Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel**Supported by the National Natural Science Foundation of China under Grant Nos. 11772162 and 11472140, the Natural Science Foundation of Inner Mongolia Autonomous Region of China under Grant Nos. 2016MS0106 and 2018MS01015, the Inner Mongolia Grassland Talent under Grant No. 12000-12102013, the Research Program of science

Abstract

This paper investigates the magnetohydrodynamic (MHD) electroosmotic flow (EOF) of Newtonian fluid through a zeta potential modulated parallel plate microchannel with patterned hydrodynamic slippage. The driven mechanism of the flow originates from the Lorentz force generated by the interaction of externally imposed lateral electric field Ey and vertical magnetic field Bz and electric field force produced by an externally applied electric field Ex. It is assumed that the wall zeta potential and the slip length are periodic functions of axial coordinate x, an analytical solution of the stream function is achieved by utilizing the method of separation of variables and perturbation expansion. The pictures of streamlines are plotted and the vortex configurations produced in flow field due to patterned wall potential and hydrodynamic slippage are discussed. Based on the stream function, the velocity field and volume flow rate are obtained, which are greatly depend on some dimensionless parameters, such as slip length ls, electrokinetic width λ, the amplitude δ of the patterned slip length, the amplitude m of the modulated zeta potential and Hartmann number Ha. The variations of velocity and volume flow rate with these dimensionless parameters are discussed in details. These theoretical results may provide some guidance effectively operating micropump in practical nanofluidic applications.