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

Abstract

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.

Hydromagnetic instability of a thin viscoelastic layer on a moving column

“…The flow stability is reduced due to the medium porosity. Many researches [16][17][18][19][20][21][22][23][24][25][26][27] investigated the problem of liquid-film flow on a solid surface. In [16], the authors discussed a condensate Newtonian film on a vertical plate subjected to a normal magnetic field in the case of small magnetic Reynolds number where the viscous and Joule's heating are ignored.…”

“…He converted the model into a dynamical system and discussed the stability. In [24], Chen et al considered a similar model to [22] where a power-law model was assumed instead of the viscoelastic one. They showed that shear-thickening type can be more stable compared with shear-thinning one.…”