Rarefied gas correction for the bubble entrapment singularity in drop impacts

Laurent Duchemin; Christophe Josserand

doi:10.1016/j.crme.2012.10.028

Rarefied gas correction for the bubble entrapment singularity in drop impacts

Laurent Duchemin ¹; Christophe Josserand ²

¹ IRPHE, CNRS & Aix-Marseille université, 49, rue Joliot-Curie, 13013 Marseille, France
² Institut DʼAlembert, CNRS & UPMC (Univ. Paris 6) UMR 7190, 4, place Jussieu, 75005 Paris, France

Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, Volume 340 (2012) no. 11-12, pp. 797-803.

Abstract

We study the non-continuous correction in the dynamics of drop impact on a solid substrate. Close to impact, a thin film of gas is formed beneath the drop so that the local Knudsen number is of order one. We consider the first correction to the dynamics which consists of allowing slip of the gas along the substrate and the interface. We focus on the singular dynamics of entrapment that can be seen when surface tension and liquid viscosity can be neglected. There we show that different dynamical regimes are present that tend to lower the singularity strength. We finally suggest how these effects might be connected to the influence of the gas pressure in the impact dynamics observed in recent experiments.

Published online: 2012-11-01

DOI: 10.1016/j.crme.2012.10.028

Keywords: Drop impact, Rarefied gas

Author's affiliations:

Laurent Duchemin ¹; Christophe Josserand ²

¹ IRPHE, CNRS & Aix-Marseille université, 49, rue Joliot-Curie, 13013 Marseille, France
² Institut DʼAlembert, CNRS & UPMC (Univ. Paris 6) UMR 7190, 4, place Jussieu, 75005 Paris, France

@article{CRMECA_2012__340_11-12_797_0,
     author = {Laurent Duchemin and Christophe Josserand},
     title = {Rarefied gas correction for the bubble entrapment singularity in drop impacts},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {797--803},
     publisher = {Elsevier},
     volume = {340},
     number = {11-12},
     year = {2012},
     doi = {10.1016/j.crme.2012.10.028},
     language = {en},
}

TY  - JOUR
AU  - Laurent Duchemin
AU  - Christophe Josserand
TI  - Rarefied gas correction for the bubble entrapment singularity in drop impacts
JO  - Comptes Rendus. Mécanique
PY  - 2012
SP  - 797
EP  - 803
VL  - 340
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crme.2012.10.028
LA  - en
ID  - CRMECA_2012__340_11-12_797_0
ER  -

%0 Journal Article
%A Laurent Duchemin
%A Christophe Josserand
%T Rarefied gas correction for the bubble entrapment singularity in drop impacts
%J Comptes Rendus. Mécanique
%D 2012
%P 797-803
%V 340
%N 11-12
%I Elsevier
%R 10.1016/j.crme.2012.10.028
%G en
%F CRMECA_2012__340_11-12_797_0

Laurent Duchemin; Christophe Josserand. Rarefied gas correction for the bubble entrapment singularity in drop impacts. Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, Volume 340 (2012) no. 11-12, pp. 797-803. doi : 10.1016/j.crme.2012.10.028. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.028/

References
Cited by

[1] H.E. Edgerton; J.R. Killian Flash, Branford, Boston, 1954

[2] M. Rein Phenomena of liquid drop impact on solid and liquid surfaces, Fluid Dyn. Res., Volume 12 (1993), p. 61

[3] R. Rioboo; M. Marengo; C. Tropea Outcomes from a drop impact on solid surfaces, At. Sprays, Volume 11 (2001), pp. 155-166

[4] S.T. Thoroddsen; T.G. Etoh; K. Takehara Air entrapment under an impacting drop, J. Fluid Mech., Volume 478 (2003), pp. 125-134

[5] S.T. Thoroddsen; T.G. Etoh; K. Takehara; N. Ootsuka; A. Hatsuki The air bubble entrapped under a drop impacting on a solid surface, J. Fluid Mech., Volume 545 (2005), pp. 203-212

[6] L. Xu; W.W. Zhang; S.R. Nagel Drop splashing on a dry smooth surface, Phys. Rev. Lett., Volume 94 (2005), p. 184505

[7] S. Mandre; M. Mani; M.P. Brenner Precursors to splashing of liquid droplets on a solid surface, Phys. Rev. Lett., Volume 102 (2009), p. 134502

[8] M. Mani; S. Mandre; M.P. Brenner Events before droplet splashing on a solid surface, J. Fluid Mech., Volume 647 (2010), pp. 163-185

[9] L. Duchemin; C. Josserand Curvature singularity and film-skating during drop impact, Phys. Fluids, Volume 23 (2011), p. 091701

[10] J.M. Kolinski; S.M. Rubinstein; S. Mandre; M.P. Brenner; D.A. Weitz; L. Mahadevan Skating on a film of air: drops impacting on a surface, Phys. Rev. Lett., Volume 108 (2012), p. 074503

[11] M.M. Driscoll; S.R. Nagel Ultrafast interference imaging of air in splashing dynamics, Phys. Rev. Lett., Volume 107 (2011), p. 154502

[12] A.A. Korobkin; A.S. Ellis; F.T. Smith Trapping of air in impact between a body and shallow water, J. Fluid Mech., Volume 611 (2008), pp. 365-394

[13] C. Josserand; S. Zaleski Droplet splashing on a thin liquid film, Phys. Fluids, Volume 15 (2003), p. 1650

[14] S. Mandre; M.P. Brenner The mechanism of a splash on a dry solid surface, J. Fluid Mech., Volume 690 (2012), pp. 148-172

Cited by Sources:

Comments - Policy