Non-Newtonian Lubrication With the Second-Order Fluid

1998 ◽  
Vol 120 (3) ◽  
pp. 622-628 ◽  
Author(s):  
W. G. Sawyer ◽  
J. A. Tichy
Keyword(s):  
Film Flow ◽  
Maxwell Model ◽  
Companion Paper ◽  
Deborah Number ◽  
Second Order ◽  
Thin Film Flow ◽  
Regular Perturbation ◽  
Leading Term ◽  
Strain Tensors ◽  
Newtonian Behavior

In certain applications where the lubricant is subjected to rapidly changing conditions along its flowing path (such as an elastohydrodynamic contact), the inherently time dependent nature of the lubricant may be significant. The simplest type of model to correctly account for such time dependence is the second-order fluid, which is a systematic small departure from Newtonian behavior, involving higher order rate-of-rate-of strain tensors. As in a companion paper using the Maxwell model, the formalities of applying such a model to thin film flow are emphasized. Using a regular perturbation in the Deborah number, with the conventional lubrication solution as the leading term, a solution can be obtained. Viscoelasticity may raise or lower pressure depending on the nature of edge boundary conditions.

Non-Newtonian Lubrication With the Convected Maxwell Model

1996 ◽  
Vol 118 (2) ◽  
pp. 344-348 ◽  
Author(s):  
J. A. Tichy
Keyword(s):  
Time Dependence ◽  
Fluid Model ◽  
Time Derivative ◽  
Maxwell Model ◽  
Deborah Number ◽  
Time Dependent ◽  
Nonlinear Coupling ◽  
Surface Slope ◽  
Regular Perturbation ◽  
Leading Term

In certain applications where the lubricant is subjected to rapidly changing conditions along its flowing path (such as an elastohydrodynamic contact), the time dependent nature of the lubricant may be significant. One of the simplest types of models to account for such fluid time dependence is the Maxwell model. The time derivative used in such a model must be written with respect to coordinates which translate and rotate with the fluid, or coordinates which deform with the fluid. Unfortunately, such derivatives greatly complicate problems and are rarely used, due to nonlinear coupling of stresses. An admissible formulation of the Maxwell viscoelastic fluid model using the convected derivative has been applied to lubrication flow. Using a regular perturbation in the Deborah number, with the conventional lubrication solution as the leading term, a solution can be obtained. Viscoelasticity may raise or lower pressure depending on combinations of surface slope and curvature.

Perturbation Solution of Non-Newtonian Lubrication With the Convected Maxwell Model

2005 ◽  
Vol 127 (2) ◽  
pp. 302-305 ◽  
Author(s):  
Rong Zhang ◽  
Xueming He ◽  
Simon X. Yang ◽  
Xinkai Li
Keyword(s):  
Viscoelastic Fluid ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Maxwell Model ◽  
Deborah Number ◽  
Perturbation Solution ◽  
Two Dimensional ◽  
Sliding Velocity ◽  
Regular Perturbation ◽  
Leading Term

There are many studies on variations of the Maxwell model. Tichy (1996) discussed an admissible formulation of the Maxwell viscoelastic fluid model using a convected derivative and applied it to two-dimensional lubrication flow. Tichy obtained a solution using a regular perturbation in the Deborah number with the conventional lubrication solution as the leading term. This paper extends Tichy’s model by using a double regular perturbation to the convected Maxwell model. A correspondence solution can also be obtained. Our sliding velocity solution is different from Tichy’s solution; and a modified Reynolds equation is also different from that by Tichy.

On the study of stationary points and uniform thickness of PTT fluid film on a vertically upward moving belt

2016 ◽  
Vol 94 (10) ◽  
pp. 982-991
Author(s):  
A.M. Siddiqui ◽  
Ahsan Walait ◽  
T. Haroon ◽  
Hameed Ashraf
Keyword(s):  
Stationary Point ◽  
Maxwell Model ◽  
Stokes Number ◽  
Deborah Number ◽  
Stationary Points ◽  
Shear Stresses ◽  
Thin Film Flow ◽  
Linear Version ◽  
Upward Moving ◽  
Ptt Fluid

This paper investigates the thin film flow of Phan-Thien Tanner (PTT) fluid on a vertically moving belt. Three different models, namely, the upper convected Maxwell model (UCM), linear version of Phan-Thien Tanner model (LPTT), and exponential version of Phan-Thien Tanner model (EPTT), are taken into consideration. Exact expressions for velocity profiles, flow rates, average velocities, film thicknesses, shear stresses, and normal stresses are obtained. Special consideration is given to the predictions of stationary points in withdrawal of these fluids from the belt. It is observed that the stationary point of the UCM model lies closer to the free surface and the stationary point of the LPTT model lies in the middle of the stationary points of UCM and EPTT models. It is also observed that the stationary points tend to move towards the belt with the increase in Stokes number, Deborah number, and elongational parameter. Graphical results are also presented for various dimensionless flow parameters.

scholarly journals Numerical exploration of thin film flow of MHD pseudo-plastic fluid in fractional space: Utilization of fractional calculus approach

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 710-721
Author(s):  
Mubashir Qayyum ◽  
Farnaz Ismail ◽  
Muhammad Sohail ◽  
Naveed Imran ◽  
Sameh Askar ◽  
...  
Keyword(s):  
Thin Film ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Film Flow ◽  
Second Order ◽  
Order Derivative ◽  
Thin Film Flow ◽  
First Order ◽  
Plastic Fluid ◽  
Fractional Space

Abstract In this article, thin film flow of non-Newtonian pseudo-plastic fluid is investigated on a vertical wall through homotopy-based scheme along with fractional calculus. Three cases were examined after considering (i) partial fractional differential equation (PFDE) by altering first-order derivative to fractional derivative in the interval (0, 1), (ii) PFDE by altering second-order derivative to fractional derivative in the interval (1, 2), and (iii) fully FDE by altering first-order derivative to fractional derivative in (0, 1) and second-order derivative to fractional derivative in (1, 2). Different physical quantities such as the velocity profile and volume flux were computed and analyzed. Validity of obtained results was checked by finding residuals. Moreover, consequence of different parameters on the velocity were also explored in fractional space.

scholarly journals Optimal Homotopy Asymptotic Method for a thin film flow of a pseudo plastic fluid draining down or lifting up on a cylindrical surface

2013 ◽  
Vol 19 (4) ◽  
pp. 513-527
Author(s):  
Kamran Alam ◽  
M.T. Rahim ◽  
S. Islam ◽  
A.M. Sidiqqui
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Cylindrical Surface ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Stokes Number ◽  
Velocity Shear ◽  
Thin Film Flow ◽  
Fluid Velocities ◽  
Optimal Homotopy Asymptotic Method

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter ?=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter ? and the thickness ? of the fluid film on the fluid velocities.

scholarly journals MHD thin film flow of the Oldroyd-B fluid together with bioconvection and activation energy

2021 ◽  
pp. 101218
Author(s):  
Farhan Ahmad ◽  
Taza Gul ◽  
Imran Khan ◽  
Anwar Saeed ◽  
Mahmoud Mohamed Selim ◽  
...  
Keyword(s):  
Thin Film ◽  
Activation Energy ◽  
Film Flow ◽  
Thin Film Flow
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