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TECHNICAL PAPERS

Nonlinear Theory of Tear Film Rupture

[+] Author and Article Information
Madhu Sudan Reddy Gorla

Eye Care Center, Pottsville, PA 17901

Rama Subba Reddy Gorla

Cleveland State University, Cleveland, OH 44115e-mail: gorla@csaxp.csuohio.edu

J Biomech Eng 122(5), 498-503 (Mar 22, 2000) (6 pages) doi:10.1115/1.1289997 History: Received July 02, 1999; Revised March 22, 2000
Copyright © 2000 by ASME
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References

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Yih,  C. S., 1968, “Instability of Unsteady Flows or Configurations, Part 1: Instability of a Horizontal Liquid Layer on an Oscillating Plane,” J. Fluid Mech., 31, pp. 737–742.
Coward,  A. V., and Renardy,  Y. Y., 1995, “Small Amplitude Oscillatory Forcing on a Two-Layer Plane Channel Flow,” Bull. Am. Phys. Soc., 40, pp. 1950–1956.
Or,  A. C., and Kelly,  R. E., 1996, “Marangoni Convections of a Thin Deformable Layer of Liquid Subjected to Finite-Amplitude Nonplanar Oscillations,” Bull. Am. Phys. Soc., 40, pp. 1949–1954.
Woods,  D. R., and Lin,  S. P., 1995, “Instability of a Liquid Film Flow Over a Vibrating Inclined Plane,” J. Fluid Mech., 58, pp. 391–400.
Ruckenstein,  E., and Jain,  R. K., 1974, “Spontaneous Rupture of Thin Liquid Films,” J. Chem. Soc., Faraday Trans., 270, pp. 132–146.
Williams,  M. B., and Davis,  S. H., 1982, “Nonlinear Theory of Film Rupture,” J. Colloid Interface Sci., 90, pp. 220–228.
Sharma,  A., and Ruckenstein,  E., 1986, “Rupture of Thin Free Films With Insoluble Surfactants: Nonlinear Aspects,” AIChE Symp. Ser., 252, pp. 129–144.
Sharma,  A., and Ruckenstein,  E., 1986, “An Analytical Nonlinear Theory of Thin Film Rupture and Its Application to Wetting Films,” J. Colloid Interface Sci., 113, pp. 456–479.
Oron,  A., Davis,  S. H., and Bankoff,  S. G., 1997, “Long-Scale Evolution of Thin Liquid Films,” Rev. Mod. Phys., 69, pp. 931–980.
Joo,  S. W., Davis,  S. H., and Bankoff,  S. G., 1991, “Long-Wave Instabilities of Heated Films: Two-Dimensional Theory of Uniform Layers,” J. Fluid Mech., 230, pp. 117–146.
Liu,  J., Schneider,  J. B., and Gollub,  J. P., 1995, “Three-Dimensional Instabilities of Film Flows,” Phys. Fluids, 7, pp. 55–59.
Reisfeld,  B., and Bankoff,  S. G., 1990, “Nonlinear Stability of a Heated Film With Variable Viscosity,” Phys. Fluids, 2, pp. 2066–2067.
Gorla,  R. S. R., and Byrd,  L., 1999, “Effect of Electrostatic Field on Film Rupture,” ASME J. Fluids Eng., 121, pp. 651–657.
Lin,  S. P., 1982, “Tear Film Rupture,” J. Colloid Interface Sci., 89, pp. 226–231.
Sharma,  A., and Ruckenstein,  E., 1985, “Mechanism of Tear Film Rupture and Formation of Dry Spots on Cornea,” J. Colloid Interface Sci., 106, pp. 12–27.
Burelbach,  J. P., Bankoff,  S. G., and Davis,  S. H., 1988, “Linear Stability of Evaporating/Condensing Liquid Films,” J. Fluid Mech., 195, pp. 463–494.
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Figures

Grahic Jump Location
Flow model for the thin film flow
Grahic Jump Location
Film thickness distribution at the rupture time
Grahic Jump Location
Minimum film thickness versus time
Grahic Jump Location
Ratio of nonlinear theory time versus linear theory rupture time as a function of initial amplitude b

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