Electrophoretic resolution versus fluctuations of the lateral dimensions of a capillary

Because the local electrical resistance is inversely proportional to the local cross-section of a capillary, the intensity of the electric field varies along the migration path if the inner diameter of the capillary is not constant. Therefore, fluctuations of the lateral dimensions of a capillary can directly affect the net elution time as well as the peak width, and, hence the final resolution. In this article, we develop the theoretical framework for the study of such effects. We then examine the simple case where both the mobility and the diffusion coefficient are field-independent; in particular, we demonstrate that resolution can be severely reduced if the inner walls are not flat, and that optimal resolution is always obtained for perfectly flat walls. Generalized to ultrathin gels, our results clearly indicate that both random and systematic variations of the gel thickness can greatly affect the performance of the separation process. Acceptable degrees of flatness are estimated for both geometries. This study thus provides a quantitative understanding of the type of quality control one requires to obtain optimal results with capillaries and ultrathin gels.