Analysis of pulse electromagnetic electroosmotic flow of Jeffrey fluid through parallel plate microchannels under a constant pressure gradient

The purpose of this work is to investigate the pulse electromagnetic electroosmotic flow (EOF) behavior of a Jeffrey fluid in parallel plate microchannels under a constant pressure gradient. Analytical solutions for the velocity and volumetric flow rate are derived by employing the Laplace transform method and the residue theorem. In particular, the electric double layer (EDL) effect is considered, and an analysis is conducted on both the near-center and near-wall velocities. The flow periodicity is also noted, and these velocities are evaluated during the first and second half-cycles, respectively. Moreover, both 3D and 2D graphics are simultaneously utilized to visualize the impact of relevant parameters on velocity and volumetric flow rate. Our analysis yielded the following key findings: The effects of relevant parameters, such as pulse width a, pressure gradient omega, Hartmann number Ha, electric field strength fl, electrokinetic width K, relaxation time 11 and retardation time 12, on the near-center velocity during the first half-cycle align with the results of previous studies. During the second half-cycle, higher values of variables Ha and fl lead to reduced velocities. Interestingly, during any half-cycle, the near-wall velocity demonstrates similar characteristics to the near-center velocity in response to variations in certain parameters, including Hartmann number Ha, electric field strength fl, relaxation time 11 and retardation time 12. It is worth mentioning that the influence of relaxation time 11 and retardation time 12 on the near-wall velocity is largely independent of the Hartmann number, especially for the retardation time. Regardless of the values of the parameters 11 and 12, a higher volumetric flow rate is observed with an increased electrokinetic width K. Additionally, the volumetric flow rate profile of the Jeffrey fluid exhibits a comparatively smoother trend over time compared to that of the Maxwell fluid. The remarkable similarity between Jeffrey fluid and blood suggests that the results presented in this paper hold immense potential as a crucial reference for studying blood transport within the field of microfluidics.