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.

scholarly journals Effect of Wind Stress on the Dynamics and Stability of Nonisothermal Power-Law Film down an Inclined Plane

2012 ◽  
Vol 2012 ◽  
pp. 1-31 ◽  
Author(s):  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Multiple Scales ◽  
Critical Value ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Nonlinear Stability Analysis ◽  
Inclined Plane ◽  
Condensate Film ◽  
Power Law Index

Dynamics and stability of a nonisothermal power-law liquid film down an inclined plane is considered in the presence of interfacial shear. Linear stability characteristics of the power-law liquid film using normal mode approach reveal that isothermal and evaporating films are unstable for any value of power-law index while there exists a critical value of power-law index for the case of condensate film above which condensate film ow system is always stable. This critical value of power-law index increases with the increase in shear stress at the interface. Weakly nonlinear stability analysis using method of multiple scales divulges the existence of zones due to supercritical stability and subcritical instability. The nonlinear evolution equation is solved numerically in a periodic domain. The results reveal that (1) for an isothermal dilatant (pseudoplastic) liquids, the maximum wave amplitude is always smaller (larger) than that for a Newtonian liquid and the amplitude of permanent wave increases with the increase in interfacial shear; (2) condensation of pseudoplastic film happens for the earlier instant of time when the phase change parameter increases and the effect of interfacial shear makes the film more corrugated; (3) dilatant (pseudoplastic) evaporating liquid film attains rupture faster (slower) than that of Newtonian liquid film, and the interfacial shear does not influence the time at which rupture occurs.

Nonlinear Stability of Thin Viscoelastic Liquid Film Down a Vertical Wall With Interfacial Phase Change

2002 ◽  
Author(s):  
B. Uma ◽  
R. Usha
Keyword(s):  
Liquid Film ◽  
Phase Change ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Flow System ◽  
Vertical Wall ◽  
Viscoelastic Liquid ◽  
Nonlinear Stability Analysis ◽  
The Stability

Wealky nonlinear stability analysis of thin viscoelastic liquid film flowing down a vertical wall 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 viscoelastic film flow system. The stability characteristics of the viscoelastic film flow are strongly influenced by the phase change parameter. The condensate (Evaporating) viscoelastic film is more stable (unstable) than the isothermal viscoelastic film and the effect of viscoelasticity is to destabilize the film flowing down a vertical wall.

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 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.

Nonlinear Stability of the Thin Micropolar Liquid Film Flowing Down on a Vertical Plate

1996 ◽  
Vol 118 (3) ◽  
pp. 498-505 ◽  
Author(s):  
Chen-I Hung ◽  
Jung-Shun Tsai ◽  
Cha’o-Kuang Chen
Keyword(s):  
Angular Momentum ◽  
Liquid Film ◽  
Nonlinear Stability ◽  
Vertical Plate ◽  
Film Flow ◽  
Flow System ◽  
Kinematic Equation ◽  
Stability Behavior ◽  
The Stability ◽  
Micropolar Liquid

A perturbation method is used to investigate analytically the nonlinear stability behavior of a thin micropolar liquid film flowing down a vertical plate. In this analysis, the conservation of mass, momentum, and angular momentum are considered and a corresponding nonlinear generalized kinematic equation for the film thickness is thereby derived. Results show that both the supercritical stability and the subcritical instability can be found in the micropolar film flow system. This analysis shows that the effect of the micropolar parameter R(=κ/μ) is to stabilize the film flow, that is, the stability of the flowing film increases with the increasing magnitude of the micropolar parameter R. Also, the present analysis shows that the micropolar coefficients, Δ(=h02/j) and Λ(=γ/μj), have very little effects on the stability of the micro-polar film.

Nonlinear Stability Analysis of the Thin Micropolar Liquid Film Flowing Down on a Vertical Cylinder

2000 ◽  
Vol 123 (2) ◽  
pp. 411-421 ◽  
Author(s):  
Po-Jen Cheng ◽  
Cha’o-Kuang Chen ◽  
Hsin-Yi Lai
Keyword(s):  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
Free Film ◽  
Micropolar Liquid

This paper investigates the weakly nonlinear stability theory of a thin micropolar liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first 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. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a micropolar film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the micropolar parameter K=κ/μ and increasing the radius of the cylinder the film flow can become relatively more stable traveling down along the vertical cylinder.

Nonlinear Stability Analysis of a Falling Film in the Presence of Gas Flow

2007 ◽  
Author(s):  
B. Uma ◽  
R. Usha
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Gas Flow ◽  
Film Flow ◽  
Flow System ◽  
Interfacial Shear Stress ◽  
Wave Theory ◽  
Falling Film ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear

A viscous liquid film flows down along the interior of an annular region under gravity with a countercurrent/cocurrent stream of gas phase adjoining the free surface. The interfacial shear stress effects on the stability of the film flow system in the presence of gas flow has been analyzed for the model that describes the motion for the annular countercurrent/cocurrent gas-liquid two-dimensional falling film. A nonlinear evolution of Benney type describing the film thickness in the presence of gasflow has been derived using long wave theory and lubrication approximation. Linear and weakly nonlinear stability analysis of the evolution equation show that both supercritical stability and subcritical instability are possible for the film flow system in the presence of gas flow. The nonlinear equation has been solved numerically in a periodic domain and the results show that the shape and amplitude of the permanent wave are greatly influenced by the countercurrent/cocurrent gas flow.

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