Hydrodynamic analysis of electroosmotic flow in capillary

The growth process and stationary flow profile of electroosmotic flow are analyzed. It is assumed that cations are distributed according to the diffuse electric double layer expressed by the Debye-Huckel theory and that the capillary-radius-to-Debye length ratio is 16400. Two time scales in the initial growth stage are estimated by analogy with similar phenomena of Rayleigh's problem. The flow retains a profile similar to the charge profile and approaches a stationary flow in the double layer. Then the laminar flow layer extends into the bulk phase, which is similar to the cylindrical thermal conduction process. The entire growth time is equivalent to that of Poiseuille flow and on the order of 16400(2) times the two time scales in the initial growth stage. A flat stationary flow profile is obtained analytically. Viscous heat is much lower than Joule heat.