Two-layer film flow over the surface of a rotating disc

1988 ◽  
Vol 55 (3) ◽  
pp. 999-1003 ◽  
Author(s):  
G. M. Sisoev ◽  
V. Ya. Shkadov
Keyword(s):  
Film Flow ◽  
Rotating Disc ◽  
Layer Film

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.

scholarly journals Thin film flow on a vertically rotating disc of finite thickness partially immersed in a highly viscous liquid

2016 ◽  
Vol 143 ◽  
pp. 226-239 ◽  
Author(s):  
Md Salim Miah ◽  
Saphwan Al-Assaf ◽  
Xiaogang Yang ◽  
Alison McMillan
Keyword(s):  
Thin Film ◽  
Viscous Liquid ◽  
Film Flow ◽  
Finite Thickness ◽  
Thin Film Flow ◽  
Rotating Disc

Laminar spread of a circular liquid jet impinging axially on a rotating disc

2019 ◽  
Vol 864 ◽  
pp. 449-489 ◽  
Author(s):  
B. Scheichl ◽  
A. Kluwick
Keyword(s):  
Numerical Solutions ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Jet Impingement ◽  
Flow Regimes ◽  
Careful Analysis ◽  
Rotating Disc ◽  
Viscous Shear ◽  
Wide Range ◽  
The Impact

The steady laminar annular spread of a thin liquid film generated by a circular jet which impinges perpendicularly in direction of gravity on the centre of a rotating disc is examined both analytically and numerically. Matched asymptotic expansions of the flow quantities provide the proper means for studying the individual flow regimes arising due to the largeness of the Reynolds number formed with the radius of the jet, its slenderness and the relative magnitude of the centrifugal body force. This is measured by a suitably defined Rossby number, $Ro$. The careful analysis of jet impingement predicts a marked influence of gravity and surface tension on the film flow, considered in the spirit of a shallow-water approach, only through the vorticity imposed by the jet flow. Accordingly, associated downstream conditions are disregarded as the local Froude and Weber numbers are taken to be sufficiently large. Hence, the parabolic problem shaped from the governing equations in a rigorous manner describes the strongly supercritical spread of a developed viscous film past an infinite disc, essentially controlled by $Ro$. Its numerical solutions are discussed for a wide range of values of $Ro$. The different flow regimes reflecting varying effects of viscous shear and centrifugal force are elucidated systematically to clarify the surprising richness of flow phenomena. Special attention is paid to the cases $Ro\gg 1$ and $Ro\ll 1$. The latter, referring to relatively high disc spin, implies a delicate breakdown of the asymptotic flow structure, thus requiring a specific analytical and numerical treatment. Finally, the impact of gravity and capillarity and thus of the disc edge on the film flow is envisaged in brief.

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.

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

Two-layer film flow over a rotating disk

2012 ◽  
Vol 17 (7) ◽  
pp. 2854-2863 ◽  
Author(s):  
B.S. Dandapat ◽  
S.K. Singh
Keyword(s):  
Film Flow ◽  
Rotating Disk ◽  
Layer Film
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