Stability analysis of thin viscoelastic liquid film flowing down on a vertical wall

Po Jen Cheng, Steven Hsin-Yi Lai, Cha'o Kuang Chen

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

This paper investigates the stability of thin viscoelastic liquid film flowing down on a vertical wall using a long-wave perturbation method to find the solution for generalized nonlinear kinematic equations with a free film interface. To begin with, a normal mode approach is employed to obtain the linear stability solution for the film flow. The linear growth rate of the amplitudes, the wave speeds and the threshold conditions are obtained subsequently as the by-products of linear solutions. The results of linear analysis indicate that the viscoelastic parameter k = k0/(ρh*02) destabilizes the film flow as its magnitude increases. To further investigate practical flow stability conditions, the weak nonlinear dynamics of a film flow are presented by using the method of multiple scales. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg-Landau equation. Modelling results indicate that both the subcritical instability and the supercritical stability conditions are possible in a viscoelastic film flow system. The results of nonlinear modelling further indicate that the threshold amplitude εa0 in the subcritical instability region becomes smaller as the viscoelastic parameter k increases. If the initial finite amplitude of disturbance is greater than the value of threshold amplitude, the system becomes explosively unstable. It is also interesting to note that both the threshold amplitude and the nonlinear wave speed in the supercritical stability region increase as the value of k increases. Therefore, the flow becomes unstable when the value of k increases. The viscoelastic parameter k indeed plays a significant role in destabilizing the film flow travelling down along a vertical plate.

Original languageEnglish
Pages (from-to)1674-1682
Number of pages9
JournalJournal of Physics D: Applied Physics
Volume33
Issue number14
DOIs
Publication statusPublished - 2000 Jul 21

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Liquid films
Thin films
liquids
thresholds
kinematic equations
flow stability
Landau-Ginzburg equations
planetary waves
Byproducts
Kinematics
disturbances
perturbation

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Surfaces, Coatings and Films

Cite this

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abstract = "This paper investigates the stability of thin viscoelastic liquid film flowing down on a vertical wall using a long-wave perturbation method to find the solution for generalized nonlinear kinematic equations with a free film interface. To begin with, a normal mode approach is employed to obtain the linear stability solution for the film flow. The linear growth rate of the amplitudes, the wave speeds and the threshold conditions are obtained subsequently as the by-products of linear solutions. The results of linear analysis indicate that the viscoelastic parameter k = k0/(ρh*02) destabilizes the film flow as its magnitude increases. To further investigate practical flow stability conditions, the weak nonlinear dynamics of a film flow are presented by using the method of multiple scales. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg-Landau equation. Modelling results indicate that both the subcritical instability and the supercritical stability conditions are possible in a viscoelastic film flow system. The results of nonlinear modelling further indicate that the threshold amplitude εa0 in the subcritical instability region becomes smaller as the viscoelastic parameter k increases. If the initial finite amplitude of disturbance is greater than the value of threshold amplitude, the system becomes explosively unstable. It is also interesting to note that both the threshold amplitude and the nonlinear wave speed in the supercritical stability region increase as the value of k increases. Therefore, the flow becomes unstable when the value of k increases. The viscoelastic parameter k indeed plays a significant role in destabilizing the film flow travelling down along a vertical plate.",
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Stability analysis of thin viscoelastic liquid film flowing down on a vertical wall. / Cheng, Po Jen; Lai, Steven Hsin-Yi; Chen, Cha'o Kuang.

In: Journal of Physics D: Applied Physics, Vol. 33, No. 14, 21.07.2000, p. 1674-1682.

Research output: Contribution to journalArticle

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