Abstract

Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in analytical chemistry and the life sciences. In capillary zone electrophoresis (CZE), the sample concentration peak migrates in a microcapillary in the presence of a background electrolyte. When concentration of the sample ions is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including skewed non-Gaussian profiles and sharp concentration jumps or “shocks”. It is shown that under certain conditions the sample concentration obeys a one dimensional nonlinear advection diffusion equation reducible to Burger’s equation in the weakly nonlinear limit. This fact can be exploited to obtain exact formulas for useful quantities such as the migration speed, width and shape of sample peaks, thereby providing a framework for understanding experimental observations. In the presence of a zeta potential at the capillary wall, induced pressure gradients cause Taylor dispersion of the sample ions, resulting in the molecular diffusivity being replaced with a concentration dependent effective diffusivity.