scholarly journals Discussion: “Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow” (Fukui, S., and Kaneko, R., 1988, ASME J. Tribol., 110, pp. 253–261)

1988 ◽  
Vol 110 (2) ◽  
pp. 262-262
Author(s):  
R. F. Gans
Keyword(s):  
Boltzmann Equation ◽  
Thermal Creep ◽  
First Report ◽  
Creep Flow ◽  
Lubrication Equation ◽  
Linearized Boltzmann Equation ◽  
Thermal Creep Flow ◽  
Film Lubrication

Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow

1988 ◽  
Vol 110 (2) ◽  
pp. 253-261 ◽  
Author(s):  
S. Fukui ◽  
R. Kaneko
Keyword(s):  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Thermal Creep ◽  
Creep Flow ◽  
Slip Boundary ◽  
Lubrication Equation ◽  
Linearized Boltzmann Equation ◽  
Knudsen Numbers ◽  
Bearing Number ◽  
Thermal Creep Flow

A generalized Reynolds-type lubrication equation valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, is derived from a linearized Boltzmann equation by semi-numerically calculating the flow rates of fundamental flows in the lubrication film: Poiseuille flow, Couette flow, and thermal creep flow. Numerical analysis of the equation for high Knudsen numbers reveals three principal results. First, Burgdorfer’s modified Reynolds equation featuring the first-order velocity slip boundary condition overestimates load carrying capacities, while the approximation equation including both the first- and second-order velocity slip boundary condition underestimates them. Second, since the flow rate of the Couette flow, which is independent of Knudsen numbers, becomes dominant as the bearing number increases, all the lubrication equation results tend toward the same asymptotic value for an infinite bearing number. Third, a new kind of load carrying capacity caused by thermal creep flow occurs if temperature gradients at the boundaries exist in the flow direction.

Axisymmetric thermal-creep flow of a slightly rarefied gas induced around two unequal spheres

1984 ◽  
Vol 144 ◽  
pp. 103-121 ◽  
Author(s):  
Yoshimoto Onishi
Keyword(s):  
Reynolds Number ◽  
Temperature Gradient ◽  
Rarefied Gas ◽  
Low Reynolds Number ◽  
Thermal Creep ◽  
Creep Flow ◽  
Low Reynolds ◽  
Thermal Creep Flow ◽  
Slightly Rarefied Gas ◽  
Thermal Conductivities

A thermal-creep flow of a slightly rarefied gas induced axisymmetrically around two unequal spheres is studied on the basis of kinetic theory. The spheres, whose thermal conductivities are assumed to be identical with that of the gas, for simplicity, are placed in an infinite expanse of the gas at rest with a uniform temperature gradient at a far distance. Owing to the poor thermal conductivities of the spheres, a tangential temperature gradient is established on the surfaces, and this causes a thermal-creep flow in its direction. Consequently, the spheres experience forces in the opposite direction.The flow considered here is a low-Reynolds-number flow in the ordinary fluid-dynamic sense (except for the Knudsen layer), and the solution is obtained in terms of bispherical coordinates, with respect to which the system of equations of Stokes type is well developed. The velocity field around the spheres and the forces acting on them are given explicitly. The results show the interesting feature that the smaller sphere experiences the minimum force at a value of the separation distance that depends on the radius ratio. This is in contrast with the case of the axisymmetric motion of two spheres treated by Stimson & Jeffery (1926) in ordinary fluid dynamics at low Reynolds number.The ultimate velocities that the spheres would have under the action of the present thermal force when they are freely suspended are also obtained by utilizing the results for the forces of axisymmetric translational problems of two spheres at low Reynolds number. For a given temperature gradient in the gas, both spheres acquire larger velocities than those they would have if they were alone, and the smaller sphere tends to move faster than the larger one in the direction opposite to the temperature gradient.Also presented, for completeness, are the results for the sphere–plane case and for the case of eccentric spheres, the solutions for which are derived as special cases of the preceding problem of two unequal spheres.

Making Monte Carlo Simulation of Thermal Creep Flow around Discs with Slits

2018 ◽  
Vol 2018 (0) ◽  
pp. J0530302
Author(s):  
Hiroaki MATSUMTO ◽  
Hiroki TANAKA ◽  
Kento KOGA ◽  
Takayuki MOROKUMA
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Thermal Creep ◽  
Creep Flow ◽  
Thermal Creep Flow

Numerical study of thermal creep flow between two ratchet surfaces

Vacuum ◽  
2014 ◽  
Vol 109 ◽  
pp. 294-301 ◽  
Author(s):  
J. Chen ◽  
L. Baldas ◽  
S. Colin
Keyword(s):  
Numerical Study ◽  
Thermal Creep ◽  
Creep Flow ◽  
Thermal Creep Flow
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