Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant

2020 ◽  
Vol 32 (3) ◽  
pp. 034105
Author(s):  
Abdelouahab El Jaouahiry ◽  
Saïd Aniss
Keyword(s):  
Stability Analysis ◽  
Liquid Film ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Inclined Plane ◽  
Presence And Absence

Weakly Nonlinear Stability Analysis of a Non-Uniformly Heated Non-Newtonian Falling Film

2007 ◽  
Author(s):  
R. Usha ◽  
I. Mohammed Rizwan Sadiq
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Film Flow ◽  
Flow System ◽  
Uniform Heating ◽  
Inclined Plane ◽  
Linear Evolution Equation ◽  
Non Linear ◽  
The Stability

A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to non-uniform 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 force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A non-linear evolution equation is derived by applying the long-wave theory and the equation governs the evolution of a power-law film flowing down an inclined plane. The linear stability analysis shows that the film flow system is stable when the plate temperature is decreasing in the downstream direction while it is less stable for increasing temperature along the plate. Weakly non-linear 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 non-linear speed of these waves are influenced by thermocapillarity. The results for the dilatant as well as pseudoplastic fluids are obtained and it is observed that the result for the Newtonian model agrees with the available literature report. The influence of non-uniform heating of the film flow system on the stability of the system is compared with the stability of the corresponding uniformly heated film flow system.

Stability of evaporating two-layered liquid film in the presence of surfactant—III. Non-linear stability analysis

1998 ◽  
Vol 53 (15) ◽  
pp. 2839-2857 ◽  
Author(s):  
Vesselin N. Paunov ◽  
Krassimir D. Danov ◽  
Norbert Alleborn ◽  
Hans Raszillier ◽  
Franz Durst
Keyword(s):  
Stability Analysis ◽  
Liquid Film ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Non Linear
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