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Drop impact on a solid surface: short-time self-similarity

Published online by Cambridge University Press:  13 April 2016

Julien Philippi ,
Pierre-Yves Lagrée  and
Arnaud Antkowiak
Julien Philippi
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Pierre-Yves Lagrée
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Arnaud Antkowiak*
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
*
†Email address for correspondence: arnaud.antkowiak@upmc.fr
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Abstract

The early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a ‘tank-treading’ motion. These observations are apprehended with the help of a variant of Wagner theory for liquid impact. This framework offers a simple analogy where the fluid motion within the impacting drop may be viewed as the flow induced by a flat rising expanding disk. The theoretical predictions are found to be in very close agreement both qualitatively and quantitatively with the numerical observations for approximately three decades in time. Interestingly, the inviscid self-similar impact pressure and velocities are shown to depend solely on the self-similar variables $(r/\sqrt{t},z/\sqrt{t})$. The structure of the boundary layer developing along the wet substrate is investigated as well. It is found to be in first approximation analogous to the boundary layer growing in the trail of a shockwave. Interestingly, the corresponding boundary layer structure only depends on the impact self-similar variables. This allows us to construct a seamless uniform analytical approximation encompassing both impact and viscous effects. The depiction of the different dynamical fields enables to quantitatively predict observables of interest, such as the evolution of the integral viscous shearing force and of the net normal force.

JFM classification

Boundary Layers: Boundary layer structure Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 96 - 135
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Copyright
© 2016 Cambridge University Press 

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