Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 65
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Yoshinaga, Takao 2018. Linear instabilities of a planar liquid sheet in a static electric field for intermediate relaxation and convection of surface charges. Fluid Dynamics Research, Vol. 50, Issue. 2, p. 025513.
    Mohammad Karim, Alireza Suszynski, Wieslaw J. Francis, Lorraine F. and Carvalho, Marcio S. 2018. Effect of viscosity on liquid curtain stability. AIChE Journal, Vol. 64, Issue. 4, p. 1448.
    Rajamanickam, Kuppuraj Mukhopadhyay, Achintya and Basu, Saptarshi 2018. Droplets and Sprays. p. 117.
    Mohammad Karim, Alireza Suszynski, Wieslaw J. Griffith, William B. Pujari, Saswati Francis, Lorraine F. and Carvalho, Marcio S. 2018. Effect of viscoelasticity on stability of liquid curtain. Journal of Non-Newtonian Fluid Mechanics, Vol. 257, Issue. , p. 83.
    Girfoglio, M. De Rosa, F. Coppola, G. and de Luca, L. 2017. Unsteady critical liquid sheet flows. Journal of Fluid Mechanics, Vol. 821, Issue. , p. 219.
    Lhuissier, H. Brunet, P. and Dorbolo, S. 2016. Blowing a liquid curtain. Journal of Fluid Mechanics, Vol. 795, Issue. , p. 784.
    Henry, D. Uddin, J. Marston, J. O. and Thoroddsen, S. T. 2016. Stability of an unsupported multi-layer surfactant laden liquid curtain under gravity. Journal of Engineering Mathematics, Vol. 99, Issue. 1, p. 119.
    Wang, Chen Yang, Li-jun Xie, Luo and Chen, Pi-min 2015. Weakly nonlinear instability of planar viscoelastic sheets. Physics of Fluids, Vol. 27, Issue. 1, p. 013103.
    Duan, Runze Chen, Zhiying and Liu, Liansheng 2015. Effect of velocity profile on instability of the viscoelastic liquid sheet. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 229, Issue. 11, p. 2031.
    Okino, Fumito Kasada, Ryuta and Konishi, Satoshi 2014. Study on flow instability for feasibility of a thin liquid film first wall. Fusion Engineering and Design, Vol. 89, Issue. 7-8, p. 1054.
    Marston, J.O. Thoroddsen, S.T. Thompson, J. Blyth, M.G. Henry, D. and Uddin, J. 2014. Experimental investigation of hysteresis in the break-up of liquid curtains. Chemical Engineering Science, Vol. 117, Issue. , p. 248.
    Yang, Li-Jun Chen, Pi-Min and Wang, Chen 2014. Effect of gas velocity on the weakly nonlinear instability of a planar viscous sheet. Physics of Fluids, Vol. 26, Issue. 7, p. 074106.
    Tong, Ming-Xi Yang, Li-Jun and Fu, Qing-Fei 2014. Thermocapillar instability of a two-dimensional viscoelastic planar liquid sheet in surrounding gas. Physics of Fluids, Vol. 26, Issue. 3, p. 033105.
    De Rosa, Fortunato Girfoglio, Michele and de Luca, Luigi 2014. Global dynamics analysis of nappe oscillation. Physics of Fluids, Vol. 26, Issue. 12, p. 122109.
    Tharakan, T. John Mukhopadhyay, Achintya Datta, Amitava and Jog, Milind A. 2013. Trends in Comprehensive Modeling of Spray Formation. International Journal of Spray and Combustion Dynamics, Vol. 5, Issue. 2, p. 123.
    Yang, Lijun Wang, Chen Fu, Qingfei Du, Minglong and Tong, Mingxi 2013. Weakly nonlinear instability of planar viscous sheets. Journal of Fluid Mechanics, Vol. 735, Issue. , p. 249.
    Yang, Li-jun Xu, Bing-rui and Fu, Qing-fei 2012. Linear instability analysis of planar non-Newtonian liquid sheets in two gas streams of unequal velocities. Journal of Non-Newtonian Fluid Mechanics, Vol. 167-168, Issue. , p. 50.
    Chen, Xiaodong Ma, Dongjun and Yang, Vigor 2012. High-Fidelity Numercial Simulations of Impinging Jet Atomization.
    BOLAÑOS-JIMÉNEZ, R. SEVILLA, A. GUTIÉRREZ-MONTES, C. SANMIGUEL-ROJAS, E. and MARTÍNEZ-BAZÁN, C. 2011. Bubbling and jetting regimes in planar coflowing air–water sheets. Journal of Fluid Mechanics, Vol. 682, Issue. , p. 519.
    BARLOW, N. S. HELENBROOK, B. T. and LIN, S. P. 2011. Transience to instability in a liquid sheet. Journal of Fluid Mechanics, Vol. 666, Issue. , p. 358.
    Download full list
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Absolute and convective instability of a liquid sheet

  • S. P. Lin (a1), Z. W. Lian (a1) and B. J. Creighton (a1)
Abstract

The linear stability of a viscous liquid sheet in the presence of ambient gas is investigated. It is shown that there are two independent modes of instability, sinuous and varicose. The large-time asymptotic amplitude of sinuous disturbances is found to be bounded but non-vanishing for all calculated values of Reynolds numbers and the gas-to-liquid density ratios when the Weber number is greater than one half. The Weber number We is defined as the ratio of the surface tension force to the inertia force per unit area of the gas–liquid interface. When We is smaller than one half, the sinuous mode is stable if the gas-to-liquid density ratio is zero, otherwise it is convectively unstable. The varicose mode is always convectively unstable unless the density ratio, Q, is zero. Then it is asymptotically stable. The spatial growth rate of the varicose mode is smaller than that of the sinuous mode for the same flow parameters. The wavelength of the most amplified waves in both modes is found to scale with the product of the sheet thickness and Q/We. It is shown, by use of the energy equation, that the mechanism of instability is a capillary rupture when We [ges ] 0.5, and the convective instability is due to the interfacial pressure fluctuation when We < 0.5.

Copyright
© 1990 Cambridge University Press
References
Hide All
Akylas, T. R. & Benney, D. J., 1980 Stud. Appl. Maths 63, 209.
Antoniandes, M. G. & Lin, S. P., 1980 J. Colloid Interface Sci. 77, 583.
Bers, A.: 1983 Handbook of Plasma Physics, vol. 1, pp. 452–516. North-Holland.
Briggs, R. J.: 1964 Electron Stream Interaction with Plasmas. MIT Press.
Brown, D. R.: 1961 J. Fluid Mech. 10, 297.
Clark, C. J. & Dombrowski, N., 1972 Proc. R. Soc. Lond. A 329, 467.
Crapper, G. D., Dombrowski, N., Jepson, W. P. & Pyott, G. A. D. 1973 J. Fluid Mech. 57, 671.
Crapper, G. D., Dombrowski, N. & Pyott, G. A. D. 1975 Proc. R. Soc. Lond. A 342, 209.
Creighton, N.: 1989 Energy balance in breakup of liquid jets and curtains. M. S. thesis, Clarkson University.
Leib, S. J. & Goldstein, M. E., 1986a J. Fluid Mech. 168, 479.
Leib, S. J. & Goldstein, M. E., 1986b Phys. Fluids 29, 952.
Kelly, R. E., Goussis, D. A., Lin, S. P. & Hsu, F. K., 1989 Phys. Fluids A 1, 819.
Kistler, S. F. & Scriven, L. E., 1984 Intl J. Numer. Meth. Fluids 4, 207.
Lin, S. P.: 1981 J. Fluid Mech. 104, 111.
Lin, S. P. & Lian, Z. W., 1989 Phys. Fluids A 1, 490.
Lin, S. P. & Roberts, G., 1981 J. Fluid Mech. 112, 443.
Muller, D. E.: 1956 Mathematical Tables and Aid to Computation, vol. 10, pp. 208–230.
Rombers, S.: 1984 Problem Solving Software System for Mathematical and Statistical FORTRAN Programming, I & II. IMSL.
Taylor, G. I.: 1959a Proc. R. Soc. Lond. A 253, 289.
Taylor, G. I.: 1959b Proc. R. Soc. Lond. A 252, 296.
Taylor, G. I.: 1959c Proc. R. Soc. Lond. A 253, 313.
Taylor, G. I.: 1963 The Scientific Papers of G. I. Taylor, vol. 3, No. 25. Cambridge University Press.
Tomotika, S.: 1934 Proc. R. Soc. Lond. A 146, 501.
Weihs, D.: 1978 J. Fluid Mech. 87, 289.
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? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 49 *
Loading metrics...

Abstract views

Total abstract views: 156 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 13th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×