On the numerical simulation of rarefied gas flows in micro-channels

Christou, Chariton; Dadzie, K.

doi:10.1088/2399-6528/aab066

Cited by 7 publications

(5 citation statements)

References 27 publications

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“…Taking into account a corrected mean-free path for flow in confined spaces, Lv et al [29] were able to improve this agreement up to a Knudsen number of 50. More recently, Christou and Dadzie achieved a match over the entire range of Knudsen number in another numerical simulation based on the Bi-velocity model [30].…”

Section: Introductionmentioning

confidence: 92%

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Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

2019

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Over the past two decades, several researchers have presented experimental data from pressure-driven liquid flows through nanotubes. They quote flow velocities which are four to five orders of magnitude higher than those predicted by the classical theory. Thus far, attempts to explain these enhanced mass flow rates at the nanoscale have focused mainly on introducing wall-slip boundary conditions on the fluid mass velocity. In this paper, we present a different theory. A change of variable on the velocity field within the classical Navier-Stokes equations is adopted to transform the equations into physically different equations. The resulting equations, termed re-casted Navier-Stokes equations, contain additional diffusion terms whose expressions depend upon the driving mechanism. The new equations are then solved for the pressure driven flow in a long nano-channel. Analogous to previous studies of gas flows in micro-and nano-channels, a perturbation expansion in the aspect ratio allows for the construction of a 2D analytical solution. In contrast to slip-flow models, this solution is specified by a no-slip boundary condition at the channel walls. The mass flow rate can be calculated explicitly and compared to available data. We conclude that the new re-casting methodology may provide an alternative theoretical physical explanation of the enhanced mass flow phenomena.

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Section: Introductionmentioning

confidence: 92%

“…As stated earlier the precise nature of this coefficient is not yet known. However, in previous investigations on rarefied gas flows [30], it was assumed that…”

Section: Governing Equationsmentioning

confidence: 99%

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

2019

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“…Furthermore, it is found that the shear stress in Dadzie's model is exactly the same as that in Brenner's model. However, in a recent paper the parameter κ m is changed to Pr/3 [12].…”

Section: "Thermo-mechanically Consistent" Burnett Equationsmentioning

confidence: 99%

On the accuracy of macroscopic equations for linearized rarefied gas flows

2020

Adv. Aerodyn.

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Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level, either from the mesoscopic Boltzmann equation or some physical arguments, including (i) Burnett, Woods, super-Burnett, augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation, (ii) Grad 13, regularized 13/26 moment equations, rational extended thermodynamics equations, and generalized hydrodynamic equations, where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials, and (iii) bi-velocity equations and "thermo-mechanically consistent" Burnett equations based on the argument of "volume diffusion". This paper is dedicated to assess the accuracy of these macroscopic equations. We first consider the Rayleigh-Brillouin scattering, where light is scattered by the density fluctuation in gas. In this specific problem macroscopic equations can be linearized and solutions can always be obtained, no matter whether they are stable or not. Moreover, the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem. Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation. We find that (i) the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion, (ii) for the moment method, the more moments are included, the more accurate the results are, and (iii) macroscopic equations based on "volume diffusion" do not work well even when the Knudsen number is very small. Therefore, among about a dozen tested equations, the regularized 26 moment equations are the most accurate. However, for moderate and highly rarefied gas flows, huge number of moments should be included, as the convergence to true solutions is rather slow. The same conclusion is drawn from the problem of sound propagation between the transducer and receiver. This slow convergence of moment equations is due to the incapability of Hermite polynomials in the capturing of large discontinuities and rapid variations of the velocity distribution function. This study sheds some light on how to choose/develop macroscopic equations for rarefied gas dynamics.

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“…In the free molecular regime, the diffusive terms have a larger effect in governing the flow profiles, thereby giving a plug flow velocity profile along the channel. This plug flow profile can be noted in the numerical simulations in the works of Christou and Dadzie [43]. The new slip conditions and analytical solutions provide an alternative physical explanation for rarefied flows in micro-channels and may be adopted to interpret other non-equilibrium flow phenomenons.…”

Section: Discussionmentioning

confidence: 62%

Diffusion-Slip Boundary Conditions for Isothermal Flows in Micro- and Nano-Channels

Tomy

Dadzie

2022

Micromachines

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Continuum description of flows in micro- and nano-systems requires ad hoc addition of effects such as slip at walls, surface diffusion, Knudsen diffusion and others. While all these effects are derived from various phenomenological formulations, a sound theoretical ground unifying these effects and observations is still lacking. In this paper, adopting the definition and existence of various type of flow velocities beyond that of the standard mass velocity, we suggest derivation of model boundary conditions that may systematically justify various diffusion process occurring in micro- and nano-flows where the classical continuum model breaks down. Using these boundary conditions in conjunction with the classical continuum flow equations we present a unified derivation of various expressions of mass flow rates and flow profiles in micro- and nano-channels that fit experimental data and provide new insights into these flow profiles. The methodology is consistent with recasting the Navier–Stokes equations and appears justified for both gas and liquid flows. We conclude that these diffusion type of boundary conditions may be more appropriate to use in simulating flows in micro- and nano-systems and may also be adapted as boundary condition models in other interfacial flow modelling.

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On the numerical simulation of rarefied gas flows in micro-channels

Cited by 7 publications

References 27 publications

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

On the accuracy of macroscopic equations for linearized rarefied gas flows

Diffusion-Slip Boundary Conditions for Isothermal Flows in Micro- and Nano-Channels

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