Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel

The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Huckel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed.