Abstract
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.
Highlights
Gravity-driven flow of a thin film down a vertical or an inclined plane has attracted much attention due to its importance in many industrial applications such as film coating and interface heat and mass transfer processes in chemical technology and energetics
Hwang and Weng 18 have examined the finite-amplitude stability analysis of liquid film down a vertical plane with and without interfacial phase change and have shown that both supercritical stability and subcritical instability are possible for condensate film flow system
The influence of prescribed cocurrent superficial shear stress on the dynamics and stability of a condensate or evaporating power-law liquid film falling down an inclined plane has been analyzed by the method of long-wave perturbation
Summary
Gravity-driven flow of a thin film down a vertical or an inclined plane has attracted much attention due to its importance in many industrial applications such as film coating and interface heat and mass transfer processes in chemical technology and energetics. The finite-amplitude stability analysis of liquid films down a vertical wall by Hwang and Weng 18 with interfacial phase change reveals that the isothermal and evaporating Newtonian films are unstable for any Reynolds number while there exists a finite critical Reynolds number for the case of condensate film below which condensate Newtonian film flow system is always stable This shows that the effect of mass transfer at the interface of a Newtonian fluid film strongly modifies the stability characteristics of the film flow when the phase change is considered. The chief motivation of the present study is to investigate the dynamics and stability of more realistic flows taking place in an environment In this case, it becomes important to include the effects of superficial shear stress and phase change at the interface of a fluid film flowing down an inclined plane. Dynamics and stability of condensate/evaporating power-law liquid film flowing down an inclined plane with the effect of wind stress and phase change at the interface are considered. Evaporating liquid film attains rupture faster than that of Newtonian and condensate liquid film, and the prescribed shear stress at the interface does not influence the time at which rupture occurs
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