Rotational electroosmotic slip flow of power-law fluid at high zeta potential in variable-section microchannel

Abstract

In this paper we study the rotating electroosmotic flow of a power-law fluid with Navier slip boundary conditions under high zeta potential subjected to the action of a vertical magnetic field in a variable cross-section microchannel. Without using the Debye–Hückel linear approximation, the finite difference method is used to numerically calculate the potential distribution and velocity distribution of the rotating electroosmotic flow subjected to an external magnetic field. When the behavior index <inline-formula><tex-math id="M4">\begin{document}$n = 1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M4.png"/></alternatives></inline-formula>, the fluid obtained is a Newtonian fluid. The analysis results in this paper are compared with the analytical approximate solutions obtained in the Debye–Hückel linear approximation to prove the feasibility of the numerical method in this paper. In addition, the influence of behavior index <i>n</i>, Hartmann number <i>Ha</i>, rotation angular velocity <inline-formula><tex-math id="M5">\begin{document}$\Omega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M5.png"/></alternatives></inline-formula>, electric width <i>K</i> and slip parameters <inline-formula><tex-math id="M6">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M6.png"/></alternatives></inline-formula> on the velocity distribution are discussed in detail. It is obtained that when the Hartmann number <i>Ha</i> > 1, the velocity decreases with the increase of the Hartmann number <i>Ha</i>; but when the Hartmann number <i>Ha</i> < 1, the magnitude of the <i>x</i>-direction velocity <i>u</i> increases with the augment of <i>Ha</i>.