Dynamics and equilibria of thin viscous coating films on a rotating sphere

2016 ◽  
Vol 791 ◽  
pp. 495-518 ◽  
Author(s):  
D. Kang ◽  
A. Nadim ◽  
M. Chugunova
Keyword(s):  
Film Thickness ◽  
Vertical Axis ◽  
Global Attractors ◽  
Solid Sphere ◽  
Steady States ◽  
Asymptotic Model ◽  
Coating Films ◽  
Gravity Forces ◽  
Viscous Liquid Film ◽  
Energy Minimizers

We examine the dynamics of a thin viscous liquid film on the outer surface of a solid sphere rotating around its vertical axis in the presence of gravity. An asymptotic model describing the evolution of the film thickness is derived in the rotating frame based on the lubrication approximation. The model includes the centrifugal and gravity forces and the stabilizing effect of surface tension. Depending on the values of the parameters, the problem admits different types of steady states: one with a uniformly positive film thickness, or those with one or two dry zones on the sphere. We prove that all steady states are energy minimizers and hence global attractors for axisymmetric states.

scholarly journals Evaluation of Coating Film Formation Process Using the Fluorescence Method

Coatings ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1076
Author(s):  
Ayako Yano ◽  
Kyoichi Hamada ◽  
Kenji Amagai
Keyword(s):  
Film Thickness ◽  
Formation Process ◽  
Film Formation ◽  
Injection Pressure ◽  
Measurement Range ◽  
Fluorescence Method ◽  
Coating Film ◽  
Coating Films ◽  
Tracer Particles ◽  
Overlap Ratio

In this paper, we invented a novel observation method of the coating film formation process using the fluorescence method. With this method, the temporal change in the coating film thickness can be evaluated quantitatively. In addition, since the thickness and flow of the coating film can be measured simultaneously, the detailed coating film formation process was clarified. In the experiment, the adhesion behavior of the spray-paint droplets when applied to a wall was investigated. The characteristics of coating films formed by the spray droplets, particularly the influence of injection pressure on the coating film formation, were determined using the fluorescence method. At the initial stage of the coating process, the coating area increased linearly. When the ratio of the coating area to the measurement range reached about 80%, the rate at which the coating area increased slowed down, and an overlap began. The amount of paint that adhered to the coating film formation could be estimated by calculating the overlap ratio. Moreover, the thickness and smoothness of the coating film were evaluated using the histogram data of the fluorescence intensity. The leveling process was discussed in relation to the standard deviation of the histogram data. In addition, the flow of the paint during the coating film formation was investigated using tracer particles, and the effect of the spray gun injection pressure on the leveling process was investigated. Changes in the film thickness and flow during the coating film formation process could be evaluated through fluorescence observation.

Comportement dynamique d'une éolienne à axe vertical (application pratique)

1988 ◽  
Vol 15 (3) ◽  
pp. 369-381
Author(s):  
Mario Veilleux ◽  
René Tinawi
Keyword(s):  
Dynamic Behaviour ◽  
Vertical Axis ◽  
Mode Shapes ◽  
Nonlinear Behaviour ◽  
Vertical Axis Wind Turbine ◽  
Initial Tension ◽  
Coriolis Forces ◽  
Gravity Forces ◽  
Vertical Axis Wind Turbines ◽  
Gyroscopic Effects

The dynamic behaviour of the vertical axis wind turbine of the ÉOLE Project is examined using a special purpose program developed for extracting the complex frequencies and mode shapes of the structure. The precise evaluation of the frequencies is an important step in the design process, to detect any dynamic instabilities of the rotor for a given speed. Gyroscopic effects and geometric nonlinearities due to centrifugal and gravity forces as well as the vertical compression due to the tension of the guys are also considered. Nonlinear behaviour of the guys is also accounted for. The influence of the variation in the stiffness of the guys on the dynamic behaviour is examined specifically for the ÉOLE Project. Results indicate that this effect is not important if the initial tension in the guy is high. Key words: Vertical axis wind turbines, guys, complex frequencies, complex mode shapes, centrifugal forces, Coriolis forces, Campbell diagrams, numerical software.

An Instability for Parallel Sliding of Solid Surfaces Separated by a Viscous Liquid Film

1976 ◽  
Vol 98 (1) ◽  
pp. 157-166 ◽  
Author(s):  
B. N. Banerjee ◽  
R. A. Burton
Keyword(s):  
Thermal Conductivity ◽  
Thermal Expansion ◽  
Film Thickness ◽  
Liquid Film ◽  
Coefficient Of Thermal Expansion ◽  
Solid Surfaces ◽  
Wave Number ◽  
Seal Failure ◽  
Viscous Liquid Film ◽  
Surface Disturbance

Thermoelastic phenomena in lubricated face type seals are analyzed for possible instabilities which may lead to large surface deformations and seal failure. Thresholds of such instabilities are found where a small, steadily moving, surface disturbance will neither grow nor decay. For a good thermal conductor sliding on a good insulator, several such thresholds exist. Only one, however, falls within a reasonable operating range, the critical sliding speed being Ucrit=hκ¯KMμαM where h¯ is the nominal film-thickness, κ the wave number of the disturbance, KM the thermal conductivity of the conductor and αM its coefficient of thermal expansion, and μ the viscosity of the oil. Expressions are given for the approximate limits of h¯ within which such a threshold lies. Finally, it is shown that, as expected, a disturbance will grow when U > Ucrit and decay when U < Ucrit.

scholarly journals Three-Dimensional Mathematical Model of the Liquid Film Downflow on a Vertical Surface

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1938
Author(s):  
Ivan Pavlenko ◽  
Oleksandr Liaposhchenko ◽  
Marek Ochowiak ◽  
Radosław Olszewski ◽  
Maryna Demianenko ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Film Thickness ◽  
Liquid Film ◽  
Three Dimensional ◽  
Friction Stress ◽  
Vertical Axis ◽  
Vertical Surface ◽  
Channel Length ◽  
Interfacial Surface ◽  
Separation Equipment

Film downflow from captured liquid without wave formation and its destruction is one of the most important aspects in the development of separation equipment. Consequently, it is necessary to create well-organized liquid draining in areas of captured liquid. Thus, the proposed 3D mathematical model of film downflow allows for the determination of the hydrodynamic parameters of the liquid film flow and the interfacial surface. As a result, it was discovered that the interfacial surface depends on the proposed dimensionless criterion, which includes internal friction stress, channel length, and fluid density. Additionally, equations for determining the averaged film thickness, the averaged velocity vectors over the film thickness, the longitudinal and vertical velocity components, and the initial angle of streamline deviation from the vertical axis were analytically obtained.

scholarly journals Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures

2006 ◽  
Vol 219 (2) ◽  
pp. 644-670 ◽  
Author(s):  
Virginie Bonnaillie-Noël ◽  
Francis Nier ◽  
Yassine Patel
Keyword(s):  
Quantum Transport ◽  
Steady States ◽  
Asymptotic Model

Influence of Operating Condition and Geometry on the Oil Film Thickness in Aeroengine Bearing Chambers

2004 ◽  
Vol 128 (1) ◽  
pp. 103-110 ◽  
Author(s):  
P. Gorse ◽  
S. Busam ◽  
K. Dullenkopf
Keyword(s):  
Film Thickness ◽  
Film Flow ◽  
Jet Engines ◽  
Gravity Forces ◽  
Wide Range ◽  
Secondary Air ◽  
Oil Films ◽  
Analytical Approaches ◽  
Complex Film

Increasing the efficiency of modern jet engines does not only imply to the mainstream but also to the secondary air and oil system. Within the oil system the bearing chamber is one of the most challenging components. Oil films on the chamber walls are generated from oil droplets, ligaments, or film fragments, which emerge from bearings, seal plates and shafts, and enter the bearing chamber with an angular momentum. Furthermore, shear forces at its surface, gravity forces, and the design of scavenge and vent ports strongly impact the behavior of the liquid film. The present paper focuses on the experimental determination of the film thickness in various geometries of bearing chambers for a wide range of engine relevant conditions. Therefore, each configuration was equipped with five capacitive probes positioned at different circumferential locations. Two analytical approaches are used for a comprehensive discussion of the complex film flow.

Influence of Operating Condition and Geometry on the Oil Film Thickness in Aero-Engine Bearing Chambers

2004 ◽  
Author(s):  
P. Gorse ◽  
S. Busam ◽  
K. Dullenkopf
Keyword(s):  
Film Thickness ◽  
Jet Engines ◽  
Gravity Forces ◽  
Wide Range ◽  
Secondary Air ◽  
Oil Films ◽  
Analytical Approaches ◽  
Complex Film ◽  
Engine Bearing

Increasing the efficiency of modern jet engines do not only imply to the mainstream but also to the secondary air and oil system. Within the oil system the bearing chamber is one of the most challenging component. Oil films on the chamber walls are generated from oil droplets, ligaments, or film fragments, which emerge from bearings, seal plates and shafts, and enter the bearing chamber with an angular momentum. Furthermore, shear forces at its surface, gravity forces, and the design of scavenge and vent ports strongly impact the behavior of the liquid film. The present paper focuses on the experimental determination of the film thickness is various geometries of bearing chambers for a wide range of engine relevant conditions. Therefore, each configuration was equipped with five capacitive probes positioned at different circumferential locations. Two analytical approaches are used for a comprehensive discussion of the complex film flow.

Sign in / Sign up

Export Citation Format

Share Document