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Onset of folding in plane liquid films

Published online by Cambridge University Press:  26 April 2006

A. L. Yarin  and
B. M. Tchavdarov
A. L. Yarin
Affiliation:
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
B. M. Tchavdarov
Affiliation:
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
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Abstract

The onset of the folding effect characteristic of highly viscous liquid films (plane jets) slowly impinging on a wall is studied. Nonlinear quasi-one-dimensional equations are derived to describe the flow. In the linear approximation they reduce to the eigenvalue problem, whose solution predicts that instability (the onset of folding) sets in when the length of the film exceeds a critical value. The critical folding heights and the oscillation frequencies at the onset of instability are predicted as a function of flow parameters. Theoretical results are compared with Cruickshank's (1988) experimental data. Agreement is quite good only in the range of parameters where the quasi-one-dimensional approximation is applicable (thin films at the onset of folding).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 307 , 25 January 1996 , pp. 85 - 99
Copyright
© 1996 Cambridge University Press

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References

Bejan, A. 1987 Buckling flows: a new frontier in fluid mechanics. Ann Rev. Numer. Fluid Mech. Heat Transfer 1, 262.Google Scholar
Benjamin, T. B. & Mullin, T. 1988 Buckling instabilities in layers of viscous liquid subjected to shearing. J. Fluid Mech. 195, 523.Google Scholar
Buckmaster, J. 1973 The buckling of thin viscous jets. J. Fluid Mech. 61, 449.Google Scholar
Buckmaster, J. D. & Nachman, A. 1978 The buckling and stretching of a viscida. II. Effects of surface tension. Q. J. Mech. Appl. Maths 31, 157.Google Scholar
Buckmaster, J. D., Nachman, A. & Ting, L. 1975 The buckling and stretching of a viscida. J. Fluid Mech. 69, 1.Google Scholar
Cruickshank, J. O. 1984 A similarity between plane and axisymmetric viscous-gravity jets. Trans. ASME I: J. Fluids Engng 106, 52.Google Scholar
Cruickshank, J. O. 1988 Low-Reynolds-number instabilities in stagnating jet flows. J. Fluid Mech. 193, 111.Google Scholar
Cruickshank, J. O. & Munson, B. R. 1981 Viscous fluid buckling of plane and axisymmetric jets. J. Fluid Mech. 113, 221.Google Scholar
Entov, V. M. & Yarin, A. L. 1984a The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91.Google Scholar
Entov, V. M. & Yarin, A. L. 1984b Dynamics of free liquid jets and films of viscous and rheologically complex liquids. Adv. Mech. VINITI, Fluid Mech. 18, 112 (in Russian).Google Scholar
Green, A. E. 1976 On the nonlinear behavior of fluid jets. Intl J. Engng Sci. 14, 49.Google Scholar
Griffiths, R. W. & Turner, J. S. 1988 Folding of viscous plumes impinging on a density or viscosity interface. Geophys. J. 95, 397.Google Scholar
Kase, S. & Matsuo, T. 1965 Studies on melt spinning.–I. Fundamental equations on the dynamics of melt spinning. J. Polymer Sci. A 3, 2541.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Theory of Elasticity. Pergamon.
Matovich, M. A. & Pearson, J. R. A. 1969 Spinning a molten threadline. Steady-state isothermal viscous flows. Indust. Engng Chem. Fundam. 8, 512.Google Scholar
Pearson, J. R. A. & Petrie, C. J. S. 1970a The flow of a tubular film. Part 1. Formal mathematical representation. J. Fluid Mech. 40, 1.Google Scholar
Pearson, J. R. A. & Petrie, C. J. S. 1970b The flow of tubular film. Part 2. Interpretation of the model and discussion of solutions. J. Fluid Mech. 42, 609.Google Scholar
Schultz, W. W. & Davis, S. H. 1982 One-dimensional liquid fibers. J. Rheol. 26, 331.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. I. Water bells. Proc. R. Soc. Lond. A 253, 289.Google Scholar
Taylor, G. I. 1969 Instability of jets, threads and sheets of viscous fluid. Proc. 12th Intl Congr. Appl. Mech., Stanford, 1968 (ed. M. Hetényi & W. G. Vincenti), p. 382. Springer.
Tchavdarov, B., Yarin, A. L. & Radev, S. 1993 Buckling of thin liquid jets. J. Fluid Mech. 253, 593.Google Scholar
Yarin, A. L. 1983 On the dynamical equations for liquid jets. Fluid Dyn. 18, 134.Google Scholar
Yarin, A. L. 1993 Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman Scientific & Technical and Wiley.
Yarin, A. L. 1994 On instability of rapidly stretching metal jets produced by shaped charges. Intl J. Engng Sci. 32, 847.Google Scholar
Yarin, A. L., Gospodinov, P. & Roussinov, V. I. 1994 Stability loss and sensitivity in hollow fiber drawing. Phys. Fluids 6, 1454.Google Scholar