Recent and earlier models of electrical field flow fractionation (ELFFF) have assumed that the electric field within the fluid domain is governed by Laplace's equation. This assumption results in a linear potential and a spatially constant field across the channel and is generally true for very dilute systems and relatively high effective potentials. Experimental studies show, however, that the effective potential within the channel may be less than 1% of the applied potential; this is apparently due to double layer formation and charge buildup at the poles. In such cases, local analyte concentrations can, nonetheless, be orders of magnitude higher than the bulk mean and the local potential small, both of which can lead to a nonlinear spatial distribution of the field strength. In such cases Poisson's equation must be used rather than Laplace's equation. Steady-state ELFFF simulations were performed using a Poisson's equation-based model. The domain in which Laplace's equation is valid was identified and the effects of concentration and effective field strength on device performance were explored.