Effect of ionic diffusion on microscale electrohydrodynamic conduction pumps

Abstract

In this work, we investigate microscale electrohydrodynamic (EHD) conduction pumps of dielectric liquids in a wide working regime range from the Ohmic to the saturation regime. We show that the electric force of microscale EHD conduction pumps differs from that of macroscale EHD conduction pumps owing to the scale effect. We reveal that the scale effect of microscale EHD conduction pumps is triggered by the enhanced ionic diffusion. When the characteristic length of the system reduces from millimeter to micrometer, the maximum order of magnitude of α increases from O(10−5) to O(10−1), resulting in significantly enhanced ionic diffusion; however, the ionic diffusion can be neglected for macroscale EHD conduction pumps, where α denotes the ratio of ionic diffusion velocity to ionic migration velocity. We found that the existing macroscale theoretical models do not work for the microscale EHD conduction pumps due to the rough estimation of heterocharge layer thickness. We show that the heterocharge layer thickness of microscale EHD conduction pumps not only depends on ionic migration but also relies on ionic diffusion. By modifying the expression of the heterocharge layer thickness with respect to ionic migration and diffusion, we develop a theoretical model of dimensionless electric force for the microscale EHD conduction pumps.

Working Regime Criteria for Microscale Electrohydrodynamic Conduction Pumps

“…There is a distinct difference between the scaling law of electric force in the two working regimes. In the ohmic regime, the dimensionless electric force F * follows F * ≈ 1/ C 0 ; however, in the saturation regime, the dimensionless electric force F * obeys F * ≈ C 0 . It should be noted that the dimensionless number C 0 = σ 0 d /2 KE 0 ε cannot distinguish the working regimes for all the cases.…”

“…The dimensionless numbers in eqs to are given by, where C 0 is the conduction number used to distinguish the work regimes, α is the dimensionless diffusion coefficient indicating the relative intensity of diffusion compared to migration triggered by an electric field, Re E is the Reynolds number built with the migration velocity of ions, and M is the mobility number indicating the ratio of the hydrodynamic mobility and the ionic mobility. To quantify the diffusion effect without changing with E 0 , Wang et al proposed a dimensionless number to characterize the diffusion effect of a given EHD conduction, where k represents the ratio of diffusion length caused by ionic thermal motion to the characteristic length of the system.…”

“…In the ohmic regime, the dimensionless electric force F* follows F* ≈ 1/C 0 ; however, in the saturation regime, the dimensionless electric force F* obeys F* ≈ C 0 . 28 It should be noted that the dimensionless number C 0 = σ 0 d/2KE 0 ε cannot distinguish the working regimes for all the cases. For example, the Onsager− Wien effect would occur for the cases of large E 0 , resulting in increased conductivity σ 0 due to the enhanced dissociation rate.…”

“…However, these studies have not demonstrated the reason for the failure. A very recent study 28 has clarified the reason by numerically investigating the dimensionless electric force of microscale EHD conduction pumps in a wide range of C 0 . The authors point out that the failure of macroscale theoretical models is attributed to the enhanced diffusion effect caused by the decrease in the characteristic length d. For macroscale conduction pumps, the diffusion effect is negligible because the dimensionless number α = D/KE 0 d is much smaller than 1.…”

“…Therefore, there is an urgent need to develop a new theoretical model for microscale EHD conduction pumps, especially in the cases of larger C 0 . Furthermore, based on the existing microscale studies, , it is reasonable to speculate that the existing dimensionless numbers C 0 and C 0 E cannot distinguish the working regimes of the microscale EHD conduction pumps due to the different ionic transport mechanism caused by the diffusion effect. Unfortunately, there is still no reliable dimensionless number to distinguish the working regimes of microscale EHD conduction pumps.…”