Equilibrium shape and hysteresis behavior of liquid jets in transverse electric fields

• The stability of liquid jets under transverse electric fields is investigated.
• The jet is stable for permittivity ratios (jet/ambient) less than Scr ≈ 27.45.
• The jet shows hysteresis behavior for permittivity ratios greater than Scr.
• The energy minimization method is more accurate than the two-point method for jets.

The stability of a liquid jet subject to a transverse electric field is investigated in the framework of electrohydrostatic theory. It is shown that depending on the magnitude of permittivity ratio of the involved fluids S = εi/εo (inner to outer) compared to a critical permittivity ratio Scr ≈ 27.45 the jet exhibits distinct behaviors; for S < Scr the jet is stable and elongates indefinitely as the electric field is increased, while for S > Scr it shows hysteresis behavior and becomes unstable beyond a critical electric capillary number Cacr. The results suggest that the jets are generally more stable than liquid drops.