Electrohydrodynamic assisted atomization (EHD) injects electrical charges into liquid within the injector nozzle, creating an electrically charged atomizing liquid. For many relevant engineering flows, including liquid fuel injection, the charge mobility time scale (time it takes the charges to relax to the fluid-gas boundary) is similar in magnitude to the charge convection time scale (relevant flow time), which leads to a nontrivial electric charge distribution. This distribution within the liquid fuel may enhance atomization, the extent to which is dependent on the ratio of the previous time scales which are known as the electric Reynolds number (Re-e). In this work, a computational approach for simulating two-phase EHD flows is used to investigate how Ree influences the resulting atomization quality. The computational approach is second order, conservative, and used to consistently transport the phase interface along with the discontinuous electric charge density and momentum. The scheme sharply handles the discontinuous electric charge density, allowing robust and accurate simulations of electric charge relaxation. Using this method, multiple three-dimensional simulations are performed with varying Ree values which highlight the effect of Ree on the atomization efficiency of a liquid jet. Comparison of these cases shows the importance of Ree on atomization and suggests that decreasing Ree (increasing charge mobility) leads to larger electric charge densities, increased Coulomb forces, and ultimately improved breakup during the atomization process.