A New Slip Model for Gas Lubrication

Tribology ◽  
2006 ◽  
Author(s):  
Sheng Shen ◽  
Robert M. Crone ◽  
Gang Chen ◽  
Manuel Anaya-Dufresne
Keyword(s):  
Gas Flow ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Rarefied Gas ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Slip Model ◽  
Slip Boundary ◽  
Physical Mechanisms ◽  
Gas Lubrication

In this paper, a new slip boundary condition is derived using the solution of the Boltzmann equation. The physical mechanisms of velocity slip in rarefied gas flow are discussed and emphasized. The Poiseuille flow rates predicted by the new slip model show better agreements with those calculated from the existing slip models such as 1st, 2nd, and 1.5th slip order. Based on the new slip model, a new modified Reynolds equation is also proposed to predict the pressure field in gas lubrication problem.

scholarly journals Numerical Study of Nanoparticle Deposition in a Gaseous Microchannel under the Influence of Various Forces

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 47
Author(s):  
Fubing Bao ◽  
Hanbo Hao ◽  
Zhaoqin Yin ◽  
Chengxu Tu
Keyword(s):  
Drag Force ◽  
Particle Deposition ◽  
Gas Flow ◽  
Numerical Study ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Deposition Efficiency ◽  
Nanoparticle Deposition ◽  
Thermophoretic Force ◽  
Slip Boundary

Nanoparticle deposition in microchannel devices inducing contaminant clogging is a serious barrier to the application of micro-electro-mechanical systems (MEMS). For micro-scale gas flow fields with a high Knudsen number (Kn) in the microchannel, gas rarefaction and velocity slip cannot be ignored. Furthermore, the mechanism of nanoparticle transport and deposition in the microchannel is extremely complex. In this study, the compressible gas model and a second-order slip boundary condition have been applied to the Burnett equations to solve the flow field issue in a microchannel. Drag, Brownian, and thermophoretic forces are concerned in the motion equations of particles. A series of numerical simulations for various particle sizes, flow rates, and temperature gradients have been performed. Some important features such as reasons, efficiencies, and locations of particle deposition have been explored. The results indicate that the particle deposition efficiency varies more or less under the actions of forces such as Brownian force, thermophoretic force, and drag force. Nevertheless, different forces lead to different particle motions and deposition processes. Brownian or thermophoretic force causes particles to move closer to the wall or further away from it. The drag force influence of slip boundary conditions and gas rarefaction changes the particles’ residential time in the channel. In order to find a way to decrease particle deposition on the microchannel surface, the deposition locations of different sizes of particles have been analyzed in detail under the action of thermophoretic force.

New slip boundary condition in high-speed rarefied gas flow simulations

2019 ◽  
Vol 234 (3) ◽  
pp. 840-856
Author(s):  
Nam TP Le ◽  
Nam H Tran ◽  
Thoai N Tran ◽  
Toan T Tran
Keyword(s):  
Boundary Condition ◽  
High Speed ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Slip Boundary Condition ◽  
Mean Free Path ◽  
Slip Condition ◽  
Monte Carlo Data ◽  
Flow Simulations ◽  
Slip Boundary

In this paper, we propose a new slip boundary condition in hypersonic gas flow simulations. It is derived by considering the Langmuir isotherm adsorption into the Kaniadarkis et al. model of the kinetic theory of gas. Moreover, the motion of the adsorbed molecules over the surface (i.e. surface diffusion) is considered for the calculation of the mean free path in new slip condition. Three aerodynamic configurations are selected for evaluating new slip condition such as (1) the sharp-leading-edge flat plate, (2) circular cylinder in cross-flow, and (3) the sharp 25°–55° biconic cases. Hypersonic gas flows have the Mach number ranging from 6.1 to 15.6, and the working gases are argon and nitrogen. The simulation results show that new slip condition predicts better slip velocity than the Maxwell slip condition and gives good agreement with the direct simulation Monte-Carlo data for all cases considered in the present work.

Subsonic gas flow in a straight and uniform microchannel

2002 ◽  
Vol 472 ◽  
pp. 125-151 ◽  
Author(s):  
YITSHAK ZOHAR ◽  
SYLVANUS YUK KWAN LEE ◽  
WING YIN LEE ◽  
LINAN JIANG ◽  
PIN TONG
Keyword(s):  
Gas Flow ◽  
Theoretical Calculations ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Perturbation Expansions ◽  
Slip Boundary ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
Flow Effects

A nonlinear equation based on the hydrodynamic equations is solved analytically using perturbation expansions to calculate the flow field of a steady isothermal, compressible and laminar gas flow in either a circular or a planar microchannel. The solution takes into account slip-flow effects explicitly by utilizing the classical velocity-slip boundary condition, assuming the gas properties are known. Consistent expansions provide not only the cross-stream but also the streamwise evolution of the various flow parameters of interest, such as pressure, density and Mach number. The slip-flow effect enters the solution explicitly as a zero-order correction comparable to, though smaller than, the compressible effect. The theoretical calculations are verified in an experimental study of pressure-driven gas flow in a long microchannel of sub-micron height. Standard micromachining techniques were utilized to fabricate the microchannel, with integral pressure microsensors based on the piezoresistivity principle of operation. The integrated microsystem allows accurate measurements of mass flow rates and pressure distributions along the microchannel. Nitrogen, helium and argon were used as the working fluids forced through the microchannel. The experimental results support the theoretical calculations in finding that acceleration and non-parabolic velocity profile effects were found to be negligible. A detailed error analysis is also carried out in an attempt to expose the challenges in conducting accurate measurements in microsystems.

Rarefied gas flow between parallel plates

1969 ◽  
Vol 66 (1) ◽  
pp. 189-196 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Volumetric Flow Rate ◽  
Slip Boundary Condition ◽  
General Boundary Condition ◽  
Boltzmann Transport ◽  
Parallel Plates ◽  
Slip Boundary

AbstractThe flow of a rarefied gas between parallel plates has been studied via the linearized Boltzmann transport equation. Using a general boundary condition, which includes an arbitrary ratio of specular to diffuse reflection from the wall, we have derived an integral equation for the mass flow velocity. The integral equation is solved by using a replication property of the kernel and application of the method of Muskelishvili.The total volumetric flow rate is obtained and a slip boundary condition is deduced for use with the hydrodynamic equations.Certain aspects of the eigenvalue spectrum associated with the Boltzmann equation are discussed.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

On the Rarefied Gas Flow in Pipes

2005 ◽  
Author(s):  
Vladan D. Djordjevic
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Natural Extension ◽  
Slip Boundary Condition ◽  
Molecular Flow ◽  
Rarefied Gas Flow ◽  
Number Range ◽  
Average Value ◽  
Linearized Boltzmann Equation

Rarefied gas flow in a pipe is treated in the paper by modeling the slip boundary condition by means of a fractional derivative. At that the order of the derivative is conveniently chosen to be a function of the average value of the Knudsen number so that the entire Knudsen number range, from continuum flow to free molecular flow, is covered. Very good agreement with the solutions of linearized Boltzmann equation is achieved. The paper represents a natural extension of the work of the same author on the rarefied micro channel flow, published earlier.

Numerical Analysis of Rarefaction and Compressibility Effects in Bent Microchannels

2010 ◽  
Author(s):  
O. Rovenskaya ◽  
G. Croce
Keyword(s):  
Gas Flow ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Outer Wall ◽  
Slip Boundary Condition ◽  
Central Line ◽  
Navier Stokes ◽  
Strong Impact ◽  
First Order ◽  
Slip Boundary

Numerical investigation of a gas flow through microchannels with a sharp, 90 degrees bend is carried out using Navier-Stokes (N-S) equations with the classical Maxwell first-order slip boundary condition, including the tangential gradient effect due to the wall curvature, and Smoluchowski first order temperature jump definition. The details of the flow structure near the corner are analyzed, investigating the competing effects of rarefaction and compressibility on the channel performances. The flow characteristics in terms of velocity profiles, slip velocity distribution along inner and outer wall, pressure, average Mach number along central line of the channel have been presented. The results showed that impact of the bend on the channel performances is smaller at high rarefaction levels. The behaviour of pressure and velocity away from the bend is similar to that of a straight microchannel; however, the asymmetry in the flow at the bend, with high velocities and high velocity gradients on its inner side, has a strong impact on wall slip velocities. The presence of a recirculation is detected on both the inner and outer walls of the corner for larger Reynolds. However, rarefaction may delay the onset of recirculation. It is also observed that the mass flux through a bend microchannel can even be slightly larger than that through a straight microchannel of the same length and subjected to the same pressure difference.

A Friction Factor Correlation for Gas Flow in Parallel Plate Microchannels by Considering Combined Effects of Compressibility and Rarefaction

2008 ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Friction Factor ◽  
Velocity Gradient ◽  
Parallel Plate ◽  
Gas Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Combined Effects ◽  
Slip Boundary

The effects of compressibility and rarefaction for gas flow in microchannels have been extensively studied separately. However, these two effects are always combined for gas flow in microchannels. In this paper, the two-dimensional compressible Navier-Stokes equations are solved for gas flow in parallel plate channels with a slip boundary condition to study the combined effects of compressibility and rarefaction on the friction factor. The numerical methodology is based on the control volume finite difference scheme. It is found that the effect of compressibility increases the velocity gradient near the wall which then increases the friction factor. On the other hand, increasing the velocity gradient near the wall leads to a much larger slip velocity and implies a stronger rarefaction effect and a corresponding decrease in the friction factor. These two opposite effects make the effect of compressibility on friction factor for slip flow weaker than that for no-slip compressible flow. A correlation among fRe, Kn and Ma is presented. The correlation is validated with available experimental and analytical results.

The half-wetted bearing. Part 1: Extended Reynolds equation

2003 ◽  
Vol 217 (1) ◽  
pp. 1-14 ◽  
Author(s):  
H. A. Spikes
Keyword(s):  
Boundary Condition ◽  
Solid Surface ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Critical Shear Stress ◽  
Slip Boundary Condition ◽  
Low Friction ◽  
Slip Boundary ◽  
Lubrication Condition ◽  
Bearing Part

Recent research has shown that, when a liquid is partially wetting or non-wetting against a very smooth solid surface, the conventional no-slip boundary condition can break down. Under such circumstances, the Reynolds equation is no longer applicable. In the current paper, the Reynolds equation is extended to consider the sliding, hydrodynamic lubrication condition where the lubricant has a no-slip boundary condition against the moving solid surface but can slip at a critical shear stress against the stationary surface. It is shown that such a ‘half-wetted’ bearing is able to combine good load support resulting from fluid entrainment with very low friction due to very low or zero Couette friction.

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