RESEARCH PAPER The gas flow diode effect: theoretical and experimental analysis of moderately rarefied gas flows through a microchannel with varying cross section I. Graur • T. Veltzke • J. G. Me ´olans • M. T. Ho • J. Tho ¨ming Received: 3 February 2014 / Accepted: 10 June 2014 Ó Springer-Verlag Berlin Heidelberg 2014 Abstract Moderately rarefied gas flows are clearly dis- tinguished from viscous flow in the continuum regime and from free molecular flow at high rarefaction. Being of relevance for various technical applications, the under- standing of such flow processes is crucial for considerable enhancement in micro electromechanical systems (MEMS) and vacuum techniques. In this work, we focus on the isothermal rarefied gas flow through long channels with longitudinally varying cross section. We apply two approaches, an analytical one and a numerical one that is based on the solution of the linearized S-model, both allowing us to predict the mass flow rate in diverging and converging flow directions for arbitrary pressure gradients. Both approaches are validated by CO 2 ,N 2 and Ar perme- ation experiments on tapered microchannels manufactured by means of micromilling. The local Knudsen numbers ranged from 0.0471 to 0.2263. All the numerical and analytical results are in good agreement to the experimental data and show that the mass flow rate is significantly higher when the duct is perfused in converging direction. The understanding of the physical phenomenon of this gas flow diode effect might pave the way for novel components in MEMS such as static one-way valves. Keywords Rarefied gas  Long tapered channel  Gas flow diode effect  Microchannel production  Mass flow rate measurement 1 Introduction The flow of rarefied gases through a long channel with rectangular cross section is a practical problem in the field of micro electromechanical systems (MEMS) and in vac- uum technology applications. This kind of flow was widely studied on the basis of the kinetic theory, and a detailed review is given in Sharipov and Seleznev (1998). Also a vast amount of experiments on microducts with various but uniform cross section were performed in the last decades (Porodnov et al. 1974; Aubert and Colin 2001; Colin et al. 2004; Ewart et al. 2007; Graur et al. 2009; Veltzke 2013). In several applications, however, the cross section varies alongside the channel. As examples of such kind of flow, the leakage through compressor valves (de Silva and Deschamps 2012) and the flow in the microbearing (Stevanovic 2007; Stevanovic and Djordjevic 2012) may be given. Only few numerical simulations are carried out on the flow through ducts with variable conical and tapered rectangular cross sections (Aubert et al. 1998; Sharipov and Bertoldo 2005; Titarev et al. 2013; Graur and Ho 2014). It was found that the permeability is higher when the duct is perfused in converging direction (Aubert et al. 1998; Veltzke et al. 2012; Veltzke 2013). In a more general I. Graur  J. G. Me ´olans  M. T. Ho CNRS, IUSTI UMR 7343, Aix-Marseille Universite ´, 13453 Marseille, France e-mail: irina.martin@univ-amu.fr J. G. Me ´olans e-mail: joseph.meolans@univ-amu.fr M. T. Ho e-mail: mtho@polytech.univ-mrs.fr T. Veltzke (&)  J. Tho ¨ming Center for Environmental Research and Sustainable Technology (UFT), University of Bremen, Leobener Strasse 1, 28359 Bremen, Germany e-mail: tveltzke@uni-bremen.de J. Tho ¨ming e-mail: thoeming@uni-bremen.de 123 Microfluid Nanofluid DOI 10.1007/s10404-014-1445-4