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A theory on the spreading of impacting droplets

Published online by Cambridge University Press:  05 March 2019

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

Here we provide a self-consistent analytical solution describing the unsteady flow in the slender thin film which is expelled radially outwards when a drop hits a dry solid wall. Thanks to the fact that the fluxes of mass and momentum entering into the toroidal rim bordering the expanding liquid sheet are calculated analytically, we show here that our theoretical results closely follow the measured time-varying position of the rim with independence of the wetting properties of the substrate. The particularization of the equations describing the rim dynamics at the instant the drop reaches its maximal extension which, in analogy with the case of Savart sheets, is characterized by a value of the local Weber number equal to one, provides an algebraic equation for the maximum spreading radius also in excellent agreement with experiments. The self-consistent theory presented here, which does not make use of energetic arguments to predict the maximum spreading diameter of impacting drops, provides us with the time evolution of the thickness and of the velocity of the rim bordering the expanding sheet. This information is crucial in the calculation of the diameters and of the velocities of the droplets ejected radially outwards for drop impact velocities above the splashing threshold.

JFM classification

Drops and Bubbles: Aerosols/atomization Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 298 - 315
Copyright
© 2019 Cambridge University Press 

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