Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 A Preview
- 2 Basic Principles
- 3 Unidirectional and One-Dimensional Flow and Heat Transfer Problems
- 4 An Introduction to Asymptotic Approximations
- 5 The Thin-Gap Approximation – Lubrication Problems
- 6 The Thin-Gap Approximation – Films with a Free Surface
- 7 Creeping Flow – Two-Dimensional and Axisymmetric Problems
- 8 Creeping Flow – Three-Dimensional Problems
- 9 Convection Effects in Low-Reynolds-Number Flows
- 10 Laminar Boundary-Layer Theory
- 11 Heat and Mass Transfer at Large Reynolds Number
- 12 Hydrodynamic Stability
- Appendix A Governing Equations and Vector Operations in Cartesian, Cylindrical, and Spherical Coordinate Systems
- Appendix B Cartesian Component Notation
- Index
6 - The Thin-Gap Approximation – Films with a Free Surface
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 A Preview
- 2 Basic Principles
- 3 Unidirectional and One-Dimensional Flow and Heat Transfer Problems
- 4 An Introduction to Asymptotic Approximations
- 5 The Thin-Gap Approximation – Lubrication Problems
- 6 The Thin-Gap Approximation – Films with a Free Surface
- 7 Creeping Flow – Two-Dimensional and Axisymmetric Problems
- 8 Creeping Flow – Three-Dimensional Problems
- 9 Convection Effects in Low-Reynolds-Number Flows
- 10 Laminar Boundary-Layer Theory
- 11 Heat and Mass Transfer at Large Reynolds Number
- 12 Hydrodynamic Stability
- Appendix A Governing Equations and Vector Operations in Cartesian, Cylindrical, and Spherical Coordinate Systems
- Appendix B Cartesian Component Notation
- Index
Summary
Although the application of the “thin-film” approximation to analyze lubrication problems is one of its most important successes, there is an even larger body of problems in which the thin-film approximation can still be applied but in which the upper surface (or in some cases both surfaces of the thin film) is an interface. Examples include such diverse applications as gravity currents in geological phenomena, such as the gravitationally driven spread of molten lava; the dynamics of foams and or emulsions for which the thin films between bubbles (or drops) play a critical role in the dynamics; the dynamics of thin films in coating operations, and a variety of other materials processing applications; and thin films in biological systems, such as the coatings of the lung. Not only are the areas of application very diverse, but such films can and do display an astonishing array of complex phenomena, in spite of the limitations inherent in the thin-film assumptions. In part this is a consequence of the wide variety of physical effects that can play a role, including the capillary and Marangoni phenomena associated with surface tension, the possibility of a significant role for nonhydrodynamic effects such as van der Waals forces across the thin film and the possibility of transport processes such as evaporation/condensation.
In this chapter, we derive the governing equations for this class of thin films and show how they can be modified to account for the presence or absence of the various physical phenomena that were mentioned above.
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- Advanced Transport PhenomenaFluid Mechanics and Convective Transport Processes, pp. 355 - 428Publisher: Cambridge University PressPrint publication year: 2007