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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bhagat, R.K. and Wilson, D.I. 2016. Flow in the thin film created by a coherent turbulent water jet impinging on a vertical wall. Chemical Engineering Science, Vol. 152, p. 606.


    Paramati, Manjula and Tirumkudulu, Mahesh S. 2016. Open water bells. Physics of Fluids, Vol. 28, Issue. 3, p. 032105.


    Wang, T. Faria, D. Stevens, L.J. Tan, J.S.C. Davidson, J.F. and Wilson, D.I. 2013. Flow patterns and draining films created by horizontal and inclined coherent water jets impinging on vertical walls. Chemical Engineering Science, Vol. 102, p. 585.


    Wilson, D.I. Le, B.L. Dao, H.D.A. Lai, K.Y. Morison, K.R. and Davidson, J.F. 2012. Surface flow and drainage films created by horizontal impinging liquid jets. Chemical Engineering Science, Vol. 68, Issue. 1, p. 449.


    LETCHFORD, NICHOLAS A. FORBES, LAWRENCE K. and HOCKING, GRAEME C. 2012. INVISCID AND VISCOUS MODELS OF AXISYMMETRIC FLUID JETS OR PLUMES. The ANZIAM Journal, Vol. 53, Issue. 03, p. 228.


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  • Journal of Fluid Mechanics, Volume 649
  • April 2010, pp. 45-68

Water bells formed on the underside of a horizontal plate. Part 2. Theory

  • ELEANOR C. BUTTON (a1), JOHN F. DAVIDSON (a2), GRAEME J. JAMESON (a3) and JOHN E. SADER (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112009993363
  • Published online: 13 April 2010
Abstract

In a companion paper (Part 1, Jameson et al. J. Fluid Mech. vol. 649, 2010, 19–43), the discovery of a new type of water bell was reported. When a vertical liquid jet impacts on the underside of a large horizontal plate, the resulting thin film spreads radially along the plate to an unspecified abrupt departure point, from whence it falls away from the plate of its own accord. The departure radius of the fluid from the plate is seen to depend strongly on the volumetric flow rate. The falling liquid may then coalesce to form a water bell. Here we present a theoretical analysis and explanation of this phenomenon. A force balance determining the maximum radial extension of the thin film flow along the plate is considered as a mechanism for fluid departure from the plate, for which an analytical model is developed. This model gives good predictions of the measured radius of departure. When a water bell has been formed, and the flow rate is altered, many interesting shapes are produced that depend on the shapes at previous flow rates. We discuss the origin of this hysteresis, and also present a leading order theory for the bell shape under a regime of changing flow rate. The models are compared with experimental results spanning two orders of magnitude in viscosity.

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Email address for correspondence: jsader@unimelb.edu.au
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J. M. Aristoff , C. Lieberman , E. Chan & J. W. M. Bush 2006 Water bell and sheet instabilities. Phys. Fluids 18, S10.


D. Benedetto & E. Caglioti 1998 A stationary action principle for the water sheet. Eur. J. Mech. B/Fluids 17, 770772.

M. P. Brenner & D. Gueyffier 1999 On the bursting of viscous films. Phys. Fluids 11, 737739.

P. Brunet , C. Clanet & L. Limat 2004 Transonic liquid bells. Phys. Fluids 16, 26682678.


C. Clanet 2007 Waterbells and liquid sheets. Annu. Rev. Fluid Mech. 39, 469496.


F. E. C. Culick 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128.

J. H. Dumbleton 1969 Effect of gravity on the shape of water bells. J. Appl. Phys. 40, 39503954.

O. G. Engel 1966 Crater depth in fluid impacts. J. Appl. Phys. 37, 17981808.


F. L. Hopwood 1952 Water bells. Proc. Phys. Soc. B 65, 25.


X. Jeandel & C. Dumouchel 1999 Influence of viscosity on the linear stability of an annular liquid sheet. Intl J. Heat Fluid Flow 20, 499506.

G. N. Lance & R. L. Perry 1953 Water bells. Proc. Phys. Soc. B 66, 10671073.


C. Pirat , C. Mathis , M. Mishra & P. Maïssa 2006 Destabilization of a viscous film flowing down in the form of a vertical cylindrical curtain. Phys. Rev. Lett. 97, 184501.

A. Rozhkov , B. Prunet-Foch & M. Vignes-Adler 2002 Impact of water drops on small targets. Phys. Fluids 14, 34853501.

G. I. Taylor 1959 aThe dynamics of thin sheets of fluid. I. Water bells. Proc. R. Soc. A 253, 289295.

G. I. Taylor 1959 bThe dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. A 253, 296312.



P. P. Wegener & J.-Y. Parlange 1964 Surface tension of liquids from water bell experiments. Zeit. Phys. Chem. 43, 245259.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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