The trajectory and stability of a spiralling liquid jet: viscous theory

S. P. Decent*, A. C. King, M. J.H. Simmons, E. I. Pǎrǎu, I. M. Wallwork, C. J. Gurney, J. Uddin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)

Abstract

We examine a spiralling slender viscous jet emerging from a rapidly rotating orifice, extending Wallwork et al. [I.M. Wallwork, S.P. Decent, A.C. King, R.M.S.M. Schulkes, The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory, J. Fluid Mech. 459 (2002) 43-65] by incorporating viscosity. The effects of viscosity on the trajectory of the jet and its linear instability are determined using a mixture of computational and asymptotic methods, and verified using experiments. A non-monotonic relationship between break-up length and rotation rate is demonstrated with the trend varying with viscosity. The sizes of the droplets produced by this instability are determined by considering the most unstable wave mode. It is also found that there is a non-monotonic relationship between droplet size and viscosity. Satellite droplet formation is also considered by analysing very short wavelength modes. The effects of long wavelength modes are examined, and a wave which propagates down the trajectory of the jet is identified for the highly viscous case. A comparison between theoretical and experimental results is made, with favourable agreement. In particular, a quantitative comparison is made between droplet sizes predicted from the theory with experimental observations, with encouraging agreement obtained. Four different types of break-up are identified in our experiments. The experimentally observed break-up mechanisms are discussed in light of our theory.
Original languageEnglish
Pages (from-to)4283-4302
Number of pages20
JournalApplied Mathematical Modelling
Volume33
Issue number12
Early online date18 Mar 2009
DOIs
Publication statusPublished - Dec 2009
Externally publishedYes

Keywords

  • Rotation
  • Jet
  • Stability
  • Surface tension
  • Viscous

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'The trajectory and stability of a spiralling liquid jet: viscous theory'. Together they form a unique fingerprint.

Cite this