scholarly journals Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

2021 ◽  
Vol 932 ◽  
Author(s):  
Andrew J. Mitchell ◽  
Brian R. Duffy ◽  
Stephen K. Wilson
Keyword(s):  
Film Thickness ◽  
Rotating Cylinder ◽  
Stationary Points ◽  
Uniform Pressure ◽  
Maximum Mass ◽  
Continuous Film ◽  
Coating Flow ◽  
Dimensional Parameters ◽  
Horizontal Circular Cylinder ◽  
Qualitative Changes

A detailed analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the absence of surface-tension effects but in the presence of a non-uniform pressure distribution due to an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Full-film solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the non-dimensional parameters $F$ and $K$ representing the speed of the far-field airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as $F$ and $K$ are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither top-to-bottom nor right-to-left symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the maximum mass of fluid can be greater than that in classical coating flow.

Continuous-Film Thickness Determination by AES of Cr Overlayers on Cu Surfaces

1989 ◽  
Vol 153 ◽  
Author(s):  
H. Lefakis ◽  
P.S. Ho
Keyword(s):  
Film Thickness ◽  
Rough Surface ◽  
Film Growth ◽  
Substrate Surface ◽  
Continuous Film ◽  
Substrate Heating ◽  
Native Oxides ◽  
Surface Oxides ◽  
Coverage Rates ◽  
Cr Film

AbstractThe characteristics of Cr coverage of Cu surfaces, including determination of tc, the minimum average film thickness required for formation of a continuous film, have been studied in-situ by Auger Electron Spectroscopy (AES). Auger signal intensities of substrate and deposit were monitored during Cr film growth by vapor deposition in UHV. It was shown that substrate surface morphology (roughness) has a dominant effect on coverage rate and tc. Slower coverage rates and larger tc′s were effected by the presence of native oxides, substrate heating (to 330°C) and H2O-vapor rich (5×10−5 Torr) ambient during Cr deposition. Surface oxides seemed to affect more the coverage of a smooth than a rough surface. Conversely, substrate heating affected more the coverage of a rough surface. The combined effect of substrate heating and water vapor rich atmosphere was pronounced for both smooth and rough surface coverages. Some of the main factors controlling these effects are discussed.

The transition region of elastohydrodynamic lubrication

1991 ◽  
Vol 432 (1886) ◽  
pp. 467-479 ◽  
Keyword(s):  
Film Thickness ◽  
Transition Region ◽  
Parameter Space ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Series Method ◽  
Chebyshev Series ◽  
Pressure Spike ◽  
Constant Coefficients ◽  
Dimensional Parameters

A semi-analytic approach is presented for the elastohydrodynamic lubrication problem of two cylinders in line contact. The model takes account of the effects of elastic deformation and piezo-viscosity in the transition region (the area of parameter space where the pressure spike emerges and develops). Following Poritsky, pressure and displacement are expressed as Chebyshev series and Fejér’s method is used to deal with the sharp crease in the film shape that is a feature of piezoviscous contacts. It is shown that the film thickness depends solely upon two non-dimensional parameters and can be accurately represented by an equation of the form: H = a 0 g 3 a 1 g 1 + a 2 g 3 a 3 , where the a i = 0, 1, 2, 3) are constant coefficients. Important features of this Chebyshev series method include accurate representations for the emerging pressure spike and the associated sharp crease in the film shape together with film thickness predictions which smoothly link those areas of parameter space on either side of the transition region.

Electrical and Structural Properties of Thin Palladium Films

1986 ◽  
Vol 41 (4) ◽  
pp. 665-670 ◽  
Author(s):  
R. Anton ◽  
K. Häupl ◽  
P. Rudolf ◽  
P. Wißmann
Keyword(s):  
Electrical Resistivity ◽  
Film Thickness ◽  
Statistical Model ◽  
Structural Information ◽  
Film Structure ◽  
X Ray Diffraction ◽  
Continuous Film ◽  
X Ray ◽  
Amorphous Substrates ◽  
Steep Decrease

The electrical resistivity of thin palladium films deposited on amorphous substrates is measured in dependence on film thickness. The data are interpreted with the help of a statistical model taking into account structural information obtained from AES, TEM and x-ray diffraction texture analysis. The steep decrease of resistivity in the ultra-thin thickness region can be immediately correlated with the formation of coherent areas in the films. A more flattened course is reached at about 8 nm thickness where a continuous film structure develops.

Experimental Studies of External Hygrocysts

1980 ◽  
Vol 102 (2) ◽  
pp. 226-230 ◽  
Author(s):  
J. P. Kovac ◽  
R. T. Balmer
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Film Thickness ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Rotating Cylinder ◽  
Surface Velocity ◽  
Data Sets ◽  
Centrifugal Acceleration ◽  
Average Film Thickness

The three-dimensional banding phenomenon that occurs on the outside of single horizontal rotating cylinders covered with a liquid film was experimentally studied. Over 400 data sets from a variety of cylinders and liquids produced an emperical correlation between the number of bands formed and the rotational Reynolds, Weber, and Froude numbers. The average film thickness on the top of the rotating cylinder was found to be independent of the physical properties of the liquid and the centrifugal acceleration of the cylinder. The surface velocity measured in the crown of the bands was found to be nearly the same as that predicted by the steady state unbanded velocity field solution of Moffatt.

Shark-Teeth Pattern in Coating Flow Inside a Horizontally Rotating Cylinder

1996 ◽  
Vol 8 (9) ◽  
pp. S10-S10 ◽  
Author(s):  
S. T. Thoroddsen ◽  
L. Mahadevan
Keyword(s):  
Rotating Cylinder ◽  
Coating Flow ◽  
Shark Teeth

The Starved Lubrication of Cylinders in Line Contact

1970 ◽  
Vol 185 (1) ◽  
pp. 1159-1169 ◽  
Author(s):  
P. E. Wolveridge ◽  
K. P. Baglin ◽  
J. F. Archard
Keyword(s):  
Analytical Solution ◽  
Film Thickness ◽  
Load Capacity ◽  
Theoretical Treatment ◽  
Line Contact ◽  
Experimental Conditions ◽  
Single Function ◽  
Dimensional Parameters ◽  
Heavy Loads ◽  
Proportional Reduction

A semi-analytical solution is presented showing the effect of variations in the position of the inlet boundary of the lubricant film upon the load capacity of cylinders in line contact. Firstly, isoviscous conditions and undeformed surfaces are assumed; by the use of appropriate non-dimensional parameters, the results of the theory can be exhibited as a single function applicable to all possible experimental conditions. This can then be transformed to deduce a similar unique expression showing the proportional reduction in the minimum film thickness for variations in the position of the inlet boundary, all other conditions being maintained constant. A similar analytical solution is presented showing the effect of the position of the inlet boundary upon the film thickness under heavy loads. This assumes full elastohydrodynamic conditions and is based upon an analysis similar to the familiar theoretical treatment of Grubin. Comparisons show that published computer solutions of these problems, for specific sets of conditions, are in good agreement with the more general analytical solutions presented here.

scholarly journals Analysis of Uniform Film Thickness and Stationarypoints for the Thin Film Flow of Carreau Fluid Model in the Presence of Surface Tension Gradient

2022 ◽  
Author(s):  
Hameed Ashraf ◽  
Abida Parveen ◽  
Hamood Ur Rehman ◽  
Muhammad Imran Asjad ◽  
Bander N. Almutairi ◽  
...  
Keyword(s):  
Surface Tension ◽  
Film Thickness ◽  
Film Flow ◽  
Fluid Model ◽  
Shear Thickening ◽  
Fluid Film ◽  
Stationary Points ◽  
Surface Tension Gradient ◽  
Carreau Fluid ◽  
Moving Cylinder

Abstract This article addresses the analysis of the uniform film thickness and stationary points forthe Carreau thin fluid film flow. The flow of fluid on a vertically upward moving cylinder takesplace in the presence of a surface tension gradient. The resulting non-linear and inhomogeneousordinary differential equation is solved for the series form solution using Adomian decompositionmethods (ADM). Stokes number St, inverse capillary number C, Weissenberg number W e andfluid behavior index n emerged as flow control parameters. The analysis showed that thepositions of stationary points transferred towards the surface of the cylinder by the increase ofSt and C while towards the fluid-air interface by the increase of n. W e delineated vice versaeffects on positions of stationary points for the shear thickening fluid film and shear thinningfluid film. The width of uniform film thickness reduces by an increment in the St and Cwhereas it increases by an increment in the n. The width of shear thickening uniform filmthickness increases whilst shear thinning uniform film thickness decreases as the W e increases. A comparison between the linearly viscous fluid and Carreau fluid is also made.

On inertial effects in the Moffatt–Pukhnachov coating-flow problem

2009 ◽  
Vol 633 ◽  
pp. 327-353 ◽  
Author(s):  
MARK A. KELMANSON
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Evolution Equation ◽  
Film Thickness ◽  
Critical Reynolds Number ◽  
Numerical Solutions ◽  
Fundamental Problem ◽  
Steady State Solution ◽  
Coating Flow ◽  
Inertial Terms

The effects are investigated of including inertial terms, in both small- and large-surface-tension limits, in a remodelling of the influential and fundamental problem first formulated by Moffatt and Pukhnachov in 1977: that of viscous thin-film free-surface Stokes flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field.An analysis of the non-dimensionalizations of previous related literature is made and the precise manner in which different rescalings lead to the asymptotic promotion or demotion of pure-inertial flux terms over gravitational-inertial terms is highlighted. An asymptotic mass-conserving evolution equation for a perturbed-film thickness is derived and solved using two-timescale asymptotics with a strained fast timescale. By using an algebraic manipulator to automate the asymptotics to high orders in the small expansion parameter of the ratio of the film thickness to the cylinder radius, consistent a posteriori truncations are obtained.Via two-timescale and numerical solutions of the evolution equation, new light is shed on diverse effects of inertia in both small- and large-surface-tension limits, in each of which a critical Reynolds number is discovered above which the thin-film evolution equation has no steady-state solution due to the strength of the destabilizing inertial centrifugal force. Extensions of the theory to the treatment of thicker films are discussed.

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