A Model for Nonlinear Electrokinetics in Electric Field Guided Assembly of Colloids
Steuber, James G.
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Electric field guided assembly of colloids is a new area of research in colloidal science where sub-micrometer particles, or colloids, are assembled using patterned electrodes. The design of these devices is often limited by an inability to characterize accurately forces and fluxes with linearized electrokinetic theory. The research presented in this dissertation describes an application of the finite element method to the nonlinear electrokinetic equations. The finite element model thus developed is then used to describe the nonlinear electrophoretic mobility of a dilute colloidal dispersion, investigate hydrodynamic and electric particle-particle interactions, and characterize particle-surface interactions. The effect of Stern layer conduction on the electrophoretic mobility and dielectric response is included using the generalized dynamic Stern layer model. The electrokinetic force is calculated using the Maxwell stress tensor method rather than the effective dipole method as it is more consistent with nonlinear electrokinetic theory. Significant results of this dissertation demonstrate the effect of nonlinear electrokinetic phenomena and extend the present electrokinetic theory. The calculation of nonlinear electrophoretic mobility of a dilute colloidal dispersion, which is valid for arbitrary particle surface charge or zeta potential, applied (AC) electric field strength, and applied AC electric field frequency. Also, the adsorption isotherm used by the generalized dynamic Stern layer theory is extended to include non-equilibrium reaction kinetics. This results in a model for Stern layer conduction which is valid for frequencies above 1 MHz. The utilization of the Maxwell stress tensor method results in a finite element model which is valid for arbitrary electric field strength and includes the effects of traveling-wave dielectrophoresis a nonlinear electrokinetic phenomena resulting from non-uniform electric field phase.