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.

Usha R

Department of Mathematics

Capillary flow

Parameter estimation

Prandtl number

Reynolds number

Surface tension

Viscoelasticity

LINEAR INSTABILITY

Temperature gradient

THERMOCAPILLARY FORCES

VISCOELASTIC PARAMETERS

Thin films

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International Journal of Engineering Science

A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to nonuniform heating has been considered. The temperature of the inclined plane is assumed to be linearly distributed and the case when the temperature gradient is positive or negative is investigated. The film flow is influenced by gravity, mean surface tension, and thermocapillary forces acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A nonlinear evolution equation is derived by applying the long-wave theory, and the equation governs the evolution of a power-law film flowing down a nonuniformly heated inclined plane. The linear stability analysis shows that the film flow system is stable when the plate temperature decreases in the downstream direction while it is less stable for increasing temperature along the plate. Weakly nonlinear stability analysis using the method of multiple scales has been investigated and this leads to a secular equation of the Ginzburg-Landau type. The analysis shows that both supercritical stability and subcritical instability are possible for the film flow system. The results indicate the existence of finite-amplitude waves, and the threshold amplitude and nonlinear speed of these waves are influenced by thermocapillarity. The nonlinear evolution equation for the film thickness is solved numerically in a periodic domain in the supercritical stable region, and the results show that the shape of the wave is influenced by the choice of wave number, non-Newtonian rheology, and nonuniform heating. Copyright © 2009 by ASME.

Journal of Fluids Engineering, Transactions of the ASME

Long-wave instabilities in a non-Newtonian film on a nonuniformly heated inclined plane

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.

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

Marangoni instability of a thin liquid film heated from below by a local heat source

Physics of Fluids

Nonlinear evolution of nonuniformly heated falling liquid films

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

Journal	International Journal of Engineering Science
ISSN	00207225
Open Access	No