Longitudinal instability of a liquid rim

We study the transverse instability of a retracting liquid rim using a long wavelength approximation model and full numerical simulations. We observe that the instability of the rim is driven both by the Rayleigh-Taylor mechanism because of the initial rim acceleration, and by the Rayleigh-Plateau one. The coupling between the rim and the sheet stabilizes the rim at long wavelength. Full numerical simulations are in good agreement with the model and the subsequent break-up of droplets is observed in the numerical simulations when the instability is strong enough.

[1]  C. Clanet,et al.  Atomization of undulating liquid sheets , 2007, Journal of Fluid Mechanics.

[2]  Pascal Ray,et al.  Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method , 2011 .

[3]  S. Bankoff,et al.  Long-scale evolution of thin liquid films , 1997 .

[4]  Geoffrey Ingram Taylor,et al.  The dynamics of thin sheets of fluid II. Waves on fluid sheets , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  J. Eggers,et al.  Wavelength selection in the crown splash , 2010 .

[6]  A. Yarin,et al.  Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity , 1995, Journal of Fluid Mechanics.

[7]  E. Villermaux,et al.  Drop fragmentation on impact , 2011, Journal of Fluid Mechanics.

[8]  Gaurav Tomar,et al.  Multiscale simulations of primary atomization , 2010 .

[9]  Stéphane Zaleski,et al.  Stability of a growing end rim in a liquid sheet of uniform thickness , 1999 .

[10]  G. Homsy,et al.  Crown-forming instability phenomena in the drop splash problem. , 2009, Journal of colloid and interface science.

[11]  G. Debrégeas,et al.  Viscous bursting of suspended films. , 1995, Physical review letters.

[12]  Philippe Brunet,et al.  Complexities of splashing , 2007 .

[13]  E. Villermaux,et al.  Physics of liquid jets , 2008 .

[14]  E. Villermaux,et al.  The destabilization of an initially thick liquid sheet edge , 2011 .

[15]  S. Zaleski,et al.  Numerical simulation of droplets, bubbles and waves: state of the art , 2009 .

[16]  J. Wesfreid,et al.  Gravitational instabilities of thin liquid layers: dynamics of pattern selection , 1992 .

[17]  M. Rein.  Phenomena of liquid drop impact on solid and liquid surfaces , 1993 .

[18]  I. Roisman.  On the instability of a free viscous rim , 2010, Journal of Fluid Mechanics.

[19]  Stéphane Popinet,et al.  An accurate adaptive solver for surface-tension-driven interfacial flows , 2009, J. Comput. Phys..

[20]  F. Durst,et al.  The retraction of the edge of a planar liquid sheet , 2002 .

[21]  C. Tropea,et al.  Spray impact: Rim transverse instability initiating fingering and splash, and description of a secondary spray , 2006 .

[22]  L. Duchemin,et al.  Asymptotic behavior of a retracting two-dimensional fluid sheet , 2011 .

[23]  R. Krechetnikov.  Stability of liquid sheet edges , 2009 .

[24]  Fred E. C. Culick,et al.  Comments on a Ruptured Soap Film , 1960 .

[25]  S. Popinet.  Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries , 2003 .