Weakly 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. © 2004 Elsevier Ltd. All rights reserved.

Usha R

Department of Mathematics

Asymptotic stability

Heat transfer

Hydrodynamics

KINEMATICS

Newtonian liquids

Nonlinear systems

Reynolds number

Shear stress

Surface tension

Viscoelasticity

INTERFACIAL PHASE CHANGE EFFECTS

LINEAR STABILITY SOLUTION

VERTICAL WALLS

VISCOELASTIC LIQUID

Thin films

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International Journal of Engineering Science

Linear instability analysis of a thin layer of viscoelastic fluid flowing down a non-uniformly heated inclined plane is considered. The study is based on the assumption of constant temperature gradient (positive or negative) along the plane. The film flow system is influenced by gravity, mean surface tension, thermocapillary forces acting along the free surface and viscoelastic forces. The role of these forces is investigated by seeking a solution of the stability problem in a series in small wave number. The results show that the critical Reynolds number is influenced by the Reynolds number, the ratio of Marangoni number to Prandtl number, the Biot number, the viscoelastic parameter and the angle of inclination. © 2005 Elsevier Ltd. All rights reserved.

Linear instability in a thin viscoelastic liquid film on an inclined, non-uniformly heated wall

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.

Journal of Applied Mechanics, Transactions ASME

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

Weakly nonlinear stability analysis of thin viscoelastic film flowing down on the outer surface of a rotating vertical cylinder

Journal of Fluids Engineering

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

International Journal of Non-Linear Mechanics

Finite amplitude long-wave instability of power-law liquid films

Journal of Physics D: Applied Physics

Stability analysis of thin viscoelastic liquid film flowing down on a vertical wall

Interfacial phase change effects on the stability characteristics of thin viscoelastic liquid film down a vertical wall

Journal	International Journal of Engineering Science
ISSN	00207225
Open Access	No