Effect of ionic diffusion on microscale electrohydrodynamic conduction pumps

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.