Weakly Nonlinear Stability Analysis of a Thin Power-Law Fluid during Spin Coating

2013 ◽  
Vol 319 ◽  
pp. 90-95
Author(s):  
Ming Che Lin ◽  
Chun I Chen ◽  
Shou Jen Huang
Keyword(s):  
Power Law ◽  
Nonlinear Stability ◽  
Spin Coating ◽  
Kinematic Model ◽  
Vital Role ◽  
Nonlinear Stability Analysis ◽  
Power Law Fluid ◽  
Pseudoplastic Fluid ◽  
Weakly Nonlinear ◽  
Dilatant Fluid

The weakly nonlinear stability of a thin Ostwald de-Waele power-law fluid during spin coating is investigated. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The study reveals that the rotation number generates a destabilizing effect either in pseudoplastic fluid or in dilatant fluid. Further, it is shown that the degree of power-law index n plays a vital role in stabilizing the film flow.

Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane

2003 ◽  
Vol 70 (6) ◽  
pp. 915-923 ◽  
Author(s):  
R. Usha ◽  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Nonlinear Stability ◽  
Flow System ◽  
Nonlinear Stability Analysis ◽  
Power Law Fluid ◽  
Inclined Plane ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Power Law Index

Weakly nonlinear stability analysis of thin power-law liquid film flowing down an inclined plane including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal power-law liquid film down an inclined plane. The stability characteristics of the power-law liquid film show that isothermal and evaporating films are unstable for any value of power-law index ‘n’ while there exists a critical value of power-law index ‘n’ for the case of condensate film above which condensate film flow system is always stable. Thus, the results of the present analysis show that the mass transfer effects play a significant role in modifying the stability characteristics of the non-Newtonian power-law fluid flow system. The condensate (evaporating) power-law fluid film is more stable (unstable) than the isothermal power-law fluid film flowing down an inclined plane.

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

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
C. K. Chen ◽  
M. C. Lin
Keyword(s):  
Liquid Film ◽  
Spin Coating ◽  
Multiple Scales ◽  
Landau Equation ◽  
Thin Liquid Film ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability

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.

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

2014 ◽  
Vol 30 (5) ◽  
pp. 505-513 ◽  
Author(s):  
C.-I. Chen ◽  
M.-C. Lin ◽  
C.-K. Chen
Keyword(s):  
Power Law ◽  
Spin Coating ◽  
Film Flow ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Landau Equation ◽  
Shear Thickening ◽  
Vital Role ◽  
Power Law Fluid ◽  
Power Law Index

AbstractThe 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.

scholarly journals Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Cha'o-Kuang Chen ◽  
Dong-Yu Lai
Keyword(s):  
Spin Coating ◽  
Film Flow ◽  
Multiple Scales ◽  
Landau Equation ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Magnetic Filed

This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Stability Analysis of a Thin Pseudoplastic Fluid with Condensation Effects Flowing on a Rotating Circular Disk

2013 ◽  
Vol 699 ◽  
pp. 413-421
Author(s):  
Ming Che Lin
Keyword(s):  
Linear Stability ◽  
Kinematic Model ◽  
Circular Disk ◽  
Vital Role ◽  
Linear Growth Rate ◽  
Flow Index ◽  
Neutral Stability ◽  
Pseudoplastic Fluid ◽  
Linear Solution ◽  
By Products

This paper investigates the linear stability of a thin axisymmetric pseudoplastic fluid with condensation effects flowing on a rotating circular disk. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The method of normal mode is applied to study the linear stability. The neutral stability curve and the linear growth rate are obtained subsequently as the by-products of linear solution. The study reveals that the rotation number generates a destabilizing effect in pseudoplastic fluid. The degree of the flow index n plays a vital role in stabilizing the film flow.

Spatio-temporal structure of the ‘fully developed’ transitional flow in a symmetric wavy channel. Linear and weakly nonlinear stability analysis

2014 ◽  
Vol 764 ◽  
pp. 250-276 ◽  
Author(s):  
S. Blancher ◽  
Y. Le Guer ◽  
K. El Omari
Keyword(s):  
Stability Analysis ◽  
Laminar Flow ◽  
Steady Flow ◽  
Nonlinear Stability ◽  
Temporal Structure ◽  
Main Stream ◽  
Nonlinear Stability Analysis ◽  
Wavy Channel ◽  
Weakly Nonlinear ◽  
Spatio Temporal

AbstractThis work addresses the transition from 2D steady to 2D unsteady laminar flow for a fully developed regime in a symmetric wavy channel geometry. We investigate the existence and characteristics of the spatio-temporal structure of the fully developed unsteady laminar flow for those particular geometries for which the steady flow presents a periodic variation of the main stream velocity component. We perform a 2D global linear stability analysis of the fully developed steady laminar flow, and we show that, for all the geometries studied, the transition is triggered by a Hopf bifurcation associated with the breaking of the symmetries and the invariance of the steady flow. Critical Reynolds numbers, most unstable modes and their characteristics are presented for large ranges of the geometric parameters, namely wavenumber${\it\alpha}$from 0.3 to 5 and amplitude from 0 (straight channel) to 0.5. We show that it is possible to define geometries for which the wavenumber is proportional to the most unstable mode wavenumber for the critical Reynolds number. From this modal study we address a weakly nonlinear stability analysis with a view to obtaining the Landau coefficient$g$, and then the sub- or supercritical nature of the first bifurcation characterising the transition. We show that a critical geometric amplitude beyond which the first bifurcation is supercritical is associated with each geometric wavenumber.

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