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Shape instability in thin viscous films and jets

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Summary

The theory of viscous liquid films and thin jets as two-and one-dimensional continua is examined. Theoretical results are presented concerning a special type of instability which leads to the loss of smoothness of the shape (wrinkling) and associated with the failure of hyperbolicity of the governing equations. The conditions for different types of such an instability are formulated in the closed analytical form.

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References

  1. Cruickshank, J. O., Munson, B. R.: Viscous fluid buckling of plane and axisymmetric jets. J. Fluid Mech.113, 221–239 (1981).

    Article  Google Scholar 

  2. McCarthy, M. J., Molloy, N. A.: Review of stability of liquid jets and the influence of nozzle design. Chem. Eng. J.7, 1–20 (1976).

    Article  Google Scholar 

  3. Suleiman, S. M., Munson, B. R.: Buckling of a thin sheet of a viscous fluid. Phys. Fluids29, 1–5 (1981).

    Article  Google Scholar 

  4. Taylor, G. I.: Instability of jets, threads an sheets of viscous fluids. Proc. Int. Congr. Appl. Mech., Berlin-Heidelberg-New York: Springer 1968.

    Google Scholar 

  5. Zak, M.: Dynamics of liquid films and thin jets. SIAM J. Appl. Math.32, 276–289 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  6. Zak, M.: On the loss of stability of the shape of an ideally flexible string. Appl. Math. and Mech.32, Moscow (1968).

  7. Zak, M.: Dynamics of film. J. Elasticity9, 171–185 (1979).

    Article  MATH  Google Scholar 

  8. Zak, M.: Surface phenomena in elasticity. J. Elasticity11, 113–127 (1981).

    Article  MATH  Google Scholar 

  9. Zak, M.: On the failure of hyperbolicity in elasticity. J. Elasticity12, 219–229 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  10. Zak, M.: A mathematical model of post-instability in fluid mechanics. Acta Mechanica43, 97–117 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  11. Lin, C. C.: The theory of hydrodynamic stability. Cambridge University Press 1955.

  12. Zak, M.: Uniqueness and stability of the solution of the small perturbation problem of a flexible string with a free end. Applied Math. and Mech.34 (1970).

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Zak, M. Shape instability in thin viscous films and jets. Acta Mechanica 55, 33–50 (1985). https://doi.org/10.1007/BF01267977

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  • DOI: https://doi.org/10.1007/BF01267977

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