The Fluid Dynamics of Taylor Cones

TLDR

Cone‑jet formation in liquids with conductivities above 10⁻⁴ S m⁻¹ has been reviewed for steady menisci and transient Coulomb fissions, noting that Taylor’s hydrostatic model underpins but does not strictly apply, and that jet structure depends critically on the charge‑transport model, which has largely assumed constant conductivity. Saville’s generalized model predicts rarefaction fronts and wide space‑charge regions near the surface in polar liquids at low flow rates, while conventional scaling laws fail at conductivities around 1 S m⁻¹ due to ion evaporation, and molten salts and liquid metals exhibit a purely ionic emission regime without drop or jet formation.

Abstract

The formation of cone-jets in charged liquids with electrical conductivities larger than 10 −4 S/m is reviewed for steady supported menisci and transient Coulomb fissions in charged drops. Taylor's hydrostatic model does not apply strictly, but it forms the basis for subsequent developments. The jet structure is critically dependent on the model used for charge transport, which has been based mostly on a constant conductivity assumption. Saville's (1997) more general model predicts the formation of rarefaction fronts with wide space charge–dominated regions near the liquid surface, which apparently do arise in polar liquids near the minimum flow rate. Known approximate scaling laws for the jet break down at electrical conductivities of about 1 S/m due to ion evaporation from the meniscus. In molten salts and liquid metals a regime of purely ionic emissions exists without drop or jet formation.