Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
H. B. Squire, “Investigation of the instability of a moving liquid film,” Br. J. Appl. Phys. 4, 167 (1953).
W. W. Hagerty and J. F. Shea, “A study of the stability of plane fluid sheets,” J. Appl. Mech. 22, 509 (1955).
N. Dombrowski and W. R. Johns, “The aerodynamic instability and disintegration of viscous liquid sheets,” Chem. Eng. Sci. 18, 203 (1963).
S. P. Lin, “Stability of a viscous liquid curtain,” J. Fluid Mech. 104, 111 (1981).
X. Li and R. S. Tankin, “On the temporal instability of a two-dimensional viscous liquid sheet,” J. Fluid Mech. 226, 425 (1991).
X. Li, “Spatial instability of plane liquid sheets,” Chem. Eng. Sci. 48, 2973 (1993).
O. Tammisola, A. Sasaki, F. Lundell, M. Matsubara, and L. D. Söderberg, “Stabilizing effect of surrounding gas flow on a plane liquid sheet,” J. Fluid Mech. 672, 5 (2011).
R. J. Dyson, J. Brander, C. J. W. Breward, and P. D. Howell, “Long-wavelength stability of an unsupported multilayer liquid film falling under gravity,” J. Eng. Math. 64, 237 (2009).
G. P. Sutton and O. Biblarz, Rocket Propulsion Elements (John Wiley & Sons, 2001), pp. 271282.
F. Zhao, L. Yang, C. Mo, and X. Li, “Characteristics of sheet formed by collision of two elliptical jets at short impact distance,” J. Fluids Eng. 138, 051201 (2016).
N. Yasuda, K. Yamamura, and Y. H. Mori, “Impingement of liquid jets at atmospheric and elevated pressures: An observational study using paired water jets or water and methylcyclohexane jets,” Proc. R. Soc. A 466, 3501 (2010).
C. H. Hertz and B. Hermanrud, “A liquid compound jet,” J. Fluid Mech. 131, 271 (1983).
M. Weder, M. Gloor, and L. Kleiser, “Decomposition of the temporal growth rate in linear instability of compressible gas flows,” J. Fluid Mech. 778, 120 (2015).
H. Ye, L. Yang, and Q. Fu, “Instability of viscoelastic compound jets,” Phys. Fluids 28, 043101 (2016).
S. P. Lin, Breakup of Liquid Sheets and Jets (Cambridge University Press, Cambridge, 2003), pp. 6670.
L. Yang, C. Wang, Q. Fu, M. Du, and M. Tong, “Weakly nonlinear instability of planar viscous sheets,” J. Fluid Mech. 735, 249 (2013).
F. Li, X. Y. Yin, and X. Z. Yin, “Axisymmetric and non-axisymmetric instability of an electrified viscous coaxial jet,” J. Fluid Mech. 632, 199 (2009).
R. Duan, Z. Chen, C. Wang, and L. Yang, “Instability of a confined viscoelastic liquid sheet in a viscous gas medium,” J. Fluids Eng. 135, 121204 (2013).
M. Altimira, A. Rivas, J. C. Ramos, and R. Anton, “Linear spatial instability of viscous flow of a liquid sheet through gas,” Phys. Fluids 22, 074103 (2010).
A. Lozano, F. Barreras, G. Hauke, and C. Dopazo, “Longitudinal instabilities in an air-blasted liquid sheet,” J. Fluid Mech. 437, 143 (2001).

Data & Media loading...


Article metrics loading...



This paper investigates the spatial instability of a double-layer viscous liquid sheet moving in a stationary gas medium. A linear stability analysis is conducted and two situations are considered, an inviscid-gas situation and a viscous-gas situation. In the inviscid-gas situation, the basic state of the entire gas phase is stationary and the analytical dispersion relation is derived. Similar to single-layer sheets, the instability of double-layer sheets presents two unstable modes, the sinuous and the varicose modes. However, the result of the base-case double-layer sheet indicates that the cutoff wavenumber of the dispersion curve is larger than that of a single-layer sheet. A decomposition of the growth rate is performed and the result shows that for small wavenumbers, the surface tension of all three interfaces and the aerodynamic forces of both the lower and upper gases contribute significantly to the unstable growth rate. In contrast, for large wavenumbers the major contribution to the unstable growth rate is only the surface tension of the upper interface and the aerodynamic force of the upper gas. In the viscous-gas situation, although the majority of the gas phase is stationary, gas boundary layers exist at the vicinity of the moving liquid sheet, and the stability problem is solved by a spectral collocation method. Compared with the inviscid-gas solution, the growth rate at large wavenumber is significantly suppressed. The decomposition of growth rate indicates that all the aerodynamic and surface tension terms behave consistently throughout the entire unstable wavenumber range. The effects of various parameters are discussed. In addition, the effect of gas viscosity and the gas velocity profile is investigated separately, and the results indicate that both factors affect the maximum growth rate and the dominant wavenumber, although the effect of the gas velocity profile is stronger than that of the gas viscosity.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd