Transient electro-osmotic flow of Oldroyd-B fluids in a straight pipe of circular cross section

The transient electro-osmotic flow of viscoelastic fluids in a narrow capillary tube is examined. With the help of integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It is shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The results of classical fluid, i.e., Newtonian fluid and those of Maxwell fluid and the second grade fluid can be obtained as the special cases of the results in present study. The effects of relaxation time and retardation time on the velocity profiles are analyzed numerically. It is pointed out that the electro-osmotic flow of viscoelastic fluids is more difficult to achieve the steady state.