Nonlinear stability analysis of the thin pseudoplastic liquid film flowing down along a vertical wall

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

This article investigates the weakly nonlinear stability theory of a thin pseudoplastic liquid film flowing down on a vertical wall. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equation with free film interface. The normal mode approach is used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg-Landau equation. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a pseudoplastic film flow system. The results also reveal that the pseudoplastic liquid film flows are less stable than Newtonian's as traveling down along the vertical wall. The degree of instability in the film flow is further intensified by decreasing the flow index n.

Original languageEnglish
Pages (from-to)8238-8246
Number of pages9
JournalJournal of Applied Physics
Volume89
Issue number12
DOIs
Publication statusPublished - 2001 Jun 1

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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