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Impact of liquids with different densities

Published online by Cambridge University Press:  30 January 2015

Y. A. Semenov ,
G. X. Wu  and
A. A. Korobkin
Y. A. Semenov
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK
G. X. Wu*
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK
A. A. Korobkin
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
*
†Email address for correspondence: g.wu@ucl.ac.uk
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Abstract

The collision of liquids of different densities is studied theoretically for the case of liquids having wedge-shaped configuration before the impact. Both liquids are assumed to be ideal and incompressible, and the velocity potential theory is used for the flow of each liquid. Surface tension and gravity effects are neglected. The problem is decomposed into two self-similar problems, one for each liquid. Across the interface between the liquids, continuity of the pressure and the normal component of the velocity is enforced through iteration. This determines the shape of the interface and other flow parameters. The integral hodograph method is employed to derive the solution consisting of analytical expressions for the complex-velocity potential, the complex-conjugate velocity, and the mapping function. They are all defined in the first quadrant of a parameter plane, in which the original boundary-value problem is reduced to a system of integro-differential equations in terms of the velocity magnitude and the velocity angle relative to the flow boundary. They are solved numerically using the method of successive approximations. The results are presented through streamlines, interface and free-surface shapes, the pressure and velocity distributions. Special attention is given to the structure of the splash jet rising as a result of the impact.

JFM classification

Drops and Bubbles: Breakup/coalescence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 5 - 27
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Copyright
© 2015 Cambridge University Press 

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