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In this paper, an investigation of the electroosmotic flow of fractional Oldroyd-B fluids in a narrow circular tube with high zeta potential is presented. The Navier linear slip law at the walls is considered. The potential field is applied along the walls described by the nonlinear Poisson-Boltzmann equation. It's worth noting here that the linear Debye-Hückel approximation can't be used at the condition of high zeta potential and the exact solution of potential in cylindrical coordinates can't be obtained. Therefore, the Matlab bvp4c solver method and the finite difference method are employed to numerically solve the nonlinear Poisson-Boltzmann equation and the governing equations of the velocity distribution, respectively. To verify the validity of our numerical approach, a comparison has been made with the previous work in the case of low zeta potential and the excellent agreement between the solutions is clear. Then, in view of the obtained numerical solution for the velocity distribution, the numerical solutions of the flow rate and the shear stress are derived. Furthermore, based on numerical analysis, the influence of pertinent parameters on the potential distribution and the generation of flow is presented graphically.Recently, electroosmosis is becoming a universal and an advantageous technique to actuate and control the flow in the micro devices, such as lab-on-a-chip devices, which are extensively used for analyzing and/or processing biofluids, polymeric solutions, colloidal suspensions, etc. [1-3]. These fluids usually exhibit the behavior of non-Newtonian fluids. Over the past few decades, various fruitful theoretical, numerical, and experimental investigations on the electroosmotic flow of non-Newtonian fluids have been carried out. It is worth mentioning here that Zhao and Yang [4] gave a comprehensive review of electrokinetics pertaining to non-Newtonian fluids. Also, we should point out to the earlier work of Das and Chakraborty [5] and Chakraborty [6], where they first investigated the non-Newtonian effects on the electroosmotic flow by using the power-law model. Berli and Olivares [7] used the power-law model, Bingham model, and Eyring model as the constitutive equations to study the electrokinetic flow of different non-Newtonian fluids in slit and cylindrical microchannels. The power-law model was also used in the literatures [8] and [9], in which the analytical solution for velocity Correspondence: Professor Haitao Qi,

The electro-osmotic flow of a non-Newtonian fluid in a slit micro-channel under the Navier's slip boundary condition is investigated. The Eyring constitutive relationship model is adopted to describe the non-Newtonian characteristics of the flow driven by the applied electric field force and pressure. In consideration of the micro-scale effects, electric field, non-Newtonian behavior and slip boundary condition, a mechanical model is built and the effects of these factors on the flow are studied. Analytical expressions are derived for the electric potential and velocity profile by solving the linearized Poisson-Boltzmann equation and the modified Cauchy equation. Approximate expressions of the velocity distribution are also given and discussed. Furthermore, by comparing the effects of electric force with that of pressure on the velocity distribution, some meaningful conclusions are drawn from the obtained graphics.