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.

On stability of parallel flow of an incompressible fluid of variable density and viscosity

1962 ◽  
Vol 58 (4) ◽  
pp. 646-661 ◽  
Author(s):  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Water Waves ◽  
Salt Water ◽  
Reynolds Numbers ◽  
Variable Density ◽  
Stability Equation ◽  
Wave Disturbances ◽  
Long Wave ◽  
Vertical Variations ◽  
The Stability

ABSTRACTSome aspects of generation of water waves by wind and of turbulence in a heterogeneous fluid may be described by the theory of hydrodynamic stability. The technical difficulties of these problems of instability have led to obscurities in the literature, some of which are elucidated in this paper. The stability equation for a basic steady parallel horizontal flow under the influence of gravity is derived carefully, the undisturbed fluid having vertical variations of density and viscosity. Methods of solution of the equation for large Reynolds numbers and for long-wave disturbances are described. These methods are applied to simple models of wind blowing over water and of fresh water flowing over salt water.

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

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.

Stability Analysis on Viscous Magnetic Fluid Film Flowing Down Along a Vertical Cylinder

2007 ◽  
Vol 23 (2) ◽  
pp. 127-134 ◽  
Author(s):  
P.-J. Cheng ◽  
K.-C. Liu
Keyword(s):  
Film Flow ◽  
Vertical Cylinder ◽  
Fluid Film ◽  
Electrically Conductive ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
The Magnetic Field ◽  
Film Interface

AbstractThe paper investigates the hydromagnetic stability theory of a thin electrically conductive fluid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results display that the degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. It is also observed that by increasing the effect of the magnetic field and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Stability of a viscous liquid flowing down a flexible boundary

1968 ◽  
Vol 46 (18) ◽  
pp. 2059-2063
Author(s):  
A. S. Gupta
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Phase Shift ◽  
Viscous Liquid ◽  
Critical Reynolds Number ◽  
Elastic Parameter ◽  
Viscous Damping ◽  
Wave Disturbances ◽  
Long Wave ◽  
The Stability

The stability characteristics of a viscous liquid flowing down a flexible boundary are investigated for long-wave disturbances. In the case of a normally compliant boundary which resembles a thin stretched membrane resting on an elastic foundation with viscous damping, it is found that the critical Reynolds number Rc increases with the elastic parameter. For a boundary showing purely tangential compliance, Rc is found to depend on the phase shift between the oscillation of the shear stress and tangential deformation.

The Hydrodynamic Stability of Two Viscous Incompressible Fluids in Parallel Uniform Shearing Motion

1979 ◽  
Vol 46 (3) ◽  
pp. 499-504 ◽  
Author(s):  
D. T. Tsahalis
Keyword(s):  
Reynolds Number ◽  
Incompressible Fluid ◽  
Viscosity Ratio ◽  
Density Ratio ◽  
Steady Motion ◽  
Wave Number ◽  
Neutral Stability ◽  
The Family ◽  
The Stability ◽  
Shearing Motion

The stability problem of a thin film of a viscous incompressible fluid bounded on one side by another more viscous and less dense incompressible fluid of semi-infinite extent and on the other side by a fixed wall, where both fluids are in steady motion parallel to their interface and each fluid has a linear velocity profile, is solved for large values of the Reynolds number and small values of the viscosity ratio. Neutral stability curves of the Reynolds number versus the wave number are presented, parametrized with either the density ratio or the viscosity ratio as the family parameters.

scholarly journals IS MORE MEMORY IN EVOLUTIONARY SELECTION (DE)STABILIZING?

2011 ◽  
Vol 16 (3) ◽  
pp. 335-357 ◽  
Author(s):  
Cars Hommes ◽  
Tatiana Kiseleva ◽  
Yuri Kuznetsov ◽  
Miroslav Verbic
Keyword(s):  
Asset Pricing ◽  
Multinomial Logit Model ◽  
Heterogeneous Beliefs ◽  
Pricing Model ◽  
Key Factors ◽  
Evolutionary Selection ◽  
Asset Pricing Model ◽  
Economic Fundamentals ◽  
Selection Dynamics ◽  
The Stability

We investigate the effects of memory on the stability of evolutionary selection dynamics based on a multinomial logit model in a simple asset pricing model with heterogeneous beliefs. Whether memory is stabilizing or destabilizing depends in general on three key factors: (1) whether or not the weights on past observations are normalized; (2) the ecology or composition of forecasting rules, in particular the average trend extrapolation factor and the spread or diversity in biased forecasts; and (3) whether or not costs for information gathering of economic fundamentals have to be incurred.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems

1996 ◽  
Vol 312 ◽  
pp. 173-200 ◽  
Author(s):  
Yuan C. Severtson ◽  
Cyrus K. Aidun
Keyword(s):  
Spectral Decomposition ◽  
Air Entrainment ◽  
Density Variation ◽  
Generalized Eigenvalue ◽  
Long Wave ◽  
Inclined Channels ◽  
The Stability ◽  
Air Liquid Interface ◽  
Sommerfeld Equation ◽  
Interfacial Mode

To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. Only one mode of instability, the interfacial mode, is obtained in the long-wave asymptotic limit. The generalized eigenvalue problem, formed by spectral decomposition and solution of the general two-layer Orr-Sommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. Results from the stability analysis of the flow near the contact line where air entrainment occurs are consistent with previous experimental observations.

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