Analysis of Lubrication Theory for the Power Law Fluid

1993 ◽  
Vol 115 (1) ◽  
pp. 71-77 ◽  
Author(s):  
M. W. Johnson ◽  
S. Mangkoesoebroto
Keyword(s):  
Thin Film ◽  
Pressure Gradient ◽  
Power Law ◽  
Arbitrary Shape ◽  
Three Dimensional ◽  
Lubrication Theory ◽  
Slider Bearing ◽  
Power Law Fluid ◽  
Rigid Walls ◽  
Working Out

A lubrication theory for the power law fluid is developed and analyzed. Only the infinite width gap is considered. Considered is flow between rigid walls of arbitrary shape under combined Couette and squeezing motion with a pressure gradient. Equations appropriate to a thin film are derived by asymptotic integration of the three-dimensional equations of fluid mechanics. Further integration of these equations yields an algebraic equation for the pressure gradient. Working out the details of the structure of this equation enables us to develop a numerical algorithm for its solution. To illustrate the theory, it is used to calculate the pressure distribution for a parabolic slider bearing and the pressure gradient and velocity distribution when the mass flux is prescribed. The latter results are compared with results obtained earlier by Dien and Elrod (1983).

On the granular lubrication theory

2005 ◽  
Vol 461 (2062) ◽  
pp. 3255-3278 ◽  
Author(s):  
J.Y Jang ◽  
M.M Khonsari
Keyword(s):  
Granular Material ◽  
Reynolds Equation ◽  
Three Dimensional ◽  
Lubrication Theory ◽  
Slider Bearing ◽  
Governing Equations ◽  
Three Dimensional Flow ◽  
Generation Capacity ◽  
Side Flow ◽  
Generalized Reynolds Equation

The governing equations for the flow of a granular material within the context of the lubrication theory are derived. The resulting analysis gives a generalized Reynolds equation that predicts the pressure generation capacity in a bearing with consideration of side flow. A series of simulations are presented that characterize the three-dimensional flow behaviour of powder in a slider bearing.

scholarly journals Penetration Grouting Mechanism of Time-Dependent Power-Law Fluid for Reinforcing Loose Gravel Soil

Minerals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1391
Author(s):  
Tingting Guo ◽  
Zhiwei Zhang ◽  
Zhiquan Yang ◽  
Yingyan Zhu ◽  
Yi Yang ◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Numerical Simulations ◽  
Power Law ◽  
Three Dimensional ◽  
Time Dependent ◽  
Rheological Parameters ◽  
Power Law Fluid ◽  
Dependent Behavior ◽  
Gravel Soil ◽  
Penetration Grouting

The time-dependent behavior of power-law fluid has a significant influence on the grouting effects of reinforcing loose gravel soil. In this paper, based on basic rheological equations and the time-dependent behavior of rheological parameters (consistency coefficient and rheological index), rheological equations and penetration equations of time-dependent power-law fluid are proposed. Its penetration grouting diffusion mechanism for reinforcing loose gravel soil was then theoretically induced. A set of indoor experimental devices for simulating penetration grouting was designed to simulate the penetration grouting of power-law fluid with different time-dependent behaviors for reinforcing loose gravel soil. Then, relying on the COMSOL Multiphysics platform and Darcy’s law, three-dimensional numerical calculation programs for this mechanism were obtained using secondary-development programming technology. Thus, the numerical simulations of the penetration grouting process of power-law fluid with different time-dependent behaviors for reinforcing loose gravel soil were carried out. This theoretical mechanism was validated by comparing results from theoretical analyses, indoor experiments, and numerical simulations. Research results show that the three-dimensional numerical calculation programs can successfully simulate the penetration diffusion patterns of a time-dependent power-law fluid in loose gravel soil. The theoretical calculation values and numerical simulation values of the diffusion radius obtained from this mechanism are closer to indoor experimental values than those obtained from the penetration grouting diffusion theory of power-law fluid without considering time-dependent behavior. This mechanism can better reflect the penetration grouting diffusion laws of a power-law fluid in loose gravel soil than the theory, which can provide theoretical support and guidance for practical grouting construction.

scholarly journals Peristaltic Transport of Power-Law Fluid in an Elastic Tapered Tube with Variable Cross-Section Induced by Dilating Peristaltic Wave

2021 ◽  
pp. 1293-1306
Author(s):  
Mohammed Ali Murad ◽  
Ahmed M. Abdulhadi
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Power Law ◽  
Variable Cross Section ◽  
Peristaltic Transport ◽  
Peristaltic Wave ◽  
Variable Cross ◽  
Power Law Fluid ◽  
Opposite Behavior ◽  
Local Shear

The peristaltic transport of power-law fluid in an elastic tapered tube with variable cross-section induced by dilating peristaltic wave is studied. The exact solution of the expression for axial velocity, radial velocity, stream function, local shear stress, volume of flow rate and pressure gradient are obtained under the assumption of long wavelength and low Reynolds number. The effects of all parameters that appear in the problem are analyzed through graphs. The results showed that the flux is sinusoidal in nature and it is an increasing function with the increase of  whereas it is a decreasing function with the increase of . An opposite behavior for shear strain is noticed compared to pressure gradient.  Finally, trapping phenomenon is presented to explain the physical behavior of various parameters. It is noted that the size of the trapping bolus increases with increasing  whereas it decreases as  increases. MATHEMATICA software is used to plot all figures.

Release of a viscous power-law fluid over an inviscid ocean

2012 ◽  
Vol 700 ◽  
pp. 63-76 ◽  
Author(s):  
Samuel S. Pegler ◽  
John R. Lister ◽  
M. Grae Worster
Keyword(s):  
Power Law ◽  
Large Time ◽  
Three Dimensional ◽  
Shear Thinning ◽  
Capillary Forces ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Initial Shape ◽  
Algebraic Decay

AbstractWe consider the two- and three-dimensional spreading of a finite volume of viscous power-law fluid released over a denser inviscid fluid and subject to gravitational and capillary forces. In the case of gravity-driven spreading, with a power-law fluid having strain rate proportional to stress to the power $n$, there are similarity solutions with the extent of the current being proportional to ${t}^{1/ n} $ in the two-dimensional case and ${t}^{1/ 2n} $ in the three-dimensional case. Perturbations from these asymptotic states are shown to retain their initial shape but to decay relatively as ${t}^{\ensuremath{-} 1} $ in the two-dimensional case and ${t}^{\ensuremath{-} 3/ (n+ 3)} $ in the three-dimensional case. The former is independent of $n$, whereas the latter gives a slower rate of relative decay for fluids that are more shear-thinning. In cases where the layer is subject to a constraining surface tension, we determine the evolution of the layer towards a static state of uniform thickness in which the gravitational and capillary forces balance. The asymptotic form of this convergence is shown to depend strongly on $n$, with rapid finite-time algebraic decay in shear-thickening cases, large-time exponential decay in the Newtonian case and slow large-time algebraic decay in shear-thinning cases.

Sign in / Sign up

Export Citation Format

Share Document