The effect of wall interactions in capillary-zone electrophoresis

Capillary-zone electrophoresis (CZE) is an efficient separation method in analytical chemistry. It exploits the difference in electrophoretic migration speeds between charged molecular species in aqueous solution when an external electric field is applied to achieve separation. In most cases the electrophoretic migration of species is also accompanied by a bulk electro-osmotic flow in the capillary due to the presence of a zeta-potential at the capillary wall. Adsorption of charged species at the wall could modify this zeta-potential in a non-uniform manner. This induces axial pressure gradients, so that the flow is no longer uniform over the capillary cross-section. The resulting shear-induced dispersion of the sample is a serious cause of band broadening in CZE particularly for species such as proteins and peptides which adsorb strongly on capillary walls. The problem of the spatio-temporal evolution of the sample concentration is studied in the presence of such wall interactions. An asymptotic theory is developed that is valid provided axial variations have characteristic length scales that are much larger than the capillary radius and temporal variations have a characteristic time scale much larger than the characteristic diffusion time over a capillary radius. These conditions are normally satisfied in CZE, except when the sample is close to the inlet, on account of the capillary length being very much larger than its radius. It is shown that the cross-sectionally averaged sample concentration obeys a one-dimensional partial differential equation. Further, the full three-dimensional concentration field may be calculated once the cross-sectionally averaged concentration field is known. The reduced system is integrated numerically and is shown to lead to predictions consistent with known observations on CZE in the presence of wall interactions.