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

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.

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

Journal of Applied Mechanics ◽

10.1115/1.1631592 ◽

2003 ◽

Vol 70 (6) ◽

pp. 915-923 ◽

Cited By ~ 7

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.

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Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

Journal of Applied Mechanics ◽

10.1115/1.3424229 ◽

1978 ◽

Vol 45 (1) ◽

pp. 19-24 ◽

Cited By ~ 20

Author(s):

V. Narayanamurthy ◽

P. K. Sarma

Keyword(s):

Liquid Film ◽

Power Law ◽

Mathematical Formulation ◽

Liquid Films ◽

Interfacial Shear ◽

Newtonian Liquid ◽

Power Law Model ◽

Falling Liquid Film ◽

Falling Liquid Films ◽

Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

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Non-Newtonian slender drops in a nonlinear extensional flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.626 ◽

2019 ◽

Vol 877 ◽

pp. 561-581 ◽

Cited By ~ 1

Author(s):

Moshe Favelukis

Keyword(s):

Stability Analysis ◽

Power Law ◽

Analytical Solutions ◽

Viscosity Ratio ◽

Extensional Flow ◽

Shear Thinning ◽

Newtonian Liquid ◽

Creeping Flow ◽

Stationary States ◽

Power Law Index

In this theoretical report we explore the deformation and stability of a power-law non-Newtonian slender drop embedded in a Newtonian liquid undergoing a nonlinear extensional creeping flow. The dimensionless parameters describing this problem are: the capillary number $(Ca\gg 1)$, the viscosity ratio $(\unicode[STIX]{x1D706}\ll 1)$, the power-law index $(n)$ and the nonlinear intensity of the flow $(|E|\ll 1)$. Asymptotic analytical solutions were obtained near the centre and close to the end of the drop suggesting that only Newtonian and shear thinning drops $(n\leqslant 1)$ with pointed ends are possible. We described the shape of the drop as a series expansion about the centre of the drop, and performed a stability analysis in order to distinguish between stable and unstable stationary states and to establish the breakup point. Our findings suggest: (i) shear thinning drops are less elongated than Newtonian drops, (ii) as non-Newtonian effects increase or as $n$ decreases, breakup becomes more difficult, and (iii) as the flow becomes more nonlinear, breakup is facilitated.

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Developing flow of a power-law liquid film on an inclined plane

Physics of Fluids ◽

10.1063/1.1605742 ◽

2003 ◽

Vol 15 (10) ◽

pp. 2973 ◽

Cited By ~ 8

Author(s):

Steven J. Weinstein ◽

Kenneth J. Ruschak ◽

Kam C. Ng

Keyword(s):

Liquid Film ◽

Power Law ◽

Inclined Plane ◽

Developing Flow

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Weakly Nonlinear Stability Analysis of a Thin Liquid Film With Condensation Effects During Spin Coating

Journal of Fluids Engineering ◽

10.1115/1.3222907 ◽

2009 ◽

Vol 131 (10) ◽

Cited By ~ 6

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.

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Long-Wave Perturbation Method to Investigate Nonlinear Stability of the Thin Power Law Liquid Film Flowing Down on a Vertical Cylinder

Journal of Mechanics ◽

10.1017/s1727719100002306 ◽

2008 ◽

Vol 24 (3) ◽

pp. 241-252 ◽

Cited By ~ 2

Author(s):

P. -J. Cheng ◽

K. -C. Liu

Keyword(s):

Liquid Film ◽

Perturbation Method ◽

Power Law ◽

Film Flow ◽

Multiple Scales ◽

Vertical Cylinder ◽

Flow Index ◽

Wave Perturbation ◽

Stability Diagrams ◽

Long Wave

ABSTRACTThe influence of both the flow index and the cylinder size on the nonlinear hydrodynamic stability of a thin power law liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a 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 weakly nonlinear dynamics of the film flow for stability analysis. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained. The modeling results 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.

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On the Flow of a Non-Newtonian Liquid Induced by Intestine-Like Contractions

Journal of Biomechanical Engineering ◽

10.1115/1.3168334 ◽

1989 ◽

Vol 111 (1) ◽

pp. 1-8 ◽

Cited By ~ 9

Author(s):

N. Phan-Thien ◽

H. T. Low

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Power Law ◽

Flow Rate ◽

Finite Amplitude ◽

Newtonian Liquid ◽

Peristaltic Motion ◽

Positive Displacement ◽

Displacement Pump ◽

Power Law Index

This paper considers the flow of an inelastic liquid which is generated by contractions like those of the intestine. Unlike regular peristaltic motion, these contractions occur locally over a finite length and have a finite amplitude. We adopt a contraction model due to Macagno and Christensen and repeat their analysis for an inelastic liquid. Our analysis, which is based on a Boundary Element Method, indicates that the net flow rate depends very weakly on the power-law index. The pumping action is therefore similar to that of a positive displacement pump.

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Surface Instabilities on a Thin Power-Law Fluid During Spin Coating

Journal of Mechanics ◽

10.1017/jmech.2014.39 ◽

2014 ◽

Vol 30 (5) ◽

pp. 505-513 ◽

Cited By ~ 1

Author(s):

C.-I. Chen ◽

M.-C. Lin ◽

C.-K. Chen

Keyword(s):

Power Law ◽

Spin Coating ◽

Film Flow ◽

Stokes Equations ◽

Multiple Scales ◽

Landau Equation ◽

Shear Thickening ◽

Vital Role ◽

Power Law Fluid ◽

Power Law Index

AbstractThe phenomena of surface instabilities in a thin power-law fluid during spin coating are investigated. The set of Navier-Stokes equations with non-Newtonian behavior in the region of low Reynolds number serves as a mathematical description of the physical systems. Long-wave perturbation analysis is proposed to derive an evolution equation of the Ostwald de-Waele type fluid to govern the propagation of surface waves. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The amplitude of instability is determined by a Ginzburg-Landau equation. The study reveals that the degree of power-law index plays a vital role in stabilizing the film flow. The shear-thinning fluid is more unstable than the shear-thickening fluid in the stability analysis. Further, the nonlinear wave speed in the supercritical stability region decreases with increasing values of power-law index.

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