Minimum flow rate of Taylor cone-jets of highly viscous liquids

Applying a high voltage to a liquid meniscus held at the exit of a metallic nozzle can deform the spherical meniscus to a conical shape, known as the Taylor cone, whose tip emits a fine jet. Steady cone-jetting is essential for applications such as electrospinning and electrohydrodynamic jet printing. However, steady jetting occurs only above a minimum imposed flow rate. It is well documented that this minimum flow rate for less viscous liquids is independent of the nozzle diameter and depends only on the properties of the liquid. In this work, using experiments and scaling analysis, we show that the minimum flow rate of highly viscous liquids, such as salt-doped glycerol, scales with the square of the nozzle diameter, besides depending on the liquid properties. We derive the scaling relations for the minimum flow rate and the corresponding jet diameter by balancing the viscous and the interfacial forces in the cone region and inertia and electrostatic suction forces in the cone-to-jet transition region. The derived scaling relations for the minimum flow rate and the corresponding jet diameter compare well with the experimental data without the need for any fitting parameter for highly viscous solutions with electrical conductivity varying over four orders of magnitude.