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 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 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.

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.

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. 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 analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Nonlinear Rupture of Thin Micropolar Liquid Film Under a Magnetic Field

2016 ◽  
Vol 33 (2) ◽  
pp. 249-256
Author(s):  
P.-J. Cheng ◽  
C.-K. Chen ◽  
Y.-C. Wang ◽  
M.-C. Lin ◽  
C.-K. Yang
Keyword(s):  
Magnetic Field ◽  
Liquid Film ◽  
Evolution Equations ◽  
Film Flow ◽  
Nonlinear Evolution Equations ◽  
Rupture Time ◽  
Initial Disturbance ◽  
Horizontal Plate ◽  
Film Rupture ◽  
Micropolar Liquid

AbstractThis paper investigates the rupture problem of a thin micropolar liquid film under a magnetic field on a horizontal plate, using long-wave perturbation to resolve nonlinear evolution equations with a free film interface. The governing equation is resolved using a finite difference method as part of an initial value problem for spatial periodic boundary conditions. The effect of a micropolar liquid under a magnetic field on the nonlinear rupture mechanism is studied in terms of the micropolar parameter, R, the Hartmann constant, m and the initial disturbance amplitude, H0. Modeling results indicate that the R, m and H0 parameters strongly affect the film flow. Enhancing the micropolar and magnetic effects is found to delay the rupture time. In addition, the results show that the film rupture time increases as the values of initial disturbance magnitude decrease. The micropolar and magnetic parameters indeed play a significant role in the film flow on a horizontal plate. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Time dependent Oldroyd-B liquid film flow over an oscillating and porous vertical plate with the effect of thermal radiation

2017 ◽  
Author(s):  
Muhammad Ismail Mohmand ◽  
Qayyum Shah ◽  
Mustafa Bin Mamat ◽  
Zahir Shah ◽  
Abdul Samad Khan
Keyword(s):  
Thermal Radiation ◽  
Liquid Film ◽  
Vertical Plate ◽  
Film Flow ◽  
Time Dependent ◽  
Liquid Film Flow

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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