Magnetohydrodynamic Electroosmotic Flow In Zeta Potential Patterned Micro-parallel Channels

Two dimensional magnetohydrodynamic(MHD)electroosmotic flow(EOF)in a zeta potential patterned micro-parallel channel is performed.The flow of fluid is driven by the combination of Lorentz force and electric field force due to externally imposed vertical magnetic field and two horizontal electric fields.The analytical solutions of stream function and velocity distribution are obtained under the condition of hydrodynamic slippage.The variations of velocities with related non-dimensional parameters,such as Hartmann number Ha,slip length B,electrokinetic width K,are addressed in detail.Results show that the patterned charged surfaces will induce a vertical velocity component,which leads to the formation of the vortexes.Also,the magnitudes of velocities increase with slip length B and electrokinetic width K.Moreover,it is interesting to note that the magnitudes of velocities become small with the increasing value of Ha,unlike the situation where there exists a critical value of the Ha in one dimensional flow.The present theoretical results can be utilized to design the efficient microfluidic devices.