Effect of Longitudinal Minigrooves on Flow Stability and Wave Characteristics of Falling Liquid Films

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Klaus Helbig ◽  
Ralph Nasarek ◽  
Tatiana Gambaryan-Roisman ◽  
Peter Stephan
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Film Flow ◽  
Flow Direction ◽  
Wave Theory ◽  
Liquid Films ◽  
Falling Film ◽  
Wave Characteristics ◽  
Falling Liquid Films

Falling liquid films are used in many industrial apparatuses. In many cases the film flow along a wall with topography is considered advantageous for intensification of the heat and mass transport. One of the promising types of the wall topography for the heat transfer intensification is comprised of minigrooves aligned along the main flow direction. The wall topography affects the development of wavy patterns on the liquid-gas interface. Linear stability analysis of the falling film flow based on the long-wave theory predicts that longitudinal grooves lead to the decrease in the disturbance growth rate and therefore stabilize the film. The linear stability analysis also predicts that the frequency of the fastest growing disturbance mode and the wave propagation velocity decrease on a wall with longitudinal minigrooves in comparison with a smooth wall. In the present work the effect of the longitudinal minigrooves on the falling film flow is studied experimentally. We use the shadow method and the confocal chromatic sensoring technique to study the wavy structure of falling films on smooth walls and on walls with longitudinal minigrooves. The measured film thickness profiles are used to quantify the effect of the wall topography on wave characteristics. The experimental results confirm the theoretical predictions.

Effect of Longitudinal Mini-Grooves on Flow Stability and Wave Characteristics of Falling Liquid Films

2007 ◽  
Author(s):  
Klaus Helbig ◽  
Ralph Nasarek ◽  
Tatiana Gambaryan-Roisman ◽  
Peter Stephan
Keyword(s):  
Wave Propagation ◽  
Film Thickness ◽  
Linear Stability ◽  
Propagation Speed ◽  
Wave Theory ◽  
Liquid Films ◽  
Transport Processes ◽  
Thickness Variation ◽  
Experimental Findings ◽  
Falling Liquid Films

Falling liquid films are used in many industrial apparatuses. In many cases the film flow along a wall with topography is considered advantageous for intensification of the transport processes. We use the shadow method and the chromatic white light sensor (CHR) method to study the wavy structure of falling films on flat walls and on walls with longitudinal grooves. We show that the wavy pattern substantially changes on walls with topography. The wave frequency, the wave propagation velocity and the area of the liquid-gas interface decrease on grooved walls. The linear stability of the film has been analyzed using the long-wave theory, which relies on the assumption that the average film thickness is much smaller than the scale of the film thickness variation. The linear stability analysis predicts that the disturbance growth rate, the frequency of the fastest growing disturbance mode and the wave propagation speed decrease on a tube with longitudinal mini-grooves in comparison with a smooth tube. These results agree well with the experimental findings.

AC electrohydrodynamic instabilities in thin liquid films

2009 ◽  
Vol 631 ◽  
pp. 255-279 ◽  
Author(s):  
SCOTT A. ROBERTS ◽  
SATISH KUMAR
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Electric Fields ◽  
Linear Stability Analysis ◽  
Floquet Theory ◽  
Thin Liquid Film ◽  
Liquid Films ◽  
Dielectric Films ◽  
High Frequencies ◽  
Ac Electric Fields

When DC electric fields are applied to a thin liquid film, the interface may become unstable and form a series of pillars. In this paper, we apply lubrication theory to examine the possibility of using AC electric fields to exert further control over the size and shape of the pillars. For perfect dielectric films, linear stability analysis shows that the influence of an AC field can be understood by considering an effective DC field. For leaky dielectric films, Floquet theory is applied to carry out the linear stability analysis, and it reveals that high frequencies may be used to inhibit the accumulation of interfacial free charge, leading to a lowering of growth rates and wavenumbers. Nonlinear simulations confirm the results of the linear stability analysis while also uncovering additional mechanisms for tuning overall pillar height and width. The results presented here may be of interest for the controlled creation of surface topographical features in applications such as patterned coatings and microelectronics.

Nonlinear Stability Analysis of a Falling Film in the Presence of Gas Flow

2007 ◽  
Author(s):  
B. Uma ◽  
R. Usha
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Gas Flow ◽  
Film Flow ◽  
Flow System ◽  
Interfacial Shear Stress ◽  
Wave Theory ◽  
Falling Film ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear

A viscous liquid film flows down along the interior of an annular region under gravity with a countercurrent/cocurrent stream of gas phase adjoining the free surface. The interfacial shear stress effects on the stability of the film flow system in the presence of gas flow has been analyzed for the model that describes the motion for the annular countercurrent/cocurrent gas-liquid two-dimensional falling film. A nonlinear evolution of Benney type describing the film thickness in the presence of gasflow has been derived using long wave theory and lubrication approximation. Linear and weakly nonlinear stability analysis of the evolution equation show that both supercritical stability and subcritical instability are possible for the film flow system in the presence of gas flow. The nonlinear equation has been solved numerically in a periodic domain and the results show that the shape and amplitude of the permanent wave are greatly influenced by the countercurrent/cocurrent gas flow.

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.

Sign in / Sign up

Export Citation Format

Share Document