Electrically-driven fluid motion in channels with streamwise gradients of the electrical conductivity

Electroosmotic motion through charged, narrow-bore channels and capillaries is analyzed for the case where there are dominantly-axial gradients in the composition of the flowing electrolyte. The channel width is assumed to be large compared with the Debye screening length, and the electroosmotic slip velocity along the channel wall is taken to vary locally with the ionic strength, pH and electric field. Owing to the wall slip condition, the velocity distribution is nonlinearly coupled to the composition variations within the fluid. The prototype problem studied is one in which buffer ions and other solutes (e.g. analytes) are initially distributed in a sample zone that is sandwiched between uniform running buffer. For the situations considered, the conductivity of the sample zone differs significantly from that of the running buffer; such configurations are common to stacking and electroosmotic pumping protocols. In a frame of reference that moves with the mean velocity of the flow, the velocity field exhibits flow separation in the neighborhood of the conductivity variations and this gives rise to solutal mixing and dispersion in and about the sample zone.