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Research Papers: Fundamental Issues and Canonical Flows

Instability of a Confined Viscoelastic Liquid Sheet in a Viscous Gas Medium

[+] Author and Article Information
Zhi-ying Chen

School of Energy and Power Engineering,
Beijing University of Aeronautics
and Astronautics,
Beijing 100191, China

Li-jun Yang

e-mail address: yanglijun@buaa.edu.cn
School of Astronautics,
Beijing University of Aeronautics
and Astronautics,
Beijing 100191, China

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 31, 2013; final manuscript received July 29, 2013; published online September 23, 2013. Assoc. Editor: John Abraham.

J. Fluids Eng 135(12), 121204 (Sep 23, 2013) (10 pages) Paper No: FE-13-1212; doi: 10.1115/1.4025250 History: Received March 31, 2013; Revised July 29, 2013

A linear analysis method was used to investigate the instability behavior of a viscoelastic liquid sheet moving through a viscous gas bounded by two horizontal parallel flat plates. The liquid sheet velocity profile was taken into account. The result showed that the velocity gradient of viscoelastic liquid sheets was greater than that of the corresponding Newtonian sheets. The effects of time-constant, elasticity number, and the ratio of distance between the liquid sheet and flat plate to liquid sheet thickness on the velocity profiles of viscoelastic liquid sheets were also investigated. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The rheological parameters and flow parameters were tested for their influence on the instability of the viscoelastic liquid sheets. It is concluded that disturbances grow faster on viscoelastic liquid sheets than on Newtonian sheets with identical zero shear viscosity. Increasing the momentum flux ratio, elasticity number, Weber number, and liquid Reynolds number accelerated the breakup of the viscoelastic liquid sheet, while increasing the time constant, ratio of the distance between the liquid sheet, and the flat plate to the liquid sheet thickness had the opposite effect.

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References

Savart, F., 1833, “Memoire sur le Choc D'une Veine Liquide Lancée Contre un Plan Circulaire,” Ann. Chim., 54, pp. 56–87.
Squire, H. B., 1953, “Investigation of the Instability of a Moving Liquid Film,” Br. J. Appl., Phys., 4, pp. 167–169. [CrossRef]
Hagerty, W. W., and Shea, J. F., 1955, “A Study Stability of Plane Fluid Sheets,” J. Appl. Mech., 22, pp. 509–514.
Dombrowski, N., and Johns, W. R., 1963, “The Aerodynamic Instability and Disintegration Viscosity Liquid Sheet,” Chem. Eng. Sci., 18, pp. 203–214. [CrossRef]
Li, X., and Tankin, R. S., 1991, “On the Temporal Instability of a Two-Dimensional Viscosity Liquid Sheet,” J. Fluid Mech., 226, pp. 425–443. [CrossRef]
Yang, L., Liu, Y., and Fu, Q., 2012, “Linear Stability Analysis of an Electrified Viscoelastic Liquid Jet,” ASME J. Fluids Eng., 134, p. 071303. [CrossRef]
Li, X., 1993, “Spatial Instability of Plan Liquid Sheets,” Chem. Eng. Sci., 48, pp. 2973–2981. [CrossRef]
Lozano, A., Barreras, F., Hauke, G., and Dopazo, C., 2001, “Longitudinal Instabilities in an Air-Blasted Liquid Sheet,” J. Fluid Mech., 437, pp. 143–173. [CrossRef]
Ibrahim, E. A., 1998, “Instability of a Liquid Sheet of Parabolic Velocity Profile,” Phys. Fluids, 10, pp. 1034–1036. [CrossRef]
Ibrahim, E. A., and Akpan, E. T., 1996, “Three-Dimensional Instability of Viscous Liquid Sheets,” Atomization Sprays, 6, pp. 649–665. Available at http://www.dl.begellhouse.com/journals/6a7c7e10642258cc,53157ffd69db9022,691ae8ce689163a0.html
Taylor, G. I., 1959, “The Dynamics of Thin Sheets of Fluid, Waves on Fluid Sheets,” Proc. R. Soc., 253, pp. 296–312. [CrossRef]
Lin, S. P., Lian, Z. W., and Creighton, B. J., 1990, “Absolute and Convective Instability of a Liquid Sheet,” J. Fluid Mech., 220, pp. 673–689. [CrossRef]
Rees, S. J., and Juniper, M. P., 2010, “The Effect of Confinement on the Stability of Viscous Planar Jets and Wakes,” J. Fluid Mech., 656, pp. 309–336. [CrossRef]
Liu, Z., Brenn, G., and Durst, F., 1998, “Linear Analysis of the Instability of Two-Dimensional Non-Newtonian Liquid Sheets,” J. Non-Newtonian Fluid Mech., 78, pp. 133–166. [CrossRef]
Yang, L., Qu, Y., and Fu, Q., 2010, “Linear Stability Analysis of a Non- Newtonian Liquid Sheet,” J. Propul. Power, 26, pp. 1212–1224. [CrossRef]
Astarita, G., and Marrucci, G., 1974, Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, New York.
Bronshtein, I. N., Semendyayev, K. A., Musiol, G., and Muhelig, H., 2004, Handbook of Mathematics, Springer, Berlin, Chap. 1.
Orszag, S. A., 1971, “Accurate Solution of the Orr–Sommerfeld Stability Equation,” J. Fluid Mech., 50, pp. 689–703. [CrossRef]
Peyret, R., 2002, Spectral Methods for Incompressible Viscous Flow, Springer, New York, Chap. 3.
Shen, J., and Tang, T., 2006, Spectral and High-Order Methods With Applications, China Press, Beijing, P. R. C., Chap. 2.
Nath, S., and Mukhopadhyay, A., 2009, “Instability Analysis of a Plane Liquid Sheet Sandwiched Between Two Gas Streams of Nonzero Unequal Velocities,” AIAA Paper No. 5157.
Liu, Z., and Liu, Z., 2006, “Linear Analysis of Three-Dimensional Instability of Non-Newtonian Liquid Jets,” J. Fluid Mech., 559, pp. 451–459. [CrossRef]
Liu, Z., and Liu, Z., 2008, “Instability of a Viscoelastic Liquid Jet With Axisymmetric and Asymmetric Disturbances,” Int. J. Multiphase Flow, 34, pp. 42–60. [CrossRef]
Ivansson, S., and Karasalo, I., 1993, “Computation of Modal Wavenumbers Using an Adaptive Winding-Number Integeral Method With Error Control,” J. Sound Vib., 161(1), pp. 173–180. [CrossRef]

Figures

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Fig. 2

Schematic diagram of a liquid sheet: (a) the varicose mode and (b) the sinuous mode

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Fig. 1

Sketch of velocity profile within and out of the liquid sheet

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Fig. 7

Effects of ratio l on growth rate (for viscoelastic fluid λ = 0.5, Re1 = 850, We = 100, El = 0.5, MFR = 0.27, varying l) (a) dispersion curves and (b) maximum growth rate

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Fig. 8

Effect of liquid weber numbers on growth rate (for viscoelastic fluid λ = 0.5, Re1 = 850, l = 2, El = 0.5, MFR = 0.27, varying We) (a) dispersion curves and (b) maximum growth rate

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Fig. 5

Effect of time constant ratio on growth rate (for viscoelastic fluid Re1 = 850, l = 2, We = 100, El = 0.5, MFR = 0.27, varying λ): (a) dispersion curves and (b) maximum growth rate

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Fig. 6

Effect of liquid Reynolds numbers on growth rate (for viscoelastic fluid λ = 0.5, l = 2, We = 100, El = 0.5, MFR = 0.27, varying Re1) (a) dispersion curves and (b) maximum growth rate

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Fig. 9

Effect of liquid elasticity numbers on growth rate (for viscoelastic fluid λ = 0.5, Re1 = 850, l = 2, We = 100, MFR = 0.27, varying El) (a) dispersion curves and (b) maximum growth rate

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Fig. 3

Variation of liquid velocity profile for viscoelastic fluid: (a) effects of the elasticity number, (b) effects of the time constant ratio, and (c) effects of the ratio l = δ/h

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Fig. 4

Variation of growth rate with wavenumber for planar liquid sheet (for viscoelastic fluid λ = 0.5, Re1 = 510, l = 2, We = 100, El = 0.5, WMF = 0.11, and λ = 0, El = 0 for Newtonian fluid)

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Fig. 10

Effect of momentum flux ratio on growth rate (for viscoelastic fluid λ = 0.5, Re1 = 850, l = 2, We = 100, El = 0.5, varying MFR) (a) dispersion curves and (b) maximum growth rate

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Fig. 11

Effect of N on growth rate (for viscoelastic fluid λ = 0.5, Re1 = 850, l = 2, We = 100, El = 0.5, MFR = 0.27 varying N)

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