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A Navier-Stokes model incorporating the effects of near-wall molecular collisions with applications to micro gas flows

Arlemark, E.J. and Dadzie, S.K. and Reese, J.M. (2008) A Navier-Stokes model incorporating the effects of near-wall molecular collisions with applications to micro gas flows. In: 1st European Conference on Microfluidics, Microflu'08, 2008-12-10 - 2008-12-12, Bologna, Italy.

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Abstract

We propose a model for describing surface effects on micro gas flows. This model consists of the Navier-Stokes equations (NS) with discontinuous velocity slip boundary conditions and a description of a geometry-dependent and effective viscosity due to special consideration of the molecular collisions with solid boundaries. By extending NS with an effective viscosity we obtain a non-linear stress/strain-rate relationship which captures some of the near-wall effects that the conventional NS are unable to describe. We show results of NS extended by using our effective viscosity applied with Maxwell's boundary condition as well as a second order boundary condition achieved by partly incorporating higher order methods, the Maxwell-Burnett boundary condition proposed by Lockerby et al. (2004). With this proposed model the simple isothermal planar channel case of 2D Poiseuille flow is solved. The results of our proposed model are compared with the conventional NS using similar boundary conditions, the BGK-method and experiments. On the one hand it is seen that our extended NS model yields results that are asymptotic to the results of conventional NS for large flow scales. On the other hand, when comparing results on the micro scale, we see that our extended NS model yields results that are closer to the results of the BGK-method and the experiments than the conventional NS. Our extended NS-model shows signs of capturing the physics of the flow to a certain rarefaction degree where it does not predict the mass flow minimum shown by the BGK-method and the experiments.

Item type: Conference or Workshop Item (Paper)
ID code: 16034
Keywords: micro gas flows, Navier-Stokes equations, mean free path, non lineasr constitutive relationships, velocity slip, Mechanical engineering and machinery, Mechanical Engineering, Computational Mechanics, Modelling and Simulation
Subjects: Technology > Mechanical engineering and machinery
Department: Faculty of Engineering > Mechanical and Aerospace Engineering
Depositing user: Ms Katrina May
Date Deposited: 20 Jan 2010 17:27
Last modified: 18 Jun 2015 07:51
URI: http://strathprints.strath.ac.uk/id/eprint/16034

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