An invited talk on a simple method for capturing some complex physics of gas flows in MEMS presented at 8th World Congress on Computational Mechanics (WCCM8) / 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) (Venice, Italy)

Lockerby, Duncan A.

Reese, Jason

English

Name not available

A simple method for capturing some complex physics of gas flows in MEMS

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryLockerby, Duncan A. and Reese, Jason (2008) A simple method for capturing some complexphysics of gas flows in MEMS. In: 8th World congress on computational mechanics / 5th EuropeanCongress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2008, 2008-06-30 - 2008-07-04, Venice. (Unpublished)Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/8th. World Congress on Computational Mechanics (WCCM8) 5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30 – July 5, 2008  Venice, Italy   A SIMPLE METHOD FOR CAPTURING SOME COMPLEX PHYSICS OF GAS FLOWS IN MEMS Duncan A. Lockerby¹ and *Jason M. Reese²¹ School of Engineering University of Warwick Coventry CV4 7AL United Kingdom duncan.lockerby@warwick.ac.uk  ² Department of Mechanical Engineering University of Strathclyde Glasgow G1 1XJ United Kingdom jason.reese@strath.ac.uk  Key Words: MEMS, gas microflows, microfluidics, Knudsen layer. ABSTRACT One difficulty in accurately modelling micro-scale gas flows is that the flow behaviour is generally dominated by the influence of any solid bounding surfaces. The non-equilibrium phenomena introduced by a solid surface are qualitatively different to that generated by the variation of hydrodynamic variables alone; if the wall is assumed to behave like a Maxwellian emitter, a discontinuity is introduced in the distribution function. Continuum-based methods (such as those, including the conventional Navier-Stokes equations, which can be derived from perturbation series solutions of the Boltzmann equation) are unable to resolve properly the region of local non-equilibrium that exists one or two molecular mean free paths from the wall in any gas flow near a surface. This region is called the “Knudsen layer” or “kinetic boundary layer” and recent comparisons of Knudsen layer predictions from a number of current high-order equation sets and concluded that none could be considered both reliable and accurate [1]. This is problematic for the future design and application of micro and nano flow devices because the momentum and energy fluxes from the region of the Knudsen layer to the boundaries has a critical influence on the overall flow behaviour.  Although not definitively proving that continuum equation sets are incapable of accurately modelling near-wall behaviour, there is therefore strong evidence to suggest that — if continuum equations are to be used at all — alternative phenomenological approaches may be just as useful in these non-equilibrium regions.  In this paper we demonstrate a simple phenomenological technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the current fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier-Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that it provides good results for Poiseuille (see figure 1) and combined Couette/Poiseuille flow, and that it can predict the stress-strain-rate inversion that molecular simulations show is evident in the latter. The model’s generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere.  It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.  REFERENCES [1] D.A. Lockerby, J.M. Reese and M.A. Gallis, “The usefulness of higher-order constitutive relations for describing the Knudsen layer”, Phys. Fluids Vol. 17, 100609, (2005).    Figure 1. Normalized mass flowrate predictions for gas micro Poiseuille flow up to Kn=1.6. Comparison of no-slip solution (– ·), slip solution (···), BGK kinetic theory (–), and our model (– –).   

The usefulness of higher-order constitutive relations for describing the Knudsen layer”,

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A simple method for capturing some complex physics of gas flows in MEMS

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