Nonlinear stability characterization of thin Newtonian film flows traveling down on a vertical moving plate

Steven Hsin-Yi Lai, Hung Ming Sung, Cha'o Kuang Chen

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The paper presents both the linear and nonlinear stability theories for the characterization of thin Newtonian film flows traveling down along a vertical moving plate. The linear model is first developed to characterize the flow behavior. After showing the inadequacy of the linear model in representing certain flow characteristics, the nonlinear kinematics model is then developed to represent the system. The long-wave perturbation method is employed to derive the generalized kinematic equations with free film surface condition. The linear model is solved by using the normal mode method for three different, namely, the quiescent, up-moving and down-moving, moving conditions. Subsequently, the elaborated nonlinear film flow model is solved by the method of multiple scales. The modeling results clearly indicate that both subcritical instability and supercritical stability conditions are possible to occur in the film flow system. The effect of the down-moving motion of the vertical plate tends to enhance the stability of the film flow.

Original languageEnglish
Pages (from-to)665-680
Number of pages16
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume10
Issue number6
DOIs
Publication statusPublished - 2005 Sep 1

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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