Summary
The breakup of thin planar liquid sheets due to the nonlinear growth of disturbances is determined. Conservation equations are derived using a control volume method and solved using MacCormack's predictor-corrector scheme. It is found that the size and geometry of ligaments, formed during breakup, vary with the weber number. Antisymmetric waves, which spontaneously intensify at higher values of the Weber number, give rise to thin ligaments. At lower values of the Weber number antisymmetric waves formed initially get transformed into symmetric interfaces giving larger ligaments. The magnitude of the initial amplitude of the disturbances is shown to strongly influence the disintegration. The results are compared with experimental results obtained for thin water sheets and good agreement is demonstrated.
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References
Squire, H. B.: Investigation of the instability of a moving fluid film. Br. J. Appl. Phys.4, 167–169 (1953).
York, J. L., Stubbs, H. E., Tek, M. R.: The mechanism of disintegration of liquid sheets. Trans. ASME75, 1279–1286 (1953).
Hagerty, W. W., Shea, J. F.: A study of the stability of plane fluid sheets. J. Appl. Mech.22, 509–514 (1955).
Dombrowski, N., Hooper, P. C.: The effect of ambient density on drop formation in sprays. Chem. Eng. Sci.17, 291–305 (1962).
Ibrahim, E. A., Akpan, E. T.: Liquid sheet instability. Acta Mech.131, 153–167 (1998).
Li, X: On the instability of plane liquid sheet in two gas streams of unequal velocities. Acta Mech.106, 137–156 (1994).
Teng, C. H., Lin, S. P., Chen, J. N.: Absolute and convective instability of a viscous liquid curtain in a viscous gas. J. Fluid Mech.332, 105–120 (1997).
Clark, C. J., Dombrowski, N.: Aerodynamic instability and disintegration of inviscid liquid sheets. Proc. R. Soc. London.A 329, 467–478 (1972).
Jazayeri, S. A., Li, X.: Nonlinear instability of plane liquid sheet. J. Fluid Mech.406, 281–308 (2000).
Rangel, R. H., Hess, C.: Nonlinear spatial instability of a fluid sheet. AIAA Paper 90-0118, 28th Aerospace Sciences Meeting, Jan. 8–11, Reno, Nevada, 1990.
Rangel, R. H., Sirignano, W. A.: The linear and nonlinear shear instability of a fluid sheet. Phys. FluidsA 3, 2392–2400 (1991).
Lozano, A., Olivares, A. G., Dopazo, C.: The instability growth leading to a liquid sheet breakup. Phys. Fluids10, 2188–2197 (1998).
Li, X., Tankin, R. S.: On the temporal instability of a two-dimensional viscous liquid sheet. J. Fluid Mech.226, 425–443 (1991).
Cousin, J., Dumouchel, C.: Effect of viscosity on the linear instability of a liquid sheet. Atom. Sprays6, 563–576 (1996).
Sellens, R. W.: A one-dimensional numerical model of capillary instability. Atom. Sprays2, 239–251 (1992).
Mehring, C., Sirignano, W. A.: Nonlinear capillary wave distortion and disintegration of plane liquid sheet. J. Fluid Mech.388, 69–113 (1999).
Kim, I., Sirignano, W. A.: Three-dimensional wave distortion and disintegration of planar liquid sheet. J. Fluid Mech.410, 147–183 (2000).
MacCormack, R. W.: Effect of viscosity in hyper velocity impact cratering. AIAA paper69–354, AIAA Hyper Velocity Impact Conference, April 30–May 2, Cincinnati, Ohio, 1969.
MacCormack, R. W.: A numerical method for solving the equations of compressible viscous flow. AIAA paper81-0110, AIAA 19th Aerospace Sciences Meeting, Jan. 12–15, St. Louis, Missouri, 1981.
Eggers, J., Dupont, T. F.: Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech.262, 205–221 (1994).
Mansour, A., Chigier, N.: Effect of turbulence on the stability of liquid jets and resulting droplet size distributions. Atom. Sprays4, 583–604 (1994).
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Tharakan, T.J., Ramamurthi, K. & Balakrishnan, M. Nonlinear breakup of thin liquid sheets. Acta Mechanica 156, 29–46 (2002). https://doi.org/10.1007/BF01188740
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DOI: https://doi.org/10.1007/BF01188740