0
Research Papers: Multiphase Flows

Weakly Nonlinear Stability Analysis of a Thin Liquid Film With Condensation Effects During Spin Coating

[+] Author and Article Information
C. K. Chen1

Department of Mechanical Engineering, National Cheng Kung University, No. 1 Ta-Hsueh Road, Tainan, Taiwan 701, R.O.C.ckchen@mail.ncku.edu.tw

M. C. Lin

Department of Mechanical Engineering, National Cheng Kung University, No. 1 Ta-Hsueh Road, Tainan, Taiwan 701, R.O.C.

1

Corresponding author.

J. Fluids Eng 131(10), 101303 (Sep 24, 2009) (8 pages) doi:10.1115/1.3222907 History: Received August 07, 2008; Revised August 03, 2009; Published September 24, 2009

This paper investigates the stability of a thin liquid film with condensation effects during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. The weakly nonlinear dynamics of a film flow are studied by the multiple scales method. The Ginzburg–Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that decreasing the rotation number and the radius of the rotating circular disk generally stabilizes the flow.

FIGURES IN THIS ARTICLE
<>
Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic diagram of a thin condensate film flowing on a rotating disk

Grahic Jump Location
Figure 2

(a) Linear neutral stability curves for three different Ro values at r=75 and (b) linear neutral stability curves for three different r values at Ro=0.1

Grahic Jump Location
Figure 3

(a) Neutral stability curves of condensate film flows for Ro=0.1 and r=75, (b) neutral stability curves of condensate film flows for Ro=0.15 and r=75, and (c) neutral stability curves of condensate film flows for Ro=0.1 and r=100

Grahic Jump Location
Figure 4

(a) Threshold amplitude in subcritical instability region for three different Ro values at Re=3 and r=75 and (b) threshold amplitude in subcritical instability region for three different r values at Re=3 and Ro=0.1

Grahic Jump Location
Figure 5

(a) Threshold amplitude in supercritical stability region for two different Ro values at Re=9 and r=100 and (b) threshold amplitude in supercritical stability region for three different r values at Re=9 and Ro=0.1

Grahic Jump Location
Figure 6

(a) Nonlinear wave speed in supercritical stability region for two different Ro values at Re=9 and r=100 and (b) nonlinear wave speed in supercritical stability region for three different r values at Re=9 and Ro=0.1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In