The unsteady electroosmotic flow (EOF) for one kind of linear viscoelastic fluid, which is Jeffrey type fluid, is investigated under the common impact of vertical magnetic field, external electric field, and pressure at high Zeta potential in a circular microchannel. The numerical solutions of the potential and velocity distributions are obtained by solving the nonlinear Poisson-Boltzmann equation, the constitutive equation of the Jeffrey fluid, and the Cauchy momentum equation applying the Chebyshev spectral method and the finite difference method. By contrast, the Chebyshev spectral method has higher accuracy and less computation. The flow characteristics of Jeffrey fluid at high Zeta potential are analyzed with the numerical solution obtained by the Chebyshev spectral method. The results show that the velocity of Jeffrey fluid increases with the increase of the wall Zeta potential and electric width. The oscillation amplitude of velocity distribution increases with the increase of relaxation time but decreases with the increase of retardation time. When the Hartmann number is smaller, the increase of relaxation time leads to the increase of velocity; when the Hartmann number is larger, the increase of relaxation time leads to the decrease of velocity. No matter what the Hartmann number is, the velocity always decreases with the increase of the retardation time. The velocity tends to be stable gradually with the increase of time.

The electroosmotic flow of non-Newtonian fluid–Eyring fluid in microparallel pipes under high zeta potential driven by the combination of pressure and electric force is studied. Without using the Debye–Hückel (DH) linear approximation, the numerical solutions of the fluid potential distribution and velocity distribution obtained using the finite difference method are compared with the analytical approximate solutions obtained using the DH linear approximation. The results show that the numerical method in this article is effectively reliable. In addition, the influence of various physical parameters on the electroosmotic flow is discussed in detail, and it is obtained that the velocity distribution of the Eyring fluid increases with the increase in the electric potential under the high zeta potential.

In this article, the magnetofluid unsteady electroosmotic flow (EOF) of Jeffrey fluid with high zeta potential is studied by using the Chebyshev spectral method and the finite difference method. By comparing the potential distribution and velocity distribution obtained by the Chebyshev spectral method and finite difference method, it is concluded that the Chebyshev spectral method has higher precision and less computation. Then the numerical solution obtained by the Chebyshev spectral method is used to analyze the flow characteristics of Jeffrey fluid at high zeta potential. The results show that the velocity of Jeffrey fluid increases with the increase of the wall zeta potential and electric field intensity. The oscillation amplitude of velocity distribution increases with the increase of relaxation time, but decreases with the increase of retardation time. With the increase of Hartmann number, the velocity first increases and then decreases. The positive pressure gradient promotes the flow of fluid, and the reverse pressure gradient impedes the flow of fluid.

This paper studies the rotating electroosmotic flow of a power-law fluid with Navier slip boundary conditions under high zeta potential under 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 with an external magnetic field. When the behavior index <i>n</i>=1, the fluid obtained is a Newtonian fluid. The analysis results in this paper are compared with the analytical approximate solutions obtained by 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 velocityΩ, electric width <i>K</i> and slip parameters <i>β</i> on the velocity distribution is 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 increase of <i>Ha</i>.

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