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

• Published in: Applied mathematical modelling 2009-12, Vol.33 (12), p.4283-4302
• Main Authors: Decent, S.P., King, A.C., Simmons, M.J.H., Părău, E.I., Wallwork, I.M., Gurney, C.J., Uddin, J.
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Drops and bubbles; Exact sciences and technology; Fluid dynamics; Fluid surfaces and fluid-fluid interfaces; Fundamental areas of phenomenology (including applications); Jet; Nonhomogeneous flows; Physics; Rotation; Stability; Surface energy (surface tension, interface tension, angle of contact, etc.); Surface tension; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Viscous
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2009.03.011

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.