| Electrically-driven separation schemes, such as zone electrophoresis (ZE), isotachophoresis (ITP) and isoelectric focusing (IEF), are used profoundly to fractionate mixtures of charged compounds for preparative and particularly analytical applications. Inherent to the separation process is the development of local variations in the electrical conductivity, pH, electric field, etc. One-dimensional, quantitative descriptions of the spatio-temporal evolution of these variations, and their role in the separation process, have been developed over the past two decades. These descriptions lend significant insight into the electromigrational behavior of analytes and buffer components. Nevertheless, because they are one-dimensional, such descriptions omit important effects of electrokinetic fluid motion. The fluid motion arises naturally in the context of the separation scheme, and affects the evolving spatial gradients associated with the separation process. One-dimensional simulations have also been plagued by numerical limitations associated with advection-dominant transport in regions of sharp concentration gradients. In this dissertation, the numerical difficulties are resolved, and a general two-dimensional model of electrokinetic separations is presented. Because the balance laws account for coupling of the velocity field to the ion transport, a variety of processes important to both microfluidic manipulations and analytical separations can be considered. High-ionic strength electroosmotic pumping and field-amplified sample stacking are examined in detail. It is demonstrated that unsteady fluid eddies disperse the gradients in the field variables, and this limits the efficacy of microanalysis processes.; Scaling arguments suggest that, at least for simple geometries, approximate solutions to the general model are possible. Semi-analytic approximations are constructed for the fluid velocity v and electric field E, and the parameter space over which they apply is defined. These approximations reduce simulation times by about two thirds, and provide general information on the dominant physics in microanalysis processes. The scale analysis and simulation results demonstrate that although cross-sectional conductivity gradients meet or exceed those in the axial direction, the electric field is essentially unidirectional. Also, at sufficiently high electric field strengths (ca. several hundred V/cm), nonlinear electrohydrodynamic stresses begin to influence the fluid motion. Finally, if the electrical stresses are negligible, the semi-analytic solutions for v and E permit 1-D macrotransport representations of the solute transport. Effective 1-D simulations yield cross-sectionally averaged values for the field variables in orders of magnitude less simulation time than 2-D simulations. |
