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Node dynamics and cusps size distribution at the border of liquid sheets
Phys. Rev. Fluids 1, 041902(R) – Published 29 August, 2016
DOI: https://doi.org/10.1103/PhysRevFluids.1.041902
Abstract
We study the intrinsic dynamics of cusps, or indentations, moving along a liquid sheet border, and characterize their ensemble statistics. Gordillo and collaborators [J. Fluid Mech. 754, R1 (2014)] have shown that the symmetrical stationary cusp is the only structure accommodating for both mass and momentum conservation at a steadily receding liquid sheet rim. Cusps are also known to typically move along a sheet border, to present an asymmetry, and to be distributed in size around a mean. We show here why a heterogeneous assembly of cusps traveling along the sheet rim occurs spontaneously, why big and small cusps coexist at the same time, and, more precisely, we establish a specific link between the microscopic dynamics directing their motion, and the ensemble averaged distribution of their sizes.
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References (25)
- W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970).
- F. Savart, Mémoire sur la constitution des Veines liquides lancées par des orifices circulaires en mince paroi, Ann. Chim. 53, 337 (1833).
- H. Lhuissier and E. Villermaux, The destabilization of an initially thick liquid sheet edge, Phys. Fluids 23, 091705 (2011).
- G. I. Taylor, The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets, Proc. R. Soc. London, Ser. A 253, 313 (1959).
- J. C. P. Huang, The break-up of axisymmetric liquid sheets, J. Fluid Mech. 43, 305 (1970).
- C. Clanet and E. Villermaux, Life of a smooth liquid sheet, J. Fluid Mech. 462, 307 (2002).
- C. Ellegaard, A. E. Hansen, A. Haaning, K. Hansen, A. Marcussen, T. Bohr, J. L. Hansen, and S. Watanabe, Creating corners in kitchen sinks, Nature (London) 392, 767 (1998).
- R. Buckingham and J. W. M. Bush, Fluid polygons, Phys. Fluids 13, S10 (2001).
- H. Lhuissier and E. Villermaux, Crumpled water bells, J. Fluid Mech. 693, 508 (2012).
- J. O. Marston, T. T. Truscott, N. B. Spiers, M. M. Mansoor, and S. T. Thoroddsen, Crown sealing and buckling instability during water entry of spheres, J. Fluid Mech. 794, 506 (2016).
- Y. D'Angelo, G. Joulin, and G. Boury, On model evolution equations for the whole surface of three-dimensional expanding wrinkled premixed flames, Combust. Theory Modell. 4, 317 (2000).
- C. Almarcha, J. Quinard, B. Denet, E. Al-Sarraf, J. M. Laugier, and E. Villermaux, Experimental two dimensional cellular flames, Phys. Fluids 27, 091110 (2015).
- E. Dressaire, L. Courbin, A. Delancy, M. Roper, and H. A. Stone, Study of polygonal water bells: Inertia-dominated thin-film flows over microtextured surfaces, J. Fluid Mech. 721, 46 (2013).
- E. Villermaux, V. Pistre, and H. Lhuissier, The viscous Savart sheet, J. Fluid Mech. 730, 607 (2013).
- H. Lhuissier, B. Néel, and L. Limat, Viscoelasticity Breaks the Symmetry of Impacting Jets, Phys. Rev. Lett. 113, 194502 (2014).
- J. M. Gordillo, H. Lhuissier, and E. Villermaux, On the cusps bordering liquid sheets, J. Fluid Mech. 754, R1 (2014).
- A. Dupré, Théorie mécanique de la chaleur, Ann. Chim. Phys. 11, 194 (1868).
- L. Rayleigh, Some applications of photography, Nature (London) 44, 249 (1891).
- P. G. de Gennes, Mechanics of soft interfaces, Faraday Discuss. 104, 1 (1996).
- H. Lhuissier and E. Villermaux, Destabilization of flapping sheets: The surprising analog of soap films, C. R. Mec. 337, 469 (2009).
- F. E. C. Culick, Comments on a ruptured soap film, J. Appl. Phys. 31, 1128 (1960).
- J. Duplat and E. Villermaux, Mixing by random stirring in confined mixtures, J. Fluid Mech. 617, 51 (2008).
- E. Villermaux, Fragmentation, Annu. Rev. Fluid Mech. 39, 419 (2007).
- A. Vledouts, N. Vandenberghe, and E. Villermaux, Fragmentation as an aggregation process, Proc. R. Soc. London, Ser. A 471, 20150678 (2015).
- A. Vledouts, N. Vandenberghe, and E. Villermaux, Fragmentation as an aggregation process: The role of defects, Proc. R. Soc. London, Ser. A 472, 20150679 (2016).