Eddies in a bottleneck: an arbitrary Debye length theory for capillary electroosmosis

Using an applied electrical field to drive fluid flows becomes desirable as channels become smaller. Although most discussions of electroosmosis treat the case of thin Debye layers, here electroosmotic flow (EOF) through a constricted cylinder is presented for arbitrary Debye lengths (kappa(-1)) using a long wavelength perturbation of the cylinder radius. The analysis uses the approximation of small potentials. The varying diameter of the cylinder produces radially and axially varying effective electric fields, as well as an induced pressure gradient. We predict the existence of eddies for certain constricted geometries and propose the possibility of electrokinetic trapping in these regions. We also present a leading-order criterion which predicts central eddies in very narrow constrictions at the scale of the Debye length. Eddies can be found both in the center of the channel and along the perimeter, and the presence of the eddies is a consequence of the induced pressure gradient that accompanies electrically driven flow into a narrow constriction.