## 1 Introduction  
For a long time, many researchers have been studying the peristaltic transport in fluid mechanics to find its significance in biological science (generally) and hydrodynamics (especially). A peristaltic transport is created by wave propagation along the flexible wall of the channel. This mechanism exists in many biological systems with smooth muscles tubes e.g., the movement of food in the digestive tract, urine transport, blood circulation in small blood vessels, and so on. Most importantly, peristaltic transport is a critical step in the reproduction of life itself. The literature for this topic (for different fluids and different channels) is quite extensively examined in the past. [PERSON] and [PERSON] [1] worked on the Pseudo-plastic fluid with viscous dissipation and Hall current effects. [PERSON] et al. [2] observed the peristaltic motion of MHD Jeffrey fluid in asymmetric conduit. [PERSON] and [PERSON] [3] analyzed the impact of the magneto-hydrodynamic peristaltic transport for Dufour and Soret effects by using thermal radiation and chemical reaction in a porous medium. [PERSON] [4] examined the electro-magneto-hydrodynamic peristaltic transport of Couple-Stress fluid along Joule heating and convective boundary conditions. Moreover, [PERSON] et al. [5] proposed the peristaltic motion model for walters-b fluid with thermal radiations and slip conditions. The peristaltic modulation of Jeffrey fluid in an inclined channel with a Newtonian fluid was scrutinized by [PERSON] et al. [6]. The peristaltic flow of Eyring-Powell nanofluid model in the asymmetric conduit was investigated by [PERSON] [7]. Also, [PERSON] et al. [8] explained the propulsion of Ree-Eyring fluid through a peristaltic duct. [PERSON] et al. [9] found the gold nanoparticles in the catheter as a third grade nanofluid. [PERSON] et al. [10] considered that the slip effects in an inclined peristaltic tube for Casson fluid. Electroosmosis is one of the main electrokinetic phenomena. It mentions the flow of an ionic solution that is tangent to the charged surface with an electric field application. The ionic species in the charged interface layer (called as electric double layer, EDL) are enforced to move due to an external electric field, which activates the movement of solvent molecules by viscous drag, resulting in Electroosmotic transport. Despite tremendous advances in the direct modeling of peristaltic flow, there has been relatively little interest in increasing the possibilities of peristaltic flow through unrelated measures. One such example is the addition of peristaltic flow by electroosmosis [11]. Microfluidic is one of the most important research areas in micro-electro-mechanical potential (MEMS) application as a tool for studying fundamental biochemical and physical processes and also a platform for performing biological and chemical assays. Lab-on-chip (LOC) is a micro-scale lab on a microchip that allows for clinical diagnosis. LOC devices are becoming more and more popular due to its outstanding nature for flow characteristics of common bio-fluids in the microchannel. In most of the studies of electroosmotic flows EOF, electroosmotic pressure-driven media is used as Newtonian fluid, which is reasonable considering that most of the electrolyte or buffer solutes used in microfluidic devices are in fact Newtonian fluids. Though, microfluidic systems also require the production of EOF from Non-Newtonian fluids that control organic fluids such as saliva, blood and DNA solutions. In the theoretical studies of this case, suitable Non-Newtonian constitutive relationships should be considered to predict EOF. Since most bio-fluids such as blood are considered as Non-Newtonian, it is necessary to study the behavior of such fluids under the influence of electro-osmotic forces for accurate LOC design. As electroosmotic micro-mixing was found more practical and efficient in micro-scale mixing of Pseudoplastic fluids (including Carreau fluid) rather than those Newtonian and different ones.