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

We present an experimental and theoretical investigation of steady Taylor cone-jetting of highly viscous liquids at the minimum flow rate required for steady jetting. To achieve a steady cone-jet, the viscous liquid is flown through a conducting needle under the action of a strong electric field acting between the needle and a flat collector plate. Experiments reveal that the minimum flow rate and the corresponding jet diameter depend on both the needle diameter and the electrical conductivity of the liquid. Subsequently, we used the experimental measurements to formulate correlations among the minimum flow rate, the needle diameter and the physical properties of the liquid, including the electrical conductivity. To elucidate the underlying physics and experimental observations, we performed an order-of-magnitude analysis. The scaling analysis reveals that in the cone region, the viscous and interfacial tension forces are of comparable magnitude, while in the current transfer region, the viscous and electrostatic suction forces are the dominant resisting and driving forces, respectively. Subsequently, we theoretically derived the scaling relations for the minimum flow rate and the corresponding jet diameter by considering the balance of forces at the cone-tip and in the current transfer region. The empirical and theoretical scaling laws for the minimum flow rate and the corresponding jet diameter agree well for highly viscous liquids with electrical conductivity spanning over four orders of magnitude. Lastly, we present the limits that describe the regime for which the minimum flow rate depends on the needle diameter, and the derived scaling laws are applicable.