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

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.

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On the assessment of stationary points and uniform film thickness for the thin film flow of Sisko fluid model

Theoretical and Computational Fluid Dynamics ◽

10.1007/s00162-014-0337-2 ◽

2014 ◽

Vol 28 (6) ◽

pp. 635-649 ◽

Cited By ~ 1

Author(s):

A. M. Siddiqui ◽

H. Ashraf ◽

T. Haroon

Keyword(s):

Thin Film ◽

Film Thickness ◽

Film Flow ◽

Fluid Model ◽

Stationary Points ◽

Thin Film Flow ◽

Sisko Fluid ◽

Sisko Fluid Model

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Developing Laminar Gravity-Driven Thin Liquid Film Flow Down an Inclined Plane

Journal of Fluids Engineering ◽

10.1115/1.4002109 ◽

2010 ◽

Vol 132 (8) ◽

Cited By ~ 24

Author(s):

H. Lan ◽

J. L. Wegener ◽

B. F. Armaly ◽

J. A. Drallmeier

Keyword(s):

Surface Tension ◽

Film Thickness ◽

Liquid Film ◽

Flow Rate ◽

Film Flow ◽

Thin Liquid Film ◽

Inclined Plane ◽

Liquid Film Flow ◽

Gravity Driven ◽

Surface Inclination

Three-dimensional (3D)—steady-developing-laminar-isothermal—and gravity-driven thin liquid film flow adjacent to an inclined plane is examined and the effects of film flow rate, surface tension, and surface inclination angle on the film thickness and film width are presented. The film flow was numerically simulated using the volume of fluid model and experimental verification was conducted by measuring film thickness and width using a laser focus displacement instrument. The steady film flow that is considered in this study does not have a leading contact line, however, it has two steady side contact lines with the substrate surface at the outer edge of its width. Results reveal that the film width decreases and the average film thickness increases as the film flows down the inclined plane. The film thickness and width decrease but its streamwise velocity increases as surface inclination angle (as measured from the horizontal plane) increases. A higher film flow rate is associated with a higher film thickness, a higher film width, and a higher average film velocity. Films with higher surface tension are associated with a smaller width and a higher average thickness. A ripple develops near the side contact line, i.e., the spanwise distribution of the film thickness exhibits peaks at the outer edges of the film width and the height of this ripple increases as the surface tension or the film flow rate increases. The width of the film decreases at a faster rate along the streamwise direction if liquid film has higher surface tension. Measurements of the film thickness and the film width compare favorably with the numerically simulated results.

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Thermohydrodynamic Analysis of Journal Bearings Lubricated by Non-Newtonian Fluids—Theory and Experiments

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1243/pime_proc_1994_208_368_02 ◽

1994 ◽

Vol 208 (3) ◽

pp. 173-181 ◽

Cited By ~ 1

Author(s):

O Sheeja ◽

B S Prabhu

Keyword(s):

Film Thickness ◽

Normal Stress ◽

Journal Bearing ◽

Fluid Model ◽

Normal Stress Difference ◽

Fluid Film ◽

Stress Difference ◽

First Normal Stress Difference ◽

Cubic Law ◽

Normal Stress Differences

Viscosity index improvers cause the lubricants to exhibit non-Newtonian flow behaviour and display shear thinning and normal stress differences. Shear thinning behaviour is studied by using a rotary shear viscometer. Owing to the non-availability of a rheogoniometer (for the measurement of normal stress differences), the first normal stress difference is calculated from the viscometric data using the Carreau viscosity function. The influence of the first normal stress difference on the hydrodynamic lubrication is analysed and shows that most of the commercial oils are inelasticoviscous in nature. Regression analysis shows that a large number of commercial lubricants follow the inelasticoviscous cubic law fluid model. Hence the cubic law fluid model is considered for the theoretical analysis. An experimental programme is developed to measure the effect of test parameters on the performance of a journal bearing lubricated with different types of non-Newtonian fluids. The experiments mainly include the measurements of the steady state characteristics like film thickness and fluid film friction. The experimental film thickness values are compared with the respective theoretical ones and are in good agreement. The theoretical performance characteristics are obtained through the simultaneous solution of the modified Reynolds equation using the cubic law fluid model and energy equation. The fluid film friction in a hydrodynamic journal bearing is experimentally determined through coastdown analysis. The results are presented in the form of an apparent Stribeck diagram of friction and are compared with the respective theoretical values.

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Gravity-driven thin film flow: The influence of topography and surface tension gradient on rivulet formation

Chemical Engineering and Processing - Process Intensification ◽

10.1016/j.cep.2012.07.003 ◽

2013 ◽

Vol 68 ◽

pp. 7-12 ◽

Cited By ~ 6

Author(s):

D. Slade ◽

S. Veremieiev ◽

Y.C. Lee ◽

P.H. Gaskell

Keyword(s):

Thin Film ◽

Surface Tension ◽

Film Flow ◽

Surface Tension Gradient ◽

Thin Film Flow ◽

Gravity Driven ◽

Rivulet Formation

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On study of horizontal thin film flow of Sisko fluid due to surface tension gradient

Applied Mathematics and Mechanics ◽

10.1007/s10483-015-1952-9 ◽

2015 ◽

Vol 36 (7) ◽

pp. 847-862 ◽

Cited By ~ 9

Author(s):

A. M. Siddiqui ◽

H. Ashraf ◽

A. Walait ◽

T. Haroon

Keyword(s):

Thin Film ◽

Surface Tension ◽

Film Flow ◽

Surface Tension Gradient ◽

Thin Film Flow ◽

Sisko Fluid

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An experimental approach to simultaneously measure the temperature field and fluid film thickness in the cylinder block/valve plate gap of an axial piston pump

Proceeding of THMT-18. Turbulence Heat and Mass Transfer 9 Proceedings of the Ninth International Symposium On Turbulence Heat and Mass Transfer ◽

10.1615/thmt-18.920 ◽

2018 ◽

Cited By ~ 2

Author(s):

A. Shorbagy ◽

R. Ivantysyn ◽

J. Weber

Keyword(s):

Temperature Field ◽

Film Thickness ◽

Experimental Approach ◽

Valve Plate ◽

Fluid Film ◽

Piston Pump ◽

Cylinder Block ◽

Axial Piston Pump ◽

Fluid Film Thickness ◽

Axial Piston

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Flow analysis of Carreau fluid model induced by the ciliary cells, smooth muscle cells and pressure gradient at the ampullar region entrance

Theory in Biosciences ◽

10.1007/s12064-021-00352-8 ◽

2021 ◽

Author(s):

H. Ashraf ◽

A. M. Siddiqui ◽

M. A. Rana

Keyword(s):

Smooth Muscle ◽

Smooth Muscle Cells ◽

Pressure Gradient ◽

Fluid Model ◽

Flow Analysis ◽

Muscle Cells ◽

Carreau Fluid

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Effect of Rolling Velocity and Maximum Hertzian Pressure on Fluid Film in Steady State EHL Line Contact with Rough Surface and Linear Piezoviscosity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.592-594.1371 ◽

2014 ◽

Vol 592-594 ◽

pp. 1371-1375

Author(s):

Nitesh Talekar ◽

Punit Kumar

Keyword(s):

Surface Roughness ◽

Steady State ◽

Film Thickness ◽

Rough Surface ◽

Computer Code ◽

Fluid Film ◽

Line Contact ◽

Rolling Velocity ◽

Load Carrying ◽

Lubricated Contact

Consideration of surface roughness in steady state EHL line contact is the first step towards understanding the lubrication of rough surface problem. Current paper investigates the use of sinusoidal waviness in the contact; more precisely it gives performance of real fluid in EHL line contact. The effect of various parameters like rolling velocity (U) and maximum Hertzian pressure (ph) on surface roughness by using properties of linear and exponential piezo-viscosity is taken into consideration to evaluate behavior of pressure distribution of load carrying fluid film and film thickness. Full isothermal, Newtonian simulation of EHL problem gives described effects. Spiking or fluctuation of pressure and film thickness curves is expected to show presence of irregularities on the surface chosen and amount of fluctuation depends on certain parameters and intensity of irregularities present. Rolling side domain of-4.5 ≤ X ≤ 1.5 with grid size ∆X=0.01375 is selected. A computer code is developed to solve Reynolds equation, which governs the generation of pressure in the lubricated contact zone is discritized and solved along with load balance equation using Newton-Raphson technique.

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