Talk about Several Time Periodic Pulse Electroosmotic Flow of Maxwell Fluid in a Circular Microchannel

Dongsheng Li,Kun Li

doi:10.4236/jamp.2021.94045

Abstract

Using the method of Laplace transform, analytical expressions are derived for the time periodic pulse electroosmotic flow (EOF) velocity of the triangle and sawtooth of Maxwell fluid in circular microchannel. The solution involves analytically solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations of inverse Laplace transform, the effects of electrokinetic width K, relaxation time and pulse width a on the above several pulse EOF velocities are investigated. In addition, we focused on the comparison and analysis of the formulas and graphs between the triangle and sawtooth pulse EOF with the rectangle pulse EOF. The study found that there are obvious differences in formulas and graphs between triangle and sawtooth pulse EOF with rectangle pulse EOF, and the difference mainly depends on the different definitions of the three kinds of time periodic pulse waves. Finally, we also studied the stability of the above three kinds of pulse EOF and the influence of relaxation time on pulse EOF velocity under different pulse widths is discussed. We find that the rectangle pulse EOF is more stable than the triangle and sawtooth pulse EOF. For any pulse, as the pulse width a increases, the influence of the relaxation time on the pulse EOF velocity will be weakened.

Highlights

IntroductionWhen an external electric field is applied to both ends of the channel, the ions in the electric double layer will move under the force of the electric field
We have obtained the semi-analytical solutions of the time periodic pulse electroosmotic flow (EOF) velocity of the triangle and sawtooth of Maxwell fluid through a circular microchannel, which rely mainly on electrokinetic width K, relaxation time λ1 and pulse width a
Because of the “fading memory” phenomenon of Maxwell fluid, increasing the relaxation time leads more to the variation of the pulse EOF velocity profiles caused by external electric field [36]

Summary

Introduction

When an external electric field is applied to both ends of the channel, the ions in the electric double layer will move under the force of the electric field This is due to the viscosity of the fluid itself, the moving free ions will drive the movement of nearby fluid clusters, and eventually form an electro-osmotic flow (EOF). A large number of theoretical and experimental studies [4]-[9] on the fully developed EOF problem of Newtonian fluids in various geometric shapes of microchannels have been completed. The target of this article is to derive the semi-analytical solutions of the above two time periodic pulse EOF for viscoelastic fluid.

Cauchy Momentum Equation and Constitutive Relation

Electric Potential Field Solution

The Analytical Solutions of the Cauchy Momentum Equation

Rectangle Pulse Wave

Results and Discussion

Conclusion