Absolute-convective instability transition of low permittivity, low conductivity charged viscous liquid jets under axial electric fields

The linear spatiotemporal instability of a charged viscous jet of low permittivity, low conductivity liquid under axial electric field is studied here. The local convective-absolute (C-A) instability transition is explored in the four-dimensional parameter space of the Reynolds number, Weber number, electrical Bond number, and externally applied tangential electric field. The locations where the C-A instability transition occurs in the four-dimensional space are identified (i.e., determining the critical Weber number) for both the axisymmetric and the first non-axisymmetric modes, covering a wide range of Reynolds numbers, electrical Bond numbers, and tangential electric field values. In contrast with the case of an uncharged jet, the C-A transition can be suppressed by the electric field at large Reynolds numbers for the axisymmetric mode, whereas the C-A transition for the first non-axisymmetric mode is always promoted by the electrical Bond number and the tangential electric field. We delimit the regions where the C-A transition is (i) always non-axisymmetric (which leads to local whipping) independent of the value of the applied tangential electric field or (ii) always axisymmetric (which leads to local dripping) below a certain charge level (electrical Bond number). The regions where one can have axisymmetric or non-axisymmetric C-A transition depending on the values of the jet charge and applied electric field are also described. The comparison of theoretical predictions with published experiments strongly supports the validity of the models proposed. These results provide the fundamentals to predict whether jetting-dripping or jetting-whipping transition can be expected in applications involving liquids of poor electrical conductivity and permittivity like many polymers, oils, and several solvents. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3637638]