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

Published online by Cambridge University Press:  07 April 2026

Anupam Choubey ,
Abhishek Kumar Singh  and
Supreet Singh Bahga Open the ORCID record for Supreet Singh Bahga [Opens in a new window]
Anupam Choubey
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Delhi , Hauz Khas, New Delhi, 110016, India
Abhishek Kumar Singh
Affiliation:
Department of Mechanical Engineering, Bennett University, Greater Noida, Uttar Pradesh, 201310, India
Supreet Singh Bahga*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Delhi , Hauz Khas, New Delhi, 110016, India
*
Corresponding author: Supreet Singh Bahga, bahga@mech.iitd.ac.in
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Abstract

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.

JFM classification

MHD and Electrohydrodynamics: Electrokinetic flows Micro-/Nano-fluid dynamics: Microfluidics Drops and Bubbles: Electrohydrodynamic effects

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JFM Papers
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Journal of Fluid Mechanics , Volume 1032 , 10 April 2026 , A64
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© The Author(s), 2026. Published by Cambridge University Press

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