Transition regime analytical solution to gas mass flow rate in a rectangular micro channel
Abstract
We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional NavierStokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly socalled 'volume diffusion hydrodynamic model'. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the nonlinear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.
 Publication:

28th International Symposium on Rarefied Gas Dynamics 2012
 Pub Date:
 November 2012
 DOI:
 10.1063/1.4769613
 Bibcode:
 2012AIPC.1501..720D