Steady electro-osmotic flow of a micropolar fluid in a microchannel

We have formulated and solved the boundary-value problem of steady, symmetric and one-dimensional electro-osmotic flow of a micropolar fluid in a uniform rectangular microchannel, under the action of a uniform applied electric field. The Helmholtz-Smoluchowski equation and velocity for micropolar fluids have also been formulated. Numerical solutions turn out to be virtually identical to the analytic solutions obtained after using the Debye-Hückel approximation, when the microchannel height exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. For a fixed Debye length, the mid-channel fluid speed is linearly proportional to the microchannel height when the fluid is micropolar, but not when the fluid is simple Newtonian. The stress and the microrotation are dominant at and in the vicinity of the microchannel walls, regardless of the microchannel height. The mid-channel couple stress decreases, but the couple stress at the walls intensifies, as the microchannel height increases and the flow tends towards turbulence.