| An electrohydrostatic analysis of the Taylor cone model, using both the Taylor and Zeleny stability criteria has revealed several inconsistencies in the model. It is shown that a dynamical treatment of the equilibrium shape and stability can resolve these apparent contradictions in the Taylor model. Specifically, using the linearized electrohydrodynamic equations with corrections up to first-order, it is shown that, at the onset of instability, the cone deforms into a cuspidal shape. From the dispersion relations, the critical voltage for the onset of instability is obtained for liquid gallium. The calculated value of 5.8 kV compares well with experimental values of ~4-7 kV. Finally, the instability is predicted to be highly localized, which agrees with the experimental observations in the TEM images or Sudraud, et. al. |
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