Analytical Solution of Electrokinetics Driven Flow in a Nanotube with Power Law Fluid by HPM Davood D. Ganji 1,a , Mofid Gorji–Bandpy 1,b and Mehdi Mostofi 2,c 1 Department of Mechanical Engineering, Babol Noshiravani University of Technology, P.O. Box 484, Babol, Iran. 2 Department of mechanical Engineering, East Tehran Branch, Islamic Azad University, Tehran, Iran. a ddg_davood@yahoo.com, b gorji@nit.ac.ir, c mehdi_mostofi@yahoo.com Keywords: Electroosmotics, Power Law Fluid, HPM, Zeta Potential. Abstract. In this paper, Poisson-Boltzmann equation and Navier-Stokes equation will be solved by Homotopy Perturbation method (HPM). Zeta potential that is used for the potential in near wall area of a tube will be small enough in order to use some simplifications. In this paper, Poisson- Boltzmann equation for a 30 nm diameter nanotube with large zeta potential has been solved by Homotopy Perturbation Method (HPM). According to the literature, results have been compared with numerical solutions and consistency of the results has been considered. Introduction In recent decades, after introducing micro- and nano-fabrication technologies, several possibilities in the case of micro- and nano-fluidic devices have been invented. This idea has been followed by some modern technologies such as Lab-on-a-Chip. One of the most important subsystems of the micro- and nano-fluidic devices is their passage or “Micro- and nano-channel”. Nano-channel term is referred to channels with hydraulic diameter below 100 nm. [1]. By decrease in size and hydraulic diameter some of the physical parameters such as surface tension will be more significant while they are negligible in normal sizes. Concentrating surface loads in liquid – solid interface makes the Electric Double Layer (EDL) to be existed. The first significant work that was done in the literature belongs to 1870 that Helmholtz introduced the EDL. According to this finding, flow and electricity parameters for electroosmotic transport were detected. Electroosmotic processes have been utilized since 1930s. Modern theoretical progresses in the case of electroosmotic flow can be found in [2-6]. Burgreen and Nakache [2] and Oshima and Kondo [3] studied the flow between two parallel plates. Also, Rice and Whitehead [4], Lo and Chan [5] and Ke and Liu [6] studied the flow in capillary tube. Solving the problem considering this fact is necessary. In most of these cases, based on the application case, working fluid is an ordinary one and assumed to be Newtonian. However, in some important cases, non- Newtonian fluids are in existence such as polymers, colloids and suspensions. The tow more important applications of the complex fluids for electroosmotic phenomena are fuel cells and biomedical issues. Berli and Olivares [7] showed that for non-Newtonian fluids, some theoretical calculations can be made. They solved electroosmotic phenomena in existence with pressure gradient for some specific complex fluids in a microchannel. Zimmerman et. al. [8] studied the electroosmotic flow in a T-junction by numerical approach. Chakraborty [9] studied blood as a non- Newtonian bio- fluid in a microchannel by analytical approach. He also investigated several aspects of electroosmotic phenomena and their influences on the flow regime. Electrophoresis as the other important phenomenon in electroosmotic studies was investigated by Lee et. al. [10]. In addition, HPM solution in nanoscale electrokinetic flow has limited history. Ganji et al. [11] incetigated electrokinetic phenomena in nanotube with Newtonian fluid.