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Surface Instabilities on a Thin Power-Law Fluid During Spin Coating

Published online by Cambridge University Press:  22 May 2014

C.-I. Chen,
M.-C. Lin and
C.-K. Chen
C.-I. Chen
Affiliation:
Department of Industrial Management, I-Shou University, Kaohsiung County, Taiwan 84041, R.O.C.
M.-C. Lin*
Affiliation:
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 80778, R.O.C.
C.-K. Chen
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University Tainan, Taiwan 70101, R.O.C.
*
*limit168@kuas.edu.tw

Abstract

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The phenomena of surface instabilities in a thin power-law fluid during spin coating are investigated. The set of Navier-Stokes equations with non-Newtonian behavior in the region of low Reynolds number serves as a mathematical description of the physical systems. Long-wave perturbation analysis is proposed to derive an evolution equation of the Ostwald de-Waele type fluid to govern the propagation of surface waves. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The amplitude of instability is determined by a Ginzburg-Landau equation. The study reveals that the degree of power-law index plays a vital role in stabilizing the film flow. The shear-thinning fluid is more unstable than the shear-thickening fluid in the stability analysis. Further, the nonlinear wave speed in the supercritical stability region decreases with increasing values of power-law index.

Keywords

Nonlinear stabilityPower-law fluidSpin coating

Information

Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 5 , October 2014, pp. 505 - 513
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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