Mean Free Path and Correction Factor for the Long Uniform Ducts of Isosceles-Triangle Cross Section

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  • 二等辺三角形断面を持つ長い一様導管の平均自由行程と形状補正係数
  • ニトウヘンサンカクケイ ダンメン オ モツ ナガイ イチヨウ ドウカン ノ ヘイキン ジユウ コウテイ ト ケイジョウ ホセイ ケイスウ

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Abstract

<p>In application of one dimensional diffusion theory to gas molecular flow in the steady state through long ducts of uniform cross section, diffusion coefficient 𝒟 is generally represented as</p><p><img align="middle" src="./Graphics/abst-61_539-1.jpg"/></p><p>here λ is a kind of mean free path and v is avarage velocity of molecules. Up to now rigorous expressions of λ＝λS where λS is Smoluchowski's expression for λ which have been given by Smoluchowski himself and other author for rectangular, ellipsoidal and annular cross section. As for triangular cross section, the rigorous expression has been obtained only on equilatera-triangle cross section. In this report, the concrete expression of λS and the correction factor α defined by the ratio of λS/λK where λK is Knudsen's expression for λ, are deduced for long ducts with isosceles-triangle cross sections. The values for λS and α, which are given by these deduced formula, are compared with those obtained from the Monte-Carlo simulation, which uses the mean free path in the duct ℓ and the mean square of free path in the axial direction of the duct <img align="middle" src="./Graphics/abst-61_539-3.jpg"/>.</p>

Journal

  • Vacuum and Surface Science

    Vacuum and Surface Science 61 (8), 539-543, 2018-08-10

    The Japan Society of Vacuum and Surface Science

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