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

Abstract

Whether an electrified jet breaks up whilst the jet maintains a straight line (varicose), or alternatively the jet trajectory becomes chaotic (whipping), depends on the competition of the interfacial forces. Starting from the competition of normal stresses on the jet surface, we derive scaling laws in different electro-hydrodynamic operating regimes as a function of fluid properties and the flow rate. The onset of whipping occurs when this scaling function reaches a threshold, which is independent of the electric field strength. However, experimental evidence indicates that this onset condition applies only when the viscosity and electrical conductivity of a liquid are small enough. As a result, we further introduce a general parameter to incorporate viscous effects into the scaling law. A unified threshold value for this parameter is found through a substantial number of experiments for liquids having a wide range of properties, and under a wide variety of operational conditions of flow rate.

Mode-tunable, micro/nanoscale electrohydrodynamic deposition techniques for optoelectronic device fabrication

“…(i) Diagram of the whipping and varicose instability, where δ μ ∝ 1/μ, Γ ∝ E 2 . 38 Copyright 2019, American Physical Society.…”

Characterization of capillary waves: A review and a new optical method

“…In the latter system, sequential images are taken with incremental trigger delay to observe the phenomena and take measurements with time interval of the order of 10 µs [75]. This provides an inexpensive visualizing system which has been used, for instance, to study the role of capillary waves in the break-up regimes of electrified jet [29] and to measure the jet break-up length [28].…”

“…The surface elasticity has been introduced only relatively recently to the dispersion condition of jet waves by Noskov [1], who derived an equation that corrects Bohr's formula [87] used for the determination of the surface tension from the wave characteristics. Another important field of investigation are waves on charged surfaces, jets and droplets, which have important role in electrojetting (see, e.g., [28,29]). To characterize capillary waves, we built our own apparatus and developed a code to process the wave images captured in the experiment.…”

“…As a result, the fundamental understanding of the wave growth is essential for the control of the destabilization of multi-phase systems. The growth rate of waves at the surface of an electrified jet can be used to estimate the break-up length [28] and understand the transition from varicose to whipping instabilities in electrohydrodynamic jetting [29]. The ripples play a role in a number of surface phenomena, sometimes in a nonintuitive way.…”

Dripping, jetting and tip streaming

“…52). Using the scaling laws (72), Xia et al (2019) have found experimentally that whipping arises in the cone-jet mode of electrospray when the dimensionless number G = Γ 2 e δ 1/3 µ takes values above the threshold G 155.…”