Effects of Electrokinetic Slip Flow on Lubrication Theory

2007 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Reynolds Equation ◽  
Slip Flow ◽  
Electrical Potential ◽  
Lubrication Theory ◽  
Boundary Slip ◽  
Navier Stokes Equation ◽  
Electroviscous Effect ◽  
Navier Slip ◽  
Navier Slip Boundary Conditions ◽  
Modified Reynolds Equation

A lubrication theory that includes the effects of electric double layer (EDL) and boundary slip is developed. Both effects are important in microflow, and thus in lubrication problems. They have opposite effects on velocity distributions between lubricating surfaces. Also, the velocity distribution induced by the EDL stream potential (electroviscous effect) is affected by the boundary slip. Under the usual assumptions of lubrication and Debye-Hu¨ckel approximation for low surface potential, the Navier-Stokes equation with body force due to the electrical potential as well as the widely accepted Navier slip boundary conditions is utilized on deriving the modified Reynolds equation. Effects of EDL and boundary slip on the 1-D bearing performance are discussed by solving the modified Reynolds equation numerically.

Analysis of Two-Layered Film Journal Bearing with Partial Slip Surface

2014 ◽  
Vol 903 ◽  
pp. 215-220 ◽  
Author(s):  
T.V.V.L.N. Rao ◽  
A.M.A. Rani ◽  
T. Nagarajan ◽  
F.M. Hashim
Keyword(s):  
Boundary Conditions ◽  
Coefficient Of Friction ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Slip Surface ◽  
Load Capacity ◽  
Partial Slip ◽  
Navier Slip ◽  
Navier Slip Boundary Conditions ◽  
Modified Reynolds Equation

Based on the approach of two-layered film consisting of different Newtonian viscosities, the present study examines the effects of partial slip bearing configuration on load capacity and friction coefficient for journal bearing. Navier slip boundary conditions are used to analyze partial slip configuration. A modified Reynolds equation for a journal bearing with two-layered film on a partial slip surface is presented. The modified Reynolds equation is derived taking into consideration of magnitude of lubricant layers film thickness, viscosities and the extent of partial slip on the bearing surface. The Reynolds boundary conditions are used in the analysis to predict nondimensional load capacity and coefficient of friction. Partial slip of bearing surfaces has a potential to improve load carrying capacity and reduce coefficient of friction for two-layered film journal bearing.

Static characteristics of hydrostatic doubled-layered porous journal bearings with slip flow including additives percolation into pores under coupled stress lubrication

2017 ◽  
Vol 232 (8) ◽  
pp. 927-939 ◽  
Author(s):  
Shitendu Some ◽  
Sisir K Guha
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Journal Bearings ◽  
Static Characteristics ◽  
Governing Equations ◽  
Modified Reynolds Equation ◽  
Film Interface ◽  
Coupled Stress ◽  
Steady State Performance

A theoretical analysis of the steady-state characteristics of finite hydrostatic double-layered porous journal bearings dealing with the effects of slip flow at the fine porous layer–film interface and percolation of additives into pores under the coupled stress fluid lubrication is presented. Based on the Beavers–Joseph’s criterion for slip flow, the modified Reynolds equation applicable to finite porous journal bearings lubricated with coupled stress fluids have been derived. The governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation of polar additives of lubricant and the modified Reynolds equation are solved simultaneously using finite difference method satisfying appropriate boundary conditions to obtain the steady-state performance characteristics for various parameter namely percolation factor, slip coefficient, bearing feeding parameter, coupled stress parameter, and eccentricity ratio. The results are exhibited in the form of graphs, which may be useful for design of such bearing.

High Knudsen Number Molecular Rarefaction Effects in Gas-Lubricated Slider Bearings for Computer Flying Heads

1987 ◽  
Vol 109 (2) ◽  
pp. 276-282 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Ambient Air ◽  
Mean Free Path ◽  
Lubricating Film ◽  
Modified Reynolds Equation ◽  
Air Film ◽  
Rarefaction Effects

This paper presents a study into the gas lubrication capability of an ultra-thin 0.025 μm film (converted value for ambient air film). The experimental results obtained using subambient helium as the lubricating film are compared with the calculated results using the modified Reynolds equation considering flow slippage due to the molecular mean free path effects. This comparison confirms that the slip flow model holds true within the range of the present experiments, and that the modified Reynolds equation is applicable for designing the computer flying heads operating at such thin spacing. The reason for the excellent agreement is discussed considering the locality of rarefaction effects on the lubricating surfaces and the anisotropy of these effects between the film thickness and the slider width.

Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient

1993 ◽  
Vol 115 (2) ◽  
pp. 289-294 ◽  
Author(s):  
Y. Mitsuya
Keyword(s):  
Thin Film ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Second Order ◽  
Flow Models ◽  
Gas Lubrication ◽  
Modified Reynolds Equation ◽  
Ultra Thin Film

A 1.5-order modified Reynolds equation for solving the ultra-thin film gas lubrication problem is derived by using an accurate higher-order slip-flow model. This model features two key differences from the current second-order slip-flow model. One is the involvement of an accommodation coefficient for momentum. The other is that the coefficient of the second-order slip-flow term is 4/9 times smaller than that for the current model. From the physical consideration of momentum transfer, the accommodation coefficient is found to have no affect on the second-order slip-flow term. Numerical calculations using the 1.5-order modified Reynolds equation are performed. The results are compared with those obtained using three kinds of currently employed modified Reynolds equations: those employing the first- and second-order slip-flow models and those utilizing the Boltzmann equation. These comparisons confirm that the present modified Reynolds equation provides intermediate characteristics between those derived from the first- and second-order slip-flow models, and produces an approximation closer to the exact solution resulting from the Boltzmann-Reynolds equation.

LOAD CAPACITY COEFFICIENT EVALUATION OF THREE-LAYERED JOURNAL BEARING WITH SLIP

2016 ◽  
Vol 78 (6-10) ◽  
Author(s):  
T. V. V. L. N. Rao ◽  
A. M. A. Rani ◽  
M. Awang ◽  
F. M. Hashim
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
High Viscosity ◽  
Bearing Surface ◽  
Surface Layers ◽  
Navier Slip ◽  
Slip Boundary ◽  
Capacity Coefficient ◽  
Navier Slip Boundary Conditions

Analysis of three-layered journal bearing with slip on bearing surface is presented. A modified classical Reynolds equation is derived for slip on bearing surface taking into consideration of bearing surface, core and journal surface layers. The modified Reynolds equation is derived taking into consideration of lubricant layer’s film thickness, viscosities and slip on the bearing surface. Navier slip boundary conditions are used to analyze slip. Results of load capacity coefficient are presented for three-layered and two-layered journal bearing with slip. The load capacity coefficient decreases with bearing surface with slip. For a three-layered journal bearing with slip, high viscosity bearing surface layer results in higher load capacity coefficient.

Lubrication Theory at Arbitrary Knudsen Number

1985 ◽  
Vol 107 (3) ◽  
pp. 431-433 ◽  
Author(s):  
R. F. Gans
Keyword(s):  
Kinetic Theory ◽  
Knudsen Number ◽  
Reynolds Equation ◽  
Approximation Scheme ◽  
Slip Flow ◽  
Lubrication Theory ◽  
Reynolds Equations ◽  
Gas Bearings ◽  
Knudsen Numbers

It is demonstrated that the slip flow Reynolds equations for ultra low clearance gas bearings can be derived from kinetic theory by an approximation scheme appropriate for arbitrary Knudsen numbers. Thus the usefulness of the slip flow Reynolds equation is extended to cases where it would not be expected to hold.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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