Nonlinear Electrophoresis of Charged Colloidal Particles

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

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.