Electrohydrodynamic Stability: Fluid Cylinders in Longitudinal Electric Fields

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Abstract
The stability of a fluid cylinder, stressed by an axial electric field, has heretofore been studied assuming that the cylinder and its surroundings behave as perfect dielectrics and viscous effects are ignored. With many fluids this is unrealistic since the existence of even a small conductivity implies that the deformed interface carries an electric charge. Upon deformation of the interface the charge interacts with the field to produce an electrical shearing stress. Thus, to avoid singular behavior viscous shear must be considered from the outset. The analysis is applicable to situations where the relaxation time for free charges is short compared with the time scale for fluid motion. It is found that electrical shearing forces can, under some conditions, completely stabilize the cylindrical interface to axisymmetric deformations. On the other hand, the conditions under which these same forces produce instability are delineated. In instances where both fluids have low viscosities a boundary layer effect produces additional damping and, in the presence of an axial electric field, electrical shearing stresses in this boundary layer may render an otherwise stable oscillation unstable.