拡散方程式の定常解に基づく分子流コンダクタンス値

摘要

In this report we derive approximation of the transmission probability K for a cylindrical pipe which is usually given with computational calculation by using Monte Carlo technique nowadays, with rather old fashioned diffusion theory. Same results as Dushman's approximation is given based on the stationary solution of the one-dimensional diffusion equation with adopting the special boundary condition, that is the boundary of Dirichlet condition n = 0 (n: number density of molecules) placing at the outer side of the real boundary (exit of the pipe). Transmission probability of the serially connected cylindrical ducts of different size is also given by those theory of diffusion.%一様円形導管内の気体の流れは分子統領域においては次のrnような一次元拡散方程式で記述できることが知られている．rnJ=-D partial detiv n/partial detiv x[D=v/3] （1）rnここにJは流束，nは分子密度，xは位置座標である．系をrn特徴つける拡散定数Dは，管内平均自由行程λ（円形導管rnでは直径dに等しい）と気体の平均速度vの積に比例し，rnその係数が1/3であることが気体分子運動論から導かれる．