Onset condition of the ramified-jet regime: an experimental and theoretical study

Abstract

This study experimentally and theoretically investigates the electrically induced transition of a gas-focused liquid jet into a rim-emitting sheet. Ultra-high-speed imaging was used to examine the effects of applied voltage, gas and liquid flow rates, and liquid properties on sheet formation and breakup. Fully developed, quasi-stable sheets formed with ethanol, whereas isopropanol exhibited only initial sheet formation. Increasing voltage promoted sheet stretching, finer and more numerous rim jets, and a narrower spray. Higher gas flow rates shifted the transition towards the nozzle and produced finer structures, while higher liquid flow rates generated larger sheets with thicker rims. A first-order theoretical model assumes an equipotential interface and neglects finite charge relaxation, hydrodynamic perturbations, and nonlinear evolution. It balances destabilizing Maxwell-pressure perturbations against restoring capillary-pressure perturbations on a conducting cylindrical jet. The model identifies the elliptic azimuthal mode, m = 2, as the first unstable mode leading to sheet formation and predicts a critical electric Bond number of 3. Predicted onset voltages agree with measurements within 20%, and the threshold was consistent with published ramified-electrospray observations. The agreement with experiments supports electrocapillary symmetry breaking as the mechanism of onset and provides a compact, physically grounded criterion for predicting the transition from electrified jets to rim-emitting sheets.