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On the breakup of spiralling liquid jets

Published online by Cambridge University Press:  15 January 2019

Yuan Li ,
Grigori M. Sisoev  and
Yulii D. Shikhmurzaev
Yuan Li
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
Grigori M. Sisoev
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
Yulii D. Shikhmurzaev*
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
*
†Email address for correspondence: Y.D.Shikhmurzaev@bham.ac.uk
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Abstract

The generation of drops from a jet spiralling out of a spinning device, under the action of centrifugal force, is considered for the case of small perturbations introduced at the inlet. Close to the inlet, where the disturbances can be regarded as small, their propagation is found to be qualitatively similar to that of a wave propagating down a straight jet stretched by an external body force (e.g. gravity). The dispersion equation has the same parametric dependence on the base flow, but the base flow is, of course, different. Further down the jet, where the amplitude of the disturbances becomes finite and eventually resulting in drop formation, the flow appears to be quite complex. As shown, for the regular/periodic process of drop generation, the wavelength corresponding to the frequency at the inlet, increasing as the wave propagates down the stretching jet, determines, in general, not the volume of the resulting drop but the sum of volumes of the main drop and the satellite droplet that follows the main one. The proportion of the total volume forming the main drop depends on how far down the jet the drops are produced, i.e. on the magnitude of the inlet disturbance. The volume of the main drop is found to be a linear function of the radius of the unperturbed jet evaluated at the point where the drop breaks away from the jet. This radius, and the corresponding velocity of the base flow, have to be found simultaneously with the jet’s trajectory by using a jet-specific non-orthogonal coordinate system described in detail in Shikhmurzaev & Sisoev (J. Fluid Mech., vol. 819, 2017, pp. 352–400). Some characteristic features of the nonlinear dynamics of the drop formation are discussed.

JFM classification

Instability: Absolute/convective instability Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 364 - 384
Copyright
© 2019 Cambridge University Press 

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