料、涂料和石油工业中很重要。一个中心目标是量化粒子的速度与电压强度的比率，这被称为电泳迁移率。这样的测量是用来推断粒子的电荷，这是预测粒子悬浮液行为的关键量。一个复杂的问题是，电泳迁移率可能以非线性的方式依赖于电压，特别是在有机电解质（例如掺杂表面活性剂分子的油）中的大电压下。然而，这种非线性的、电压相关的迁移率的预测模型是缺乏的。因此，本项目的智力价值在于发展理论和数值计算来预测非线性迁移率，并将其与实验测量结果进行比较。更广泛的技术影响是确定粒子电荷的新方法的发展，以帮助设计具有增强稳定性的分散体，这将有利于使用有机溶剂的家庭和个人护理产品的配方。该项目对教育的广泛影响包括课程开发、本科生研究和推广活动。对于后者，将开发K-12学生的教育模块，并将其整合到卡内基梅隆大学现有的外展项目中。这个项目的智力价值是通过对控制流体流动、离子传输和反应动力学以及电泳静电场的电动力学方程的数值解来预测带电胶体粒子的电场依赖迁移率。这些预测将与实验测量进行比较，这将使反馈能够改进建模假设。数值方案将采用一个自定义的谱元代码，它非常适合于这项任务。该项目分为两个技术目标。目的1的重点是在均匀、稳定（dc）场下的稳定电泳，其迁移率与时间无关。目标是计算整个实验相关场强范围内的场相关迁移率。在目标2中，粒子在单频交流场下的运动将被检查，其迁移率是时间相关的。这里的假设是，由于电解质中阳离子和阴离子的扩散系数不匹配，德拜云的非线性扭曲，超过弱场极限，导致交流场下的整流迁移。该项目是新颖的，因为之前的工作主要集中在弱应用领域，在这些领域，流动性与领域无关。该项目将产生新的计算工具来分析非线性电泳实验。这将对胶体科学和软物质社区产生更广泛的影响，他们将能够利用结果从场相关迁移率测量中推断表面电荷。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The goal of this project is to predict and measure how electrically charged particles in electrolyte solutions move under strong voltages. Such motion is called electrophoresis and is important in lab-on-a-chip devices, e-ink displays, pigments, coatings, and the petroleum industry. A central objective is to quantify the ratio of the speed of the particle to the voltage strength, which is known as the electrophoretic mobility. Such measurements are conducted to infer the electrical charge of a particle, a key quantity in predicting the behavior of suspensions of particles. One complication is that electrophoretic mobility may depend on the voltage in non-linear way, particularly with large voltages in organic electrolytes (e.g. oils doped with surfactant molecules). However, predictive models for this nonlinear, voltage-dependent mobility are lacking. Thus, the intellectual merit of this project is to develop theory and numerical computations to predict the nonlinear mobility, which will be compared to experimental measurements. A broader technological impact is the development of new methods to determine particle charge to aid in designing dispersions with enhanced stability, which will benefit the formulation of household and personal-care products that use organic solvents. The educational broader impact of this project includes course development, undergraduate research, and outreach activities. For the latter, educational modules for K-12 students will be developed and integrated into existing outreach programs at Carnegie Mellon University.The intellectual merit of this project is to predict the electric field-dependent mobility of a charged colloidal particle via numerical solution of the electrokinetic equations governing fluid flow, ion transport and reaction kinetics, and electrostatic fields in electrophoresis. These predictions will be compared against experimental measurements, which will enable feedback to refine modeling assumptions. The numerical scheme will employ a custom spectral element code that is ideally suited to the task. The project is split into two technical objectives. Objective 1 is focused on steady electrophoresis under a uniform, steady (dc) field, for which the mobility is time independent. The goal is to compute the field-dependent mobility over the entire range of experimentally relevant field strength. In objective 2, particle motion under a single frequency ac field will be examined, for which the mobility is time dependent. Here, the hypothesis is that the nonlinear distortion of the Debye cloud, beyond the weak-field limit, leads to rectified migration under an ac field, due to a mismatch in the diffusion coefficients of the cations and anions in an electrolyte. The project is novel since previous efforts have predominantly focused on weak applied fields, where the mobility is field-independent. The project will generate new computational tools to analyze experiments on nonlinear electrophoresis. This will have a broader impact to the colloid science and soft matter communities, who will be able to use the results to infer surface charge from field-dependent mobility measurements.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.