Percolation and Reynolds Flow in Elastic Contacts of Isotropic and Anisotropic, Randomly Rough Surfaces

Abstract In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting solids. We find the percolation threshold to depend on the fluid flow direction when the Peklenik number indicates anisotropy unless the system size clearly exceeds the roll-off wave length parallel to the easy flow direction. A critical contact area near 0.415 is confirmed. Heuristically corrected effective-medium treatments satisfactorily provide Reynolds fluid flow conductances, e.g., for isotropic roughness, we identify accurate closed-form expressions, which only depend on the mean gap and the relative contact area. Graphic Abstract

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Hydraulic Resistance and Permeability in Human Lumbar Vertebral Bodies

Journal of Biomechanical Engineering ◽

10.1115/1.1503793 ◽

2002 ◽

Vol 124 (5) ◽

pp. 533-537 ◽

Cited By ~ 14

Author(s):

Ruth S. Ochia ◽

Randal P. Ching

Keyword(s):

Fluid Flow ◽

Hydraulic Resistance ◽

High Speed ◽

Lumbar Vertebrae ◽

Pressure Flow ◽

Flow Rates ◽

Flow Through ◽

Vertebral Bodies ◽

The Mean ◽

The Creation

Hydraulic resistance (HR) was measured for ten intact human lumbar vertebrae to further understand the mechanisms of fluid flow through porous bone. Oil was forced through the vertebral bodies under various volumetric flow rates and the resultant pressure was measured. The pressure-flow relationship for each specimen was linear. Therefore, HR was constant with a mean of 2.22±1.45kPa*sec/ml. The mean permeability of the intact vertebral bodies was 4.90×10−10±4.45×10−10m2. These results indicate that this methodology is valid for whole bone samples and enables the exploration of the effects of HR on the creation of high-speed fractures.

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Elastic-Plastic Contact Behavior Considering Asperity Interactions for Surfaces With Various Height Distributions

Journal of Tribology ◽

10.1115/1.2162557 ◽

2005 ◽

Vol 128 (2) ◽

pp. 245-251 ◽

Cited By ~ 25

Author(s):

Yeau-Ren Jeng ◽

Shin-Rung Peng

Keyword(s):

Contact Area ◽

Rough Surfaces ◽

Local Deformation ◽

Real Contact Area ◽

Recent Experimental Data ◽

The Real ◽

Surface Separation ◽

Real Contact ◽

The Mean ◽

Non Gaussian

This study investigates the effects of asperity interactions on the mean surface separation and the real contact area for rough surfaces with non-Gaussian height distributions. The effects of the asperity interactions on the local deformation behavior of a given microcontact are modeled using the Saint Venant principle and Love’s formula. The non-Gaussian rough surfaces are described by the Johnson translatory system. The results indicate that asperity interactions can significantly affect the mean separation of surfaces with non-Gaussian height distributions. The findings also reveal that the contact load and the real contact area of surfaces with non-Gaussian height distributions are significantly different from those of surfaces with Gaussian height distributions. This study uncovers that skewed surfaces tend to deform more elastically, which provides underlying physics for the long-time conventional wisdom and recent experimental data [Y. R. Jeng, 1996, Tribol. Trans., 39, 354–361;Y. R. Jeng, Z. W. Lin, and S. H. Shyo, 2004, ASME J. Tribol., 126, 620–625] that running-in surfaces have better wear resistance.

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Jumplike Variation of the Contact Area between Randomly Rough Surfaces

Technical Physics Letters ◽

10.1134/1.2061731 ◽

2005 ◽

Vol 31 (9) ◽

pp. 735

Author(s):

A. É. Filippov

Keyword(s):

Contact Area ◽

Rough Surfaces ◽

Randomly Rough Surfaces

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Towards the exact solutions of Burger’s fluid flow through arteries with fractional time derivative magnetic field and thermal radiation effects

Proceedings of the Institution of Mechanical Engineers Part E Journal of Process Mechanical Engineering ◽

10.1177/09544089211013317 ◽

2021 ◽

pp. 095440892110133

Author(s):

Dauda G Yakubu ◽

Mohammed Abdulhameed ◽

Adamu G Tahiru ◽

Rozaini Roslan ◽

Alibek Issakhov ◽

...

Keyword(s):

Magnetic Field ◽

Fluid Flow ◽

Constitutive Equations ◽

Radiation Effects ◽

Fluid Model ◽

Flow Direction ◽

Time Derivative ◽

Cylindrical Tube ◽

Blood Velocity ◽

Flow Through

We consider the unsteady flow of Burger fluid within a circular cylindrical tube, driven by a time-dependent pressure gradient, a body acceleration and a magnetic field acting normal to the flow direction. The solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow through arterial walls were obtained via the Laplace transform and the finite Hankel transform. The effects of magnetic field on parameters such as blood temperature and velocity were studied by Caputo time-fractional derivatives. We note that the solutions of many particular models such as fractional Oldroyd-B fluid, fractional Maxwell fluid, fractional second grade fluid and fractional Newtonian fluid models can be recovered from the solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow by particularizing the material coefficients (i.e. special and limiting cases of the earlier Burger’s fluid model). The numerical computations have been carried out to analyze the effects of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R0 and material parameter λ2 on the blood velocity and temperature. Some interesting flow and temperature characteristics are presented graphically and discussed. The study reveals that blood velocity, temperature and fractional parameters are reduced in the presence of magnetic field. The importance of this study can be found in the application fields of magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering, medicine, etc.

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Fluid Flow Through a Crack Network in Rocks

Journal of Applied Mechanics ◽

10.1115/1.3167133 ◽

1983 ◽

Vol 50 (4a) ◽

pp. 707-711 ◽

Cited By ~ 62

Author(s):

R. Englman ◽

Y. Gur ◽

Z. Jaeger

Keyword(s):

Fluid Flow ◽

Gas Flow ◽

Random Distribution ◽

Crack Density ◽

Two Dimensional ◽

Threshold Density ◽

Crack Network ◽

Area Density ◽

Flow Through ◽

The Mean

A network of cracks pervading a rock is modeled by a random distribution of two-dimensional intersecting, complex, narrow cracks. The percolation properties of the resulting network are studied as functions of the crack-area density and size of the medium. Gas flow commences at a finite value of the crack density which in Arkansas Novaculite rocks amounts according to our model to 670 cracks per cm2. The mean probability of finding at least one crack intersecting another is 0.57 at the threshold density. Above that, the rock gas-flow permeability increases superlinearly with crack density due to the enhancement of short percolative paths.

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