This paper presents the results of the numerical simulation of the through electrohydrodynamic (EHD) flow in a symmetric system of electrodes placed in a channel with dielectric walls and filled with a liquid dielectric. Based on this model, we study the changes in the structure of the through flow at different levels of the low-voltage conduction of the dielectric fluid. The analysis of the solutions shows that the flow structure with conductivities up to 10-11 S/m hardly differs from the case of the zero conduction. The recombination of the charge grows at the larger values of the low-voltage conduction in the near-electrode layers, resulting in the lower penetration of the injected charge into the bulk and reorganization of the kinematics of the arising EHD through flow, which is reflected in a shift of the acceleration zone towards the active electrode. © 2014 Allerton Press, Inc.