On the modelling of isothermal gas flows at the microscale
Lockerby, Duncan and Reese, Jason. (2008) On the modelling of isothermal gas flows at the microscale. Journal of Fluid Mechanics, Vol.604 . pp. 235-261. ISSN 0022-1120
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Official URL: http://dx.doi.org/10.1017/S0022112008001158
This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave 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 non-equilibrium 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 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 this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. 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.
|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, Navier-Stokes equations -- Numerical solutions, Transport theory, Gas dynamics, Fluid dynamics|
|Journal or Publication Title:||Journal of Fluid Mechanics|
|Publisher:||Cambridge University Press|
|Official Date:||June 2008|
|Number of Pages:||27|
|Page Range:||pp. 235-261|
|Access rights to Published version:||Open Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC)|
|Grant number:||EP/D007488/1 (EPSRC)|
Allen, M. D. & Raabe, O. G. 1985 Slip correction measurements of spherical solid aerosol-particles in an improved Millikan apparatus. Aerosol Sci. Tech. 4, 269–286.
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