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Blowing a liquid curtain

Published online by Cambridge University Press:  21 April 2016

H. Lhuissier*
Affiliation:
IUSTI, UMR 7343, CNRS, Aix-Marseille Université, 13453 Marseille, France
P. Brunet
Affiliation:
MSC, UMR 7057, CNRS, Université Paris-Diderot, 75205 Paris, France
S. Dorbolo
Affiliation:
GRASP, FRS-FNRS, Université de Liège, B4000 Liège, Belgium
*
Email address for correspondence: henri.lhuissier@univ-amu.fr

Abstract

We study the response of a steady free-falling liquid curtain perturbed by focused air jets blowing perpendicularly against it. Asymmetric and symmetric perturbations are applied by using either a single pulsed jet or two identical steady jets facing each other. The response strongly depends on the curtain flow rate, and the location and strength of the perturbation. For pulsed asymmetric perturbations of increasing amplitude, sinuous wave, drop ejection, bubble ejection and hole opening are successively observed. For steady symmetric perturbations, a steady hole forms downstream in the wake. For this latter case, we present a model for the curtain thickness and the location of the hole in the wake in terms of the curtain flow rate and the size, flow rate and location of the jets. The adjustable-parameter-free expression we obtain compares favourably to the experiments provided that the perturbation is sufficiently small (jet stagnation pressure smaller than curtain stagnation pressure) and the liquid viscosity is negligible.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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References

Alleborn, N. & Raszillier, H. 2004 Linear response of a viscous liquid sheet to oscillatory external pressure perturbation in the long wave approximation. Varicose excitation. Acta Mech. 170, 77119.CrossRefGoogle Scholar
Berendsen, C. W. J., Zeegers, J. C. H. & Darhuber, A. A. 2013 Deformation and dewetting of thin liquid films induced by moving gas jets. J. Colloid Interface Sci. 407, 505515.CrossRefGoogle ScholarPubMed
Brown, D. R. 1961 A study of the behaviour of a thin sheet of moving liquid. J. Fluid Mech. 10, 297305.CrossRefGoogle Scholar
Brunet, P., Flesselles, J. M. & Limat, L. 2007 Dynamics of a circular array of liquid columns. Eur. Phys. J. B 55, 297322.CrossRefGoogle Scholar
Clanet, C. 2007 Waterbells and liquid sheets. Annu. Rev. Fluid Mech. 39, 469496.CrossRefGoogle Scholar
Clarke, A., Weinstein, S. J., Moon, A. G. & Simister, E. A. 1997 Time-dependent equations governing the shape of a two-dimensional liquid curtain. Part 2: experiment. Phys. Fluids 9, 36373644.CrossRefGoogle Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 11281129.CrossRefGoogle Scholar
De Luca, L. & Costa, M. 1997 Instability of a spatially developing liquid sheet. J. Fluid Mech. 331, 127144.CrossRefGoogle Scholar
Dombrowski, N. & Fraser, R. P. 1954 A photographic investigation into the disintegration of liquid sheets. Phil. Trans. R. Soc. Lond. A 247, 101130.Google Scholar
Emile, J. & Emile, O. 2013 Mapping of the Marangoni effect in soap films using Young’s double-slit experiment. Europhys. Lett. 104, 14001.CrossRefGoogle Scholar
Finnicum, D. S., Weinstein, S. J. & Ruschak, K. J. 1993 The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the influence of gravity. J. Fluid Mech. 255, 647665.CrossRefGoogle Scholar
Fourier, J. 1822 Théorie Analytique de la Chaleur. Firmin Didot.Google Scholar
Giorgiutti, F., Limat, L. & Weisfreid, J. E. 1995 Dynamics of a one-dimensional array of liquid columns. Phys. Rev. Lett. 74, 538541.CrossRefGoogle ScholarPubMed
Gordillo, J. M., Lhuissier, H. & Villermaux, E. 2014 On the cusps bordering liquid sheets. J. Fluid Mech. 754, R1.CrossRefGoogle Scholar
Le Grand, N., Brunet, P., Lebon, L. & Limat, L. 2006 Propagative wave pattern on a falling liquid curtain. Phys. Rev. E 74, 026305.Google Scholar
Lhuissier, H. & Villermaux, E. 2011 The destabilization of an initially thick liquid sheet edge. Phys. Fluids 23, 091705.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2013 ‘Effervescent’ atomization in two dimensions. J. Fluid Mech. 714, 361392.CrossRefGoogle Scholar
Lin, S. P., Lian, Z. W. & Creighton, B. J. 1990 Absolute and convective instability of a liquid sheet. J. Fluid Mech. 220, 673689.CrossRefGoogle Scholar
Lin, S. P. & Roberts, G. 1981 Waves in a viscous liquid curtain. J. Fluid Mech. 112, 443458.CrossRefGoogle Scholar
Mehring, C. & Sirignano, W. A. 2003 Disintegration of planar liquid film impacted by two-dimensional gas jets. Phys. Fluids 15 (5), 11581177.CrossRefGoogle Scholar
Miyamoto, K. & Katagiri, Y. 1997 Curtain coating. In Liquid Film Coating, pp. 463494. Springer.CrossRefGoogle Scholar
Pritchard, G. M. 1986 Instability and chaotic behaviour in a free-surface flow. J. Fluid Mech. 165, 160.CrossRefGoogle Scholar
Roche, J. S., Le Grand, N., Brunet, P., Lebon, L. & Limat, L. 2006 Perturbations on a liquid curtain near break-up: wakes and free-edges. Phys. Fluids 18, 082101.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Soderberg, D. & Alfredsson, P. H. 1998 Experimental and theoretical stability investigations of plane liquid jets. Eur. J. Mech (B/Fluids) 17, 689737.CrossRefGoogle Scholar
Squire, H. B. 1953 Investigation of the stability of a moving liquid film. Brit. J. Appl. Phys. 4, 167169.CrossRefGoogle Scholar
Tammisola, O., Sasaki, A., Lundell, F., Matsubara, M. & Söderberg, L. D. 2011 Stabilizing effect of surrounding gas flow on a plane liquid sheet. J. Fluid Mech. 672, 532.CrossRefGoogle Scholar
Taylor, G. I. 1959a The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. Lond. A 253 (1274), 296312.Google Scholar
Taylor, G. I. 1959b The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253 (1274), 313321.Google Scholar
Teng, C. H., Lin, S. P. & Chen, J. N. 1997 Absolute and convective instability of a viscous liquid curtain in a viscous gas. J. Fluid Mech. 332, 105120.CrossRefGoogle Scholar
Trouton, J. T. 1906 On the coefficient of viscous traction and its relation to that of viscosity. Proc. R. Soc. Lond. A 77, 426440.Google Scholar
Villermaux, E., Pistre, V. & Lhuissier, H. 2013 The viscous Savart sheet. J. Fluid Mech. 730, 607625.CrossRefGoogle Scholar
Weinstein, S. J., Clarke, A., Moon, A. G. & Simister, E. A. 1997 Time-dependent equations governing the shape of a two-dimensional liquid curtain. Part 1: theory. Phys. Fluids 9 (12), 36253636.CrossRefGoogle Scholar