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A note on the aerodynamic splashing of droplets

Published online by Cambridge University Press:  24 May 2019

José Manuel Gordillo Open the ORCID record for José Manuel Gordillo [Opens in a new window]  and
Guillaume Riboux Open the ORCID record for Guillaume Riboux [Opens in a new window]
José Manuel Gordillo*
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n 41092, Sevilla, Spain
Guillaume Riboux
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n 41092, Sevilla, Spain
*
†Email address for correspondence: jgordill@us.es
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Abstract

When a drop of a low-viscosity liquid of radius $R$ impacts against an inclined smooth solid substrate at a velocity $V$, a liquid sheet of thickness $H_{t}\ll R$ is expelled at a velocity $V_{t}\gg V$. If the impact velocity is such that $V>V^{\ast }$, with $V^{\ast }$ the critical velocity for splashing, the edge of the expanding liquid sheet lifts off from the wall as a consequence of the gas lubrication force at the wedge region created between the advancing liquid front and the substrate. Here we show that the magnitude of the gas lubrication force is limited by the values of the slip length $\ell _{\unicode[STIX]{x1D707}}$ at the gas–liquid interface and of the slip length $\ell _{g}\propto \unicode[STIX]{x1D706}$ at the solid, with $\unicode[STIX]{x1D706}$ the mean free path of gas molecules. We demonstrate that the splashing regime changes depending on the value of the ratio $\ell _{\unicode[STIX]{x1D707}}/\ell _{g}$ – a fact explaining the spreading–splashing–spreading–splashing transition for a fixed (low) value of the gas pressure as the drop impact velocity increases (Xu et al., Phys. Rev. Lett., vol. 94, 2005, 184505; Hao et al., Phys. Rev. Lett., vol. 122, 2019, 054501). We also provide an expression for $V^{\ast }$ as a function of the inclination angle of the substrate, the drop radius $R$, the material properties of the liquid and the gas, and the mean free path $\unicode[STIX]{x1D706}$, in very good agreement with experiments.

JFM classification

Drops and Bubbles: Aerosols/atomization Drops and Bubbles: Breakup/coalescence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , R3
Copyright
© 2019 Cambridge University Press 

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