Stability of a Two-Layer Film Flow of Viscous Fluids down an Inclined Plane

1979 ◽  
Vol 47 (2) ◽  
pp. 646-653 ◽  
Author(s):  
Hirohumi Tougou
Keyword(s):  
Film Flow ◽  
Viscous Fluids ◽  
Inclined Plane ◽  
Layer Film

Multi-layer film flow down an inclined plane: experimental investigation

2014 ◽  
Vol 55 (12) ◽  
Author(s):  
D. Henry ◽  
J. Uddin ◽  
J. Thompson ◽  
M. G. Blyth ◽  
S. T. Thoroddsen ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Film Flow ◽  
Inclined Plane ◽  
Layer Film ◽  
Multi Layer Film

Instability of a liquid film flow over a vibrating inclined plane

1995 ◽  
Vol 294 ◽  
pp. 391-407 ◽  
Author(s):  
David R. Woods ◽  
S. P. Lin
Keyword(s):  
Gravity Waves ◽  
Film Flow ◽  
Shear Waves ◽  
Faraday Waves ◽  
Critical Amplitude ◽  
Inclined Plane ◽  
Flow Parameters ◽  
Chebychev Polynomials ◽  
Liquid Film Flow ◽  
Faraday Wave

The problem of the onset of instability in a liquid layer flowing down a vibrating inclined plane is formulated. For the solution of the problem, the Fourier components of the disturbance are expanded in Chebychev polynomials with time-dependent coefficients. The reduced system of ordinary differential equations is analysed with the aid of Floquet theory. The interaction of the long gravity waves, the relatively short shear waves and the parametrically resonated Faraday waves occurring in the film flow is studied. Numerical results show that the long gravity waves can be significantly suppressed, but cannot be completely eliminated by use of the externally imposed oscillation on the incline. At small angles of inclination, the short shear waves may be exploited to enhance the Faraday waves. For a given set of relevant flow parameters, there exists a critical amplitude of the plane vibration below which the Faraday wave cannot be generated. At a given amplitude above this critical one, there also exists a cutoff wavenumber above which the Faraday wave cannot be excited. In general the critical amplitude increases, but the cutoff wavenumber decreases, with increasing viscosity. The cutoff wavenumber also decreases with increasing surface tension. The application of the theory to a novel method of film atomization is discussed.

scholarly journals Effect of imposed shear on the dynamics of a contaminated two-layer film flow down a slippery incline

2020 ◽  
Vol 32 (10) ◽  
pp. 102113
Author(s):  
Muhammad Sani ◽  
Siluvai Antony Selvan ◽  
Sukhendu Ghosh ◽  
Harekrushna Behera
Keyword(s):  
Film Flow ◽  
Layer Film

Mechanism of the long-wave inertialess instability of a two-layer film flow

2008 ◽  
Vol 608 ◽  
pp. 379-391 ◽  
Author(s):  
PENG GAO ◽  
XI-YUN LU
Keyword(s):  
Free Surface ◽  
Film Flow ◽  
Underlying Mechanism ◽  
Continuity Condition ◽  
Layer Film ◽  
Long Wave ◽  
Pressure Driven Flow ◽  
Intuitive Interpretation ◽  
Additional Phase Shift ◽  
Additional Phase

This paper provides an intuitive interpretation of the long-wave inertialess instability of a two-layer film flow. The underlying mechanism is elucidated by inspecting the longitudinal perturbation velocity associated with the surface and interfacial deflections. The velocity is expressed by the composition of three parts, related to the shear stress at the free surface, the continuity condition at the interface, and the pressure disturbance induced by gravity. The effect of each velocity component on the evolutions of the surface and the interface is examined in detail. Specifically, the growth of the free surface is caused by the continuity-induced first-order velocity disturbance associated with an additional phase shift between the surface and interfacial waves, while the growth of the interface is due to the pressure-driven flow. The proposed mechanism gives an alternatively reliable prediction of the wave velocity and growth rate.

Developing Film Flow on an Inclined Plane With a Critical Point

2001 ◽  
Vol 123 (3) ◽  
pp. 698-702 ◽  
Author(s):  
Kenneth J. Ruschak ◽  
Steven J. Weinstein ◽  
Kam Ng
Keyword(s):  
Velocity Profile ◽  
Critical Point ◽  
Film Flow ◽  
Boundary Layer Equation ◽  
Critical Conditions ◽  
Integral Approach ◽  
Inclined Plane ◽  
Navier Stokes Equation ◽  
Moderate Reynolds Number ◽  
Momentum Integral

Viscous, laminar, gravitationally-driven flow of a thin film on an inclined plane is analyzed for moderate Reynolds number under critical conditions. A previous analysis of film flow utilized a momentum integral approach with a semiparabolic velocity profile to obtain an ordinary differential equation for the film thickness for flow over a round-crested weir, and the singularity associated with the critical point for a subcritical-to-supercritical transition was removable. For developing flow on a plane with a supercritical-to-subcritical transition, however, the same approach leads to a nonremovable singularity. To eliminate the singularity, the film equations are modified for a velocity profile of changing shape. The resulting predictions compare favorably with those from the two-dimensional boundary-layer equation obtained by finite differences and with those from the Navier-Stokes equation obtained by finite elements.

Effect of surfactants on the long-wave stability of two-layer oscillatory film flow

2021 ◽  
Vol 928 ◽  
Author(s):  
Cheng-Cheng Wang ◽  
Haibo Huang ◽  
Peng Gao ◽  
Xi-Yun Lu
Keyword(s):  
Film Flow ◽  
Viscosity Ratio ◽  
Density Ratio ◽  
Thickness Ratio ◽  
High Frequency Oscillation ◽  
Key Factors ◽  
Layer Film ◽  
Wave Disturbances ◽  
Long Wave ◽  
The Stability

The stability of the two-layer film flow driven by an oscillatory plate under long-wave disturbances is studied. The influence of key factors, such as thickness ratio ( $n$ ), viscosity ratio ( $m$ ), density ratio ( $r$ ), oscillatory frequency ( $\beta$ ) and insoluble surfactants on the stability behaviours is studied systematically. Four special Floquet patterns are identified, and the corresponding growth rates are obtained by solving the eigenvalue problem of the fourth-order matrix. A small viscosity ratio ( $m\le 1$ ) may stabilize the flow but it depends on the thickness ratio. If the viscosity ratio is not very small ( $m>0.1$ ), in the $(\beta ,n)$ -plane, stable and unstable curved stripes appear alternately. In other words, under the circumstances, if the two-layer film flow is unstable, slightly adjusting the thickness of the upper film may make it stable. In particular, if the upper film is thin enough, even under high-frequency oscillation, the flow is always stable. The influence of density ratio is similar, i.e. there are curved stable and unstable stripes in the $(\beta ,r)$ -planes. Surface surfactants generally stabilize the flow of the two-layer oscillatory membrane, while interfacial surfactants may stabilize or destabilize the flow but the effect is mild. It is also found that gravity can generally stabilize the flow because it narrows the bandwidth of unstable frequencies.

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