A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems

Abstract

This paper proposes the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films. The database is created by numerical calculations based on the linearized Boltzmann equation. The proposed interpolation method is verified to reduce calculation time to several tenths of that required to perform rigorous calculations with the same accuracy.

A slip model for rarefied gas flows at arbitrary Knudsen number

“…The mass flow rates for other models are available from the listed references. [2][3][4][5] The figure shows that the current slip model predicts a mass flow rate very close to the FK model and in this sense outperforms other slip models in the whole modified inversed Knudsen number range. Slight divergence between the current model and the FK model is observed when the modified inversed Knudsen number is reduced below 0.02.…”

“…5 The 1st order, 2nd order, and 1.5 order slip models are derived from kinetic theory by considering the momentum transfer rate of gas molecules impinging on the wall. The FK model is a database of direct numerical solutions of linearized Boltzmann equation.…”

Mechanism of Levitation of a Slider with a Micro/Nanoscale Surface Structure on a Rotating Disk

“…(18) because Q P ðDÞ changes only slightly against D for the range of D considered here. The range of values of Q P ðDÞ is 1:539\Q P ðDÞ\3:060 for 0:01\D\10 [23]. On the other hand, although the inverse Knudsen number D changes along the parallel channel in proportion to the pressure p, the spatial change of Q P ðDÞ along the channel is also small for the same reason.…”

“…The gradient dQ P ðDÞ=dD is positive for D [ 1 and negative for D\1 [23]. Since the pressure P i ð¼ p i =p a Þ at the inlet X ¼ 0 is larger than the pressure P o ð¼ p o =p a Þ at the outlet X ¼ 1, there is one point, X ¼ c ð0\c\1Þ, at which dP=dX is negative.…”

“…where R is the ordinary gas constant, i.e., gas constant per unit mass, and is given by k=m, k is the Boltzmann constant, m is the molecular mass, D is the inverse Knudsen number given by D ¼ ffiffiffi p p =ð2KnÞ, and Q P ðDÞ is the flow rate coefficient for the Poiseuille flow given as follows [23]:…”