Two-dimensional instability response of an electrified viscoelastic planar liquid sheet subjected to unrelaxed axial elastic tension

The viscoelastic liquid sheet can present novel, if reasonable, behavior when subjected to noticeable unrelaxed axial tension, which has not been considered in previous studies on electrospraying. The temporal instability of electrified viscoelastic planar liquid sheets, subjected to unrelaxed axial tension, is investigated here for varicose and sinuous disturbances. The Oldroyd eight-constant model is used to describe the rheological characteristics of the viscoelastic fluids. The corresponding dispersion relation between wave growth rate and wave number is derived using linear analysis. From inspection of the analysis, the present theory suggests that electrified viscoelastic sheets with reasonable values of parameters can behave with greater stability than corresponding Newtonian sheets for varicose disturbances and sinuous disturbances; this coincides with most experimental evidence that the addition of polymers generally stabilizes the liquid sheet and delays breakup. In addition, an electrified viscoelastic liquid sheet can be stabilized by decreasing the electrical Euler number or increasing the distance between the flat electrode and the liquid sheet.