Scaling Laws for Transition from Varicose to Whipping Instabilities in Electrohydrodynamic Jetting

The manner in which an electrified jet breaks up is a key point in many applications, such as direct writing, electrospinning, and electrospray mass spectrometry. Controlling the instability mode of an electrified jet is always challenging, though, as there are many governing parameters. This study presents a robust, easy-to-use model to predict the transition from the axisymmetric (varicose) mode to the nonaxisymmetric (whipping) mode. The authors derive scaling laws based on competition of surface stresses in different electrohydrodynamic operating regimes, as a function of fluid properties and flow rate, and experiments on a variety of liquids reveal a unified threshold value.