Working Regime Criteria for Microscale Electrohydrodynamic Conduction Pumps

We investigated the microscale electrohydrodynamic (EHD) conduction pumps in a wide range of working regimes, from the saturation regime to the ohmic regime. We showed that the existing macro- and microscale theoretical models could not accurately predict the electric force of microscale EHD conduction pumps, especially for the cases of a strong diffusion effect. We clarified that the failure is caused by a rough estimate of the heterocharge layer thickness. We revised the expression of heterocharge layer thickness by considering the diffusion effect and developed a new theoretical model for the microscale EHD conduction pumps based on the revised expression of heterocharge layer thickness. The results showed that our model can accurately predict the dimensionless electric force of the microscale EHD conduction pumps even for the cases of a strong diffusion effect. Furthermore, we developed a working regime map of microscale EHD conduction pumps and found that the microscale EHD conduction pumps more easily fall into the saturation regime compared with the macroscale EHD conduction pumps due to the enhanced diffusion effect; in other words, the microscale EHD conduction pumps have a wider saturation regime. We showed that the conduction number C₀ could not distinguish the working regime of the microscale EHD conduction pumps because it does not take the diffusion effect into account. By employing the revised expression of heterocharge layer thickness, we proposed a new dimensionless number, C₀^D to distinguish the working regimes of microscale EHD conduction pumps.