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On the modelling of isothermal gas flows at the microscale
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Lockerby, Duncan A. and Reese, Jason M.. (2008) On the modelling of isothermal gas flows at the microscale. Journal of Fluid Mechanics, Vol.604 . pp. 235261. ISSN 00221120

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Official URL: http://dx.doi.org/10.1017/S0022112008001158
Abstract
This paper makes two new propositions regarding the modelling of rarefied (nonequilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking highorder, or extended, hydrodynamic models for these flows. This standing timevarying shearwave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.
Our second proposition is a simple technique for introducing nonequilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a nearwall scaling of the NavierStokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional secondorder slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strainrate inversion that is evident from molecular simulations. The model's generality to nonplanar geometries is demonstrated by examining lowspeed flow around a microsphere. 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.
Item Type:  Journal Article  

Subjects:  T Technology > T Technology (General) Q Science > QA Mathematics Q Science > QC Physics 

Divisions:  Faculty of Science > Engineering  
Library of Congress Subject Headings (LCSH):  Rarefied gas dynamics, Geometry, Plane, NavierStokes equations  Numerical solutions, Transport theory, Gas dynamics, Fluid dynamics  
Journal or Publication Title:  Journal of Fluid Mechanics  
Publisher:  Cambridge University Press  
ISSN:  00221120  
Official Date:  June 2008  
Dates: 


Volume:  Vol.604  
Number of Pages:  27  
Page Range:  pp. 235261  
Identifier:  10.1017/S0022112008001158  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Open Access  
Funder:  Engineering and Physical Sciences Research Council (EPSRC)  
Grant number:  EP/D007488/1 (EPSRC)  
References:  Allen, M. D. & Raabe, O. G. 1985 Slip correction measurements of spherical solid aerosolparticles in an improved Millikan apparatus. Aerosol Sci. Tech. 4, 269–286. 
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