Application of Average Flow Model to Thin Film Gas Lubrication

1993 ◽  
Vol 115 (1) ◽  
pp. 185-190 ◽  
Author(s):  
T. Makino ◽  
S. Morohoshi ◽  
S. Taniguchi
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Mean Free Path ◽  
Perturbation Approach ◽  
Roughness Effects ◽  
Load Carrying ◽  
Gas Lubrication ◽  
Induced Flow ◽  
Average Film Thickness ◽  
Average Flow Model

The flow factors for the average Reynolds equation introduced by Patir and Cheng (1978, 1979) are extended to be valid for thin film gas lubrication. The effects of molecular mean free-path on the roughness-induced flow factors are included on the assumption that the local compressibility is small. The derivation of flow factors is carried out by means of the perturbation approach developed by Tripp (1983). The results are expressed in terms of Knudsen number, Peklenik parameter and nondimensional film thickness defined as the ratio of average film thickness and standard deviation of composite roughness. Two-dimensional roughness effects on the load-carrying capacity of a gas lubricated finite slider are also investigated.

Averaged Reynolds Equation Extended to Gas Lubrication Possessing Surface Roughness in the Slip Flow Regime: Approximate Method and Confirmation Experiments

1989 ◽  
Vol 111 (3) ◽  
pp. 495-503 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo ◽  
H. Ota
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Approximate Method ◽  
Flow Regime ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Roughness Effects ◽  
Gas Lubrication ◽  
Slip Flow Regime ◽  
Average Film Thickness

The average film thickness theory is extended to gas lubrication possessing surface roughness in the slip flow regime. A simplified averaged Reynolds equation is derived and its applicability is confirmed through comparing with experiments. This averaging equation makes use of the mixed average film thickness defined as Havem = αHm + (1 − α)Hmˆ, where m = 1, 2 and 3; α indicates the mixing ratio; and H¯ and Hˆ denote the arithmetically and harmonically averaged film thicknesses. The experiments were performed using computer flying heads having precisely photolithography-fabricated longitudinal, transverse or checkered pattern roughnesses under submicron spacing conditions. From the excellent agreement obtained between the calculated and experimental results, it can be concluded that the assumption that velocity slippage occurs along the surface even if roughnes is present is justified, and that the approximate method is applicable for determining the surface roughness effects in the slip flow regime.

Thin Film In-Plane Silicon Thermal Conductivity Dependence on Molecular Dynamics Surface Boundary Conditions

2004 ◽  
Author(s):  
Carlos J. Gomes ◽  
Marcela Madrid ◽  
Cristina H. Amon
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Mean Free Path ◽  
Surface Boundary ◽  
Repulsive Potential ◽  
Surface Boundary Conditions ◽  
Weber Potential

The in-plane thermal conductivity of thin silicon films is predicted using equilibrium molecular dynamics, the Stillinger-Weber potential and the Green-Kubo relationship. Film thicknesses range from 2 to 200 nm. Periodic boundary conditions are used in the directions parallel to the thin film surfaces. Two different strategies are evaluated to treat the atoms on the surfaces perpendicular to the thin film direction: adding four layers of atoms kept frozen at their crystallographic positions, or restraining the atoms near the surfaces with a repulsive potential. We show that when the thin-film thickness is smaller than the phonon mean free path, the predictions of the in-plane thermal conductivity at 1000K differ significantly depending on the potential applied to the atoms near the surfaces. In this limit, the experimentally observed trend of decreasing thermal conductivity with decreasing film thickness is predicted when the surface atoms are subject to a repulsive potential in addition to the Stillinger-Weber potential, but not when they are limited by frozen atoms.

An Average Lubrication Equation for Thin Film Grain Flow With Surface Roughness Effects

2002 ◽  
Vol 124 (4) ◽  
pp. 736-742 ◽  
Author(s):  
Hung-Jung Tsai ◽  
Yeau-Ren Jeng
Keyword(s):  
Thin Film ◽  
Surface Roughness ◽  
Particle Size ◽  
Coordinate Transformation ◽  
Surface Characteristics ◽  
Perturbation Approach ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Grain Flow ◽  
Standard Derivation

A closed-form average lubrication equation for thin film grain flow with the effects of surface roughness is derived. This equation is based on Haff’s grain flow theory and also the flow factors proposed by Patir and Cheng. The flow factors, derived by the perturbation approach and coordinate transformation, are expressed in terms of surface characteristics (three characteristics for each surface: roughness orientation, Peklenik number and standard derivation) and particle size. Finally, the flow factors under different surface characteristics and particle size are discussed.

scholarly journals Further Increasing the Accuracy of Characterization of a Thin Dielectric or Semiconductor Film on a Substrate from Its Interference Transmittance Spectrum

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4681
Author(s):  
Dorian Minkov ◽  
Emilio Marquez ◽  
George Angelov ◽  
Gavril Gavrilov ◽  
Susana Ruano ◽  
...  
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Refractive Index ◽  
Film Thickness ◽  
High Accuracy ◽  
Transmittance Spectrum ◽  
Semiconductor Film ◽  
Envelope Method ◽  
Average Film Thickness

Three means are investigated for further increasing the accuracy of the characterization of a thin film on a substrate, from the transmittance spectrum T(λ) of the specimen, based on the envelope method. Firstly, it is demonstrated that the accuracy of characterization, of the average film thickness d¯ and the thickness non-uniformity ∆d over the illuminated area, increases, employing a simple dual transformation utilizing the product T(λ)xs(λ), where Tsm(λ) is the smoothed spectrum of T(λ) and xs(λ) is the substrate absorbance. Secondly, an approach is proposed for selecting an interval of wavelengths, so that using envelope points only from this interval provides the most accurate characterization of d¯ and ∆d, as this approach is applicable no matter whether the substrate is transparent or non-transparent. Thirdly, the refractive index n(λ) and the extinction coefficient k(λ) are computed, employing curve fitting by polynomials of the optimized degree of 1/λ, instead of by previously used either polynomial of the optimized degree of λ or a two-term exponential of λ. An algorithm is developed, applying these three means, and implemented, to characterize a-Si and As98Te2 thin films. Record high accuracy within 0.1% is achieved in the computation of d¯ and n(λ) of these films.

Study on Thin Film Lubrication With Second-Order Fluid

2002 ◽  
Vol 124 (3) ◽  
pp. 547-552 ◽  
Author(s):  
Ping Huang ◽  
Zhi-heng Li ◽  
Yong-gang Meng ◽  
Shi-zhu Wen
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Normal Stress ◽  
Journal Bearing ◽  
Deborah Number ◽  
Second Order ◽  
Thin Film Lubrication ◽  
Stress Changes ◽  
Load Carrying ◽  
Film Lubrication

The basic lubrication equations are deduced from the original second-order fluid constitutive equations. Two examples of lubrication, a plane inclined slider and a journal bearing, are calculated respectively. The Reynolds boundary conditions are used in the calculation of the journal bearing. In this calculation, it is found that the load carrying capacities of the slider and the journal bearing are of different tendencies with the increase of the Deborah number. Furthermore, the results show that with the decrease of the film thickness, the increase of the normal stress of second-order fluid is greater than that of Newtonian fluid. Finally, it is found that the distribution of the normal stress changes significantly at a certain thickness.

Numerical Study of Film Thickness Averaging in Compressible Lubricating Films Incurring Stationary Surface Roughness

1990 ◽  
Vol 112 (2) ◽  
pp. 230-237 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Hayashi
Keyword(s):  
Film Thickness ◽  
Numerical Study ◽  
Wave Number ◽  
Numerical Comparison ◽  
Load Carrying Capacity ◽  
Roughness Effects ◽  
Individual Unit ◽  
Wide Range ◽  
Load Carrying ◽  
Compressibility Effects

The compressibility effects of lubricating films incurring a roughness on film thickness averaging were studied numerically with a focus on the physical interpretation of the roughness effects. A numerical comparison between load-carrying capacities resulting from rough film thickness and from averaged film thickness are presented for a wide range of bearing numbers up to 107. It is found that currently indicated particular features such as the appearance of the maximum or minimum load-carrying capacity can be induced from the superimposition of local compressibility effects (LCEs) caused by individual unit roughness on compressibility effects owing to averaged film thickness. The most noticeable difference between the case of small LCEs and that of saturated LCEs is that the roughness phase results in a minimal effect with the increasing wave number for the former, while it creates a dominant effect for the latter. The results confirm that the same averaging method as that for incompressible films can be applied for small LCEs, and that Greengard’s method is applicable for nearly saturated LCEs. It should be noted that the averaged film thickness can be determined physically for small LCE regions, while it is defined mathematically for nearly saturated LCE regions.

Roughness Effects on the Dynamic Coefficients of Ultra-Thin Gas Film in Magnetic Recording

1996 ◽  
Vol 118 (4) ◽  
pp. 774-782 ◽  
Author(s):  
Wang-Long Li ◽  
Cheng-I Weng ◽  
Chi-Chuan Hwang
Keyword(s):  
Knudsen Number ◽  
Surface Characteristics ◽  
Mean Free Path ◽  
Roughness Effects ◽  
Roughness Effect ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Induced Flow ◽  
Bearing Number ◽  
Stiffness And Damping

The stiffness and damping coefficients of a slider gas bearing operating under arbitrary Knudsen number are calculated. A perfect gas is used as the lubricant, and its behavior is described by the modified average Reynolds equation proposed by Makino et al. (1993). The effects of molecular mean free-path on the roughness-induced flow factors are included. The effects of the nondimensional film thickness, Hs0, the surface characteristics, (γ1, γ2). the inverse Knudsen number, D0, the nondimensional frequency, Ω, and the modified bearing number, Λb, on the dynamic coefficients are discussed in this paper. As expected, the values of dynamic coefficients for various roughness orientations approach the smooth value as the ratio, Hs0, becomes greater and greater, and thus the roughness effect is getting smaller and smaller. The air film of two-sided longitudinal oriented roughness is stiffer than the other two-sided oriented cases. The effect on translational damping coefficients for various two-sided oriented roughnesses is reversed as D0 greater than some value, and this value is affected significantly by Λb. Transversely rough stationary case has the lowest critical value of Λb, at which the negative translational damping appears. The results show that the roughness effect and rarefaction effect on dynamic coefficients are significant, and they cannot be ignored for stability analysis.

Research on Seebeck Coefficient of Thin-Film Thermocouple on Temperature-Testing Cutter

2015 ◽  
Vol 757 ◽  
pp. 139-146 ◽  
Author(s):  
Yun Xian Cui ◽  
Yang An ◽  
Jia Hui Zhao ◽  
Xiao Xing Sheng
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Seebeck Coefficient ◽  
Thermoelectric Power ◽  
Free Path ◽  
Mean Free Path ◽  
Cutting Edge ◽  
Transient Temperature ◽  
Thin Film Thermocouple ◽  
Electron Mean Free Path

Performance of current temperature sensor is not satisfactory on monitoring transient temperature of cutting edge. A temperature-testing cutter is presented in this paper and analysis of Seebeck coefficient on thin film thermocouple is proposed with experiments. Thin film thermocouple is embedded into the cutting edge using magnetron sputtering technology. According to the fact that electrical conductivity can be replaced by the multiplication of electron mean free path λ and effective Fermi surface area A, a universal formula of thermoelectric power is given based on the diffuse thermoelectric power equation put forward by Mott and Jones. Using the expression of electron mean free path in gas model λ, the relationship of thermoelectric power between thin film and bulk material can be deduced. Result shows that the main influential factor of Seebeck coefficient is film thermal junction thickness. In addition, the Seebeck coefficient of different junction size and film thickness were tested by LabVIEW automatic calibration system. The experimental data indicates that Seebeck coefficient is determined by thermal junction thickness, and the sensor is found to be linear from room temperature up to 600°C while the Seebeck coefficient of thin film thermocouple becomes closer to standard thermocouple as the film thickness increments. However, junction size does not have a major influence on the Seebeck coefficient which is agreed by both theoretical analysis and test.

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