Finite amplitude long-wave instability of power-law liquid films

Jenn Sen Lin, Chi-Chuan Hwang

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

This paper investigates the non-linear long-wave stability of power-law liquid films flow down an inclined plane. The method of long-wave theory is first used to derive a non-linear evolution equation of film thickness. After linearizing the non-linear evolution equation, the method of normal mode is applied to study its linear stability. Then the method of perturbation with multiple scales is used to solve this non-linear equation. The results reveal that the system will be more unstable when power-law exponent n decreases. Near the neutral stable state, the subcritical instability and explosive solution are possible at small n, and the supercritical and unconditional stable region exist only when n exceeds a certain value. Also, decreasing the magnitude of n will increase the dimensional wave speed of the unstable mode.

Original languageEnglish
Pages (from-to)769-777
Number of pages9
JournalInternational Journal of Non-Linear Mechanics
Volume35
Issue number5
DOIs
Publication statusPublished - 2000 Jan 1

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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