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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.\ud \ud 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

Topics:
T1, QA, QC

Publisher: Cambridge University Press

Year: 2008

OAI identifier:
oai:wrap.warwick.ac.uk:863

Provided by:
Warwick Research Archives Portal Repository

- 1879 On stresses in rareﬁed gases arising from inequalities of temperature.
- 1888 A Treatise on Hydrodynamics.
- (2003). Acceleration schemes of the discrete velocity method: gaseous ﬂows in rectangular microchannels.
- (2007). An extended Navier–Stokes formulation for gas ﬂows in the Knudsen layer near a wall.
- (2005). Capturing the Knudsen layer in continuumﬂuid models of nonequilibrium gas ﬂows.
- (2003). Comment on Cercignani’s second-order slip coeﬃcient.
- (1988). Couette ﬂow of a binary gas mixture.
- (2005). Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature and concentration gradients.
- (2007). H theorem, regularization, and boundary conditions for linearized 13 moment equations.
- (2002). Kinetic Theory and Fluid Dynamics.
- (2004). L o c k e r b y ,D .A . ,R e e s e ,J .M . ,E m e r s o n
- (2005). Macroscopic Transport Equations for Rareﬁed Gas Flows.
- (1982). Motion of a sphere in a rareﬁed gas.
- (2003). New directions in ﬂuid dynamics: nonequilibrium aerodynamic and microsystem ﬂows.
- O h w a d a ,T . ,S o n e ,Y .&A o k i ,K .1989a Numerical analysis of the Poiseuille and thermal transpiration ﬂows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules.
- (2009). O h w a d a ,T . ,S o n e ,Y .&A o k i ,K .1989b Numerical analysis of the shear and thermal creep ﬂows of a rareﬁed gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules.
- (1949). On the kinetic theory of rareﬁed gases.
- (2003). Regularization of Grad’s 13-moment equations: derivation and linear analysis.
- (1985). Slip correction measurements of spherical solid aerosol-particles in an improved Millikan apparatus.
- (1935). The distribution of molecular velocities and the mean motion in a non-uniform gas.
- (2005). The driven cavity ﬂow over the whole range of the Knudsen number.
- (1923). The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reﬂection from surfaces.
- (2007). The structure of shock waves as a test of Brenner’s modiﬁcations to the Navier–Stokes equations.
- (2005). The usefulness of higher-order constitutive relations for describing the Knudsen layer.
- (2007). Velocity gradient singularity and structure of the velocity proﬁle in the Knudsen layer according to the Boltzmann equation.

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