Analytical solution of the transient electro-osmotic flow of a generalized fractional Maxwell fluid in a straight pipe with a circular cross-section

摘要

In this study, we examine the transient electro-osmotic flow of a generalized Maxwell fluid with a fractional derivative in a narrow capillary tube. Using the 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. We show that the distribution and establishment of the velocity comprises two parts: the steady and unsteady parts. We demonstrate the effects of the relaxation time, fractional derivative parameter, and the Debye-Hilckel parameter on the generation of flow in a graphical manner and we analyze them numerically. The velocity overshoot and oscillation are observed and discussed. (C) 2015 Elsevier Masson SAS. All rights reserved.