Effect of patterned hydrodynamic slip on electromagnetohydrodynamic flow in parallel plate microchannel* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11772162 and 11472140), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2016MS0106 and 2018MS01015), and the Inner Mongolia Grassland Talent, China (Grant No. 12000-12102013).

Abstract

A fully developed electromagnetohydrodynamic (EMHD) flow through a microchannel with patterned hydrodynamic slippage on the channel wall is studied. The flow is driven by the Lorentz force which originates from the interaction between an externally imposed lateral electric field and a perpendicular magnetic field. The governing equations for the velocity with patterned slip boundary conditions are solved analytically by perturbation techniques under the assumption of small Reynolds number Re. In addition, the numerical solutions for the velocity are obtained by using the finite-difference method, and they are found to be in good agreement with the analytical solutions within admissible parameter range. The effects of different parameters on the velocity and volume flow rate due to patterned hydrodynamic slippage are discussed in detail, including wave-number K, Hartmann number Ha, amplitude δ of the patterned slip length, and normalized electric field strength S. The results show that patterned slippage over microchannel walls can induce transverse flows, which will increase the mixing rates in microfluidic devices. In addition, we also find that precise flow control can be achieved by controlling the magnetic flux and the wave-number and also by well choosing the electric field intensity. Our analysis can be used for designing the efficient micro-fluidic mixers.