The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory

I. M. WALLWORK; S. P. DECENT; A. C. KING; R. M. S. M. SCHULKES

doi:10.1017/S0022112002008108

Abstract

We examine a spiralling slender inviscid liquid jet which emerges from a rapidly rotating orifice. The trajectory of this jet is determined using asymptotic methods, and the stability using a multiple scales approach. It is found that the trajectory of the jet becomes more tightly coiled as the Weber number is decreased. Unstable travelling wave modes are found to grow along the jet. The breakup length of the jet is calculated, showing good agreement with experiments.

Information

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Decent, S.P. King, A.C. and Wallwork, I.M. 2002. Free jets spun from a prilling tower. Journal of Engineering Mathematics, Vol. 42, Issue. 3-4, p. 265.

Wong, D.C.Y. Simmons, M.J.H. Decent, S.P. Parau, E.I. and King, A.C. 2004. Break-up dynamics and drop size distributions created from spiralling liquid jets. International Journal of Multiphase Flow, Vol. 30, Issue. 5, p. 499.

Partridge, L. Wong, D.C.Y. Simmons, M.J.H. Părău, E.I. and Decent, S.P. 2005. Experimental and Theoretical Description of the Break-up of Curved Liquid Jets in the Prilling Process. Chemical Engineering Research and Design, Vol. 83, Issue. 11, p. 1267.

Părău, E.I. Decent, S.P. King, A.C. Simmons, M.J.H. and Wong, D.C. 2006. Nonlinear travelling waves on a spiralling liquid jet. Wave Motion, Vol. 43, Issue. 7, p. 599.

Decent, S. P. 2006. On the instability of microjets. Continuum Mechanics and Thermodynamics, Vol. 17, Issue. 7, p. 525.

Uddin, J. Decent, S. P. and Simmons, M. J. 2006. The Instability of Shear Thinning and Shear Thickening Spiralling Liquid Jets: Linear Theory. Journal of Fluids Engineering, Vol. 128, Issue. 5, p. 968.

Părău, E. I. Decent, S. P. Simmons, M. J. H. Wong, D. C. Y. and King, A. C. 2007. Nonlinear viscous liquid jets from a rotating orifice. Journal of Engineering Mathematics, Vol. 57, Issue. 2, p. 159.

Uddin, J. Decent, S.P. and Simmons, M.J.H. 2008. Non-linear waves along a rotating non-Newtonian liquid jet. International Journal of Engineering Science, Vol. 46, Issue. 12, p. 1253.

Panda, Satyananda Marheineke, Nicole and Wegener, Raimund 2008. Systematic derivation of an asymptotic model for the dynamics of curved viscous fibers. Mathematical Methods in the Applied Sciences, Vol. 31, Issue. 10, p. 1153.

Eggers, Jens and Villermaux, Emmanuel 2008. Physics of liquid jets. Reports on Progress in Physics, Vol. 71, Issue. 3, p. 036601.

Uddin, Jamal and Decent, Stephen P. 2009. Curved Non-Newtonian Liquid Jets With Surfactants. Journal of Fluids Engineering, Vol. 131, Issue. 9,

Decent, S.P. King, A.C. Simmons, M.J.H. Părău, E.I. Wallwork, I.M. Gurney, C.J. and Uddin, J. 2009. The trajectory and stability of a spiralling liquid jet: Viscous theory. Applied Mathematical Modelling, Vol. 33, Issue. 12, p. 4283.

MARHEINEKE, NICOLE and WEGENER, RAIMUND 2009. Asymptotic model for the dynamics of curved viscous fibres with surface tension. Journal of Fluid Mechanics, Vol. 622, Issue. , p. 345.

Hawkins, V L Gurney, C J Decent, S P Simmons, M J H and Uddin, J 2010. Unstable waves on a curved non-Newtonian liquid jet. Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue. 5, p. 055501.

Gurney, C.J. Simmons, M.J.H. Hawkins, V.L. and Decent, S.P. 2010. The impact of multi-frequency and forced disturbances upon drop size distributions in prilling. Chemical Engineering Science, Vol. 65, Issue. 11, p. 3474.

ARNE, WALTER MARHEINEKE, NICOLE MEISTER, ANDREAS and WEGENER, RAIMUND 2010. NUMERICAL ANALYSIS OF COSSERAT ROD AND STRING MODELS FOR VISCOUS JETS IN ROTATIONAL SPINNING PROCESSES. Mathematical Models and Methods in Applied Sciences, Vol. 20, Issue. 10, p. 1941.

Marheineke, Nicole 2010. Progress in Industrial Mathematics at ECMI 2008. Vol. 15, Issue. , p. 589.

Arne, Walter Marheineke, Nicole Schnebele, Johannes and Wegener, Raimund 2011. Fluid-fiber-interactions in rotational spinning process of glass wool production. Journal of Mathematics in Industry, Vol. 1, Issue. 1,

ARNE, WALTER MARHEINEKE, NICOLE and WEGENER, RAIMUND 2011. ASYMPTOTIC TRANSITION FROM COSSERAT ROD TO STRING MODELS FOR CURVED VISCOUS INERTIAL JETS. Mathematical Models and Methods in Applied Sciences, Vol. 21, Issue. 10, p. 1987.

Mescher, Axel Möller, Arne Dirks, Martin and Walzel, Peter 2012. Gravity affected break-up of laminar threads at low gas-relative-velocities. Chemical Engineering Science, Vol. 69, Issue. 1, p. 181.

Download full list

Article contents

The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory

Abstract

Information

Access options

Article purchase

Temporarily unavailable

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory

Abstract

Information

Access options

Article purchase

Temporarily unavailable

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests