The plasma sheath near a probe surface is a non-neutral, non-equilibrium flow. Two implementations of a non-neutral detailed model electron fluid are compared in this study. Both formulations derive from the electron conservation laws and the electrostatic Poisson equation, but differ in the usage of the Poisson equation. The first implementation (detailed formulation) uses the Poisson equation to compute electron density from the plasma potential. The second implementation (Poisson-consistent

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... ormulation) explicitly solves the Poisson equation for potential. Both formulations are incorporated as part of a hybrid fluid Particle In Cell computational code, which is used for simulation of the axisymmetric plasma flow in the sheath near a Faraday probe. The two implementations produce markedly different results for the extent of the sheath. The Poissonconsistent formulation is in good agreement with the collisionless Bohm sheath solution, but the detailed formulation predicts more compact sheaths. The Poisson-consistent formulation is more computationally sensitive: the ion distribution must be primarily at speeds greater than the Bohm velocity to avoid spurious pseudo-presheath structures. The Poisson-consistent formulation also requires nearly 50% more time than the detailed formulation to complete a simulation. Differences between the Poisson-consistent formulation and the detailed formulation may stem from differing techniques to compute a non-linear term in electron density.