A theoretical study on the transient electro-osmotic flow through a cylindrical microcapillary containing a salt-free medium is presented for both constant surface charge density and constant surface potential. The exact analytical solutions for the electric potential distribution and the transient electro-osmotic flow velocity are derived by solving the nonlinear Poisson-Boltzmann equation and the Navier-Stokes equation. Based on these results, a systematic parametric study on the characteristics of the transient electro-osmotic flow is detailed. The general behavior of transient electro-osmotic flow in a cylindrical tube is similar to that observed in a microchannel containing an electrolyte solution. However, the steady-state electro-osmotic flow significantly deviates from the typical plug flow at higher surface charge and the rate of increase in the electro-osmotic mobility is strongly suppressed due to the effect of counterion condensation. In addition, the applicability limit of these solutions is also discussed.
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