In general, electrically neutral liquids have a distribution of electrical charges near a surface because of a charged solid surface. This region is well known as the electrical double layer (EDL) and its thickness ranges from a few nanometers up to several hundred nanometers. As the characteristic dimensions of the cylindrical capillary decrease to micro ranges, the electrokinetic effects induced by an EDL between the fluid and charged channel surface are believed to play an important role in studying the heat transfer and flow phenomena. Applications of cylindrical microcapillaries are encountered in biological chips (Biochip) such as micropumps, capillary electrophoretic devices for separation of proteins, and coaxial jet mixing devices used in chemical analysis and biomedical diagnostics. Therefore, an understanding of the electrokinetic transport phenomena in a cylindrical microcapillary is needed for design and operation of microfluid flow in Biochips.

Salt-free dispersions comprise a special colloidal system in which the liquid phase contains only counterions dissociated from the surface of the dispersed entities. A typical example in practice includes a dispersion of polyelectrolytes such as DNA, RNA, filamentous actin, microtubules and polyacrylic acid (PAA) in an electrolyte-free liquid medium. Although theoretical studies on the transient electrokinetic flow in a salt-free solution are particularly important for analyzing experimental electrokinetic data for nonaqueous media, which contain essentially no salts, no study has been reported to investigate the transient response of electrokinetic flow in a salt-free solution. Therefore, the main objective of this paper is to derive the exact or accurate analytical solution for the transient electrokinetic flow of a salt-free medium containing counterions only in cylindrical capillaries. Based on these results, the corresponding transient electrokinetic transport phenomena such as electro-osmosis velocity, electric current, streaming potential, electroviscous effect, and heat transfer coefficient can be obtained in closed form.