A revision on Rayleigh capillary jet breakup

TL;DR

This paper revises the understanding of Rayleigh capillary jet breakup, emphasizing the role of invariant modes with positive and negative group velocities in determining breakup length, supported by experimental validation.

Contribution

It introduces a new theoretical framework based on invariant modes with different group velocities to explain jet breakup length independence and proportionality.

Findings

Breakup length is independent of ambient conditions due to long-term resonance.

Breakup length is proportional to the inverse of the dominant positive group velocity IM's growth rate.

Experimental results since 1965 support the proposed model.

Abstract

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity $\hat{U}$ (negligible external forces) must be determined by the selection of normal modes with time-independent amplitude and wavelength (invariant modes, IMs). Both positive and negative group velocity IMs exist in ample ranges of the parameter domain (Weber and Ohnesorge numbers), which explains (i) the average breakup length independence on ambient conditions (long-term resonance), and (ii) its proportionality to the inverse of the spatial growth rate of the dominant positive group velocity IM. Published experimental results since Grace (1965, PhD Thesis) confirm our proposal.