Molecular flows in annuli with corrugated walls

Department of Physics, Northwest Normal University, Gansu, Lanzhou 730070, PR China

Corresponding author: chukh01@nwnu.edu.cn

Received: 13 April 2001
Revised: 28 August 2001
Accepted: 30 October 2001
Published online: 15 February 2002

Abstract

Weakly nonlinear coupling comes from deterministic noises due to fixed boundaries and mean stochastic motion of molecular gases inside interior domains is investigated. The effect of deterministic surface wavy-roughness on molecular flows inside annuli with microfabricated solid walls was presented. The continuum-limit equations are being solved using perturbation methods with incorporated microscopic slip conditions along the small wavy-wall. The volume flow rate thus obtained, considering fully-developed parallel flow cases, contains terms which are related to the Knudsen number (K_n) of the fluid; the ratio of the inner to outer radius (); roughness ratio (ϵ), phase shift (β) and wave number (k) of the small wavy-roughness elements. There are critical pairs (k,β) which tell us under certain K_n and larger cases, the trend for the second order volume flow rate is increasing or decreasing.