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.

Usha R

Department of Mathematics

Boundary conditions

Condensation

Evaporation

KINEMATICS

MASS TRANSFER

Nonlinear systems

Reynolds number

Rheology

Supercritical fluid extraction

Thermal conductivity

Thin films

Liquid films

NONLINEAR STABILITY

Newtonian liquids

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

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It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

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

Journal of Applied Mechanics, Transactions ASME

The temporal stability of a Carreau fluid flowing down an inclined porous substrate is considered. A reduced model is derived under the assumption of small permeability which decouples the flow in the liquid layer from the filtration flow in the porous medium and incorporates the effect of the porous medium by means of an effective slip condition at the liquid-solid interface. The slip coefficient in the effective slip condition is a function of the structure, permeability of the porous medium and the rheology of the fluid saturating the porous medium. The effects of shear-thinning rheology and permeability of the substrate on the stability of the film flow system are investigated. This problem gives rise to a generalized eigenvalue formulation which is solved through two approaches. The problem is solved analytically for long waves in the limiting cases of weakly and strongly non-Newtonian behaviors (power-law limit). A numerical investigation is carried out in the general case. The results are shown to agree well for the weakly non-Newtonian limit. Further, the power-law model and the Carreau model agree on a wide range of shear-thinning parameter values for a thin film over a rigid substrate. However, when considering a porous medium, this trend is not observed. The Carreau model gives valid results for the entire range of shear-thinning parameter values for a film over a rigid/porous substrate. The novelty of the present investigation lies in the inclusion of both the effects of bottom permeability and shear-thinning rheology. Both permeability and shear-thinning rheology have a destabilizing effect on the film flow system. The numerical results indicate the correlation between the effects due to shear-thinning properties and permeability. An energy balance analysis performed on the perturbation fields shows that destabilization induced by both shear-thinning and permeability is linked to the viscous shear work rate on the free surface. © 2011 Elsevier Ltd.

Chemical Engineering Science

Shear-thinning film on a porous substrate: Stability analysis of a one-sided model

Non-linear waves on the surface of a falling film of power-law fluid on a vertical porous plane are investigated. The waves are described by evolution equations generalising equations previously derived in the case of solid plane. It is shown that the slip condition on the interface between pure liquid and the porous substrate drastically changes structure of the steady waves travelling in the film. © 2009 Elsevier Ltd. All rights reserved.

International Journal of Non-Linear Mechanics

Wave regimes on power-law fluid film flowing down a porous plane

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

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.

International Journal of Engineering Science

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

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

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

Rheologica Acta

Solitary waves on the surface of a viscoelastic fluid running down an inclined plane

Journal of Fluids Engineering

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

Waves and Nonlinear Processes in Hydrodynamics Fluid Mechanics and Its Applications

Continuous Bores on a Viscous Fluid Down an Incline

Journal of Physics D: Applied Physics

Linear stability of power law liquid film flows down an inclined plane

Journal	Journal of Applied Mechanics, Transactions ASME
ISSN	00218936
Open Access	No