Skip to main content
×
Home
    • Aa
    • Aa

The viscous Savart sheet

  • E. Villermaux (a1), V. Pistre (a2) and H. Lhuissier (a1)
Abstract
Abstract

We study the viscous version of the planar Savart sheet problem, using an impacting liquid jet up to 300 times more viscous than water. Two surprising observations are made, contrasting with the traditional case introduced by Savart where viscosity plays no role. First, if the radius of a viscous sheet is typically reduced compared to the case of water for a given jet radius and impacting velocity, the smooth–flapping transition is delayed, allowing for smooth sheet radii substantially bigger than those permitted with water at large impacting Weber number. Second, the drop size distribution is bimodal, with a substantial fraction of the drops having a very small, well-defined diameter. We understand these two facts in terms of an additional model experiment, and simple physical arguments.

Copyright
Corresponding author
Also at: Institut Universitaire de France. Email address for correspondence: villermaux@irphe.univ-mrs.fr
References
Hide All
O. A. Basaran , H. Gao & P. P. Bhat 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85113.

E. A. Boucher & J. B. Evans 1975 Pendent drop profiles and related capillary phenomena. Proc. R. Soc. Lond. A 346, 349374.

N. Bremond , C. Clanet & E. Villermaux 2007 Atomization of undulated liquid sheets. J. Fluid Mech. 585, 421456.

N. Bremond & E. Villermaux 2006 Atomization by jet impact. J. Fluid Mech. 549, 273306.

M. P. Brenner , X. D. Shi & S. R. Nagel 1994 Iterated instabilities during droplet fission. Phys. Rev. Lett. 73 (25), 33913394.

A. A. Castrejon-Pita , J. R. Castrejon-Pita & I. M. Hutchings 2012 Breakup of liquid ligaments. Phys. Rev. Lett. 108, 074506.

Y. Christianti & L. M. Walker 2000 Surface tension driven jet break up of strain-hardening polymer solutions. J. Non-Newtonian Fluid Mech. 100, 926.

C. Clanet & E. Villermaux 2002 Life of a smooth liquid sheet. J. Fluid Mech. 462, 307340.

F. E. C. Culick 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 11281129.

P. Dokic , J. Jakovljevic & L. Dokic-Baucal 1998 Molecular characteristics of maltodextrins and rheological behaviour of diluted and concentrated solutions. Colloids Surf. A 141, 435440.

J. Eggers & M. A. Fontelos 2005 Isolated inertialess drops cannot break up. J. Fluid Mech. 530, 177180.

J. Eggers & E. Villermaux 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.

V. M. Entov & E. J. Hinch 1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newtonian Fluid Mech. 72, 3153.

S. Gier & C. Wagner 2012 Visualization of the flow profile inside a thinning filament during capillary breakup of a polymer solution via particle image velocimetry and particle tracking velocimetry. Phys. Fluids 24, 053102.

W. D. Harkins & F. E. Brown 1919 The determination of surface tension (free surface energy), and the weight of falling drops: the surface tension of water and benzene by the capillary height method. J. Am. Chem. Soc. 41, 499524.

D. Henderson , H. Segur , L. B. Smolka & M. Wadati 2000 The motion of a falling liquid filament. Phys. Fluids 12 (3), 550565.

S. D. Hoath , S. Jung & I. M. Hutchings 2013 A simple criterion for filament break-up in drop-on-demand inkjet printing. Phys. Fluids 25, 021701.

J. C. P. Huang 1970 The break-up of axisymmetric liquid sheets. J. Fluid Mech. 43, 305319.

P. Lafrance & R. C. Ritter 1977 Capillary breakup of a liquid jet with a random initial perturbation. J. Appl. Mech. 385388.

L. Landau & E. Lifshitz 1987 Fluid Mechanics. Pergamon.

H. Lhuissier & E. Villermaux 2009 Soap films burst like flapping flags. Phys. Rev. Lett. 103, 054501–(4).

H. Lhuissier & E. Villermaux 2012 Crumpled water bells. J. Fluid Mech. 693, 508540.

L. G. Mastin 2007 Generation of fine hydromagmatic ash by growth and disintegration of glassy rinds. J. Geophys. Res. 112, B02203.

P. K. Notz & O. A. Basaran 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223256.

M. Oliveira & G. McKinley 2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of high extensible flexible polymers. Phys. Fluids 17, 071704.

Lord Rayleigh 1899 Investigations in capillarity. Phil. Mag. 48, 321337.

N. Savva & J. W. M. Bush 2009 Viscous sheet retraction. J. Fluid Mech. 626, 211240.

M. G. Semenova , L. E. Belyakova , A. S. Antipova , Y. N. Polikarpov , L. Klouda , A. Markovic & M. M. Il’in 2003 Effect of maltodextrins on the surface activity of small-molecule surfactants. Colloids Surf. B 31, 4754.

H. B. Squire 1953 Investigation of the stability of a moving liquid film. British J. Appl. Phys. 4, 167169.

H. A. Stone 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65102.

G. I. Taylor 1959b The dynamics of thin sheets of fluid. Part 3. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313321.

G. I. Taylor 1959b The dynamics of thin sheets of fluid. Part 3. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313321.

M. Tjahjadi , H. A. Stone & J. M. Ottino 1992 Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243, 297317.

S. Tomotika 1936 Breaking up of a drop of viscous liquid immersed in another fluid which is extending at uniform rate. Proc. R. Soc Lond. A 153, 302318.

E. Villermaux 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419446.

E. Villermaux 2012 The formation of filamentary structures from molten silicates: Pele’s hair, angel hair, and blown clinker. C. R. Mécanique 340, 555564.

E. Villermaux & C. Clanet 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 341363.

E. J. Watson 1964 The radial spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481499.

D. C. Y. Wong , M. J. H. Simmons , S. P. Decent , E. I. Parau & A. C. King 2004 Break-up dynamics and drop size distributions created from spiralling liquid jets. Intl J. Multiphase Flow 30, 499520.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 28 *
Loading metrics...

Abstract views

Total abstract views: 95 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.