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Unipolar charge current can be generated through corona discharge from a thin wire enclosed in a shield electrode. Except for an ionization sheath adjacent to the coronating wire surface, most parts of the region in the enclosing shield contain drifting ions of a single polarity in response to the electric field. Momentum transfer as a consequence of collisions between drifting ions and electrically neutral air molecules gives rise to the electrohydrodynamic flow known as “corona wind.” Although primarily driven by the Coulomb force due to unipolar charge in the electric field, the electrohydrodynamic flow cannot simply follow the direction of electric field lines because of the confinement of the solid walls of the shield. Therefore, the structure of the electrohydrodynamic flow can vary significantly depending on the system configuration. In the present work, the electrohydrodynamic flow in a rectangular shield is studied by solving the nonlinearly coupled governing equations via the Galerkin finite-element method. A highly symmetric system with the wire positioned at the center of a square shield is shown to contain eight equal-sized, two-dimensional recirculation vortices. The number of recirculation vortices tends to be reduced by a slight asymmetry in the system. The flow structure of two major counter-rotating recirculation vortices is found to be most common in systems where the wire is positioned off the center of the rectangular shield in a two-dimensional domain. The results reported here may be brought to bear upon the “corona wind” effect in charging devices such as corotrons and scorotrons used in electrophotographic printing processes. © 1999 American Institute of Physics.