Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation

Loyalka, Sudarshan K.; Hamoodi, S. A.

doi:10.1063/1.857681

Cited by 140 publications

(98 citation statements)

References 11 publications

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“…Figure 7 shows that the minimum normalized flow rate and the corresponding Knudsen number generally increase with pressure ratio. When P is close to unity ͑i.e., a gas flow with the Knudsen number nearly unchanged along the tube length͒, the corresponding Knudsen number is approximately 3, and the Knudsen's minimum is 0.915; this is consistent with results reported in the literature 20,25 for these lower pressure ratios.…”

Section: A Mass Flow Ratesupporting

confidence: 81%

“…The model is validated against experimental results in the transitional flow regime obtained as part of this work, as well as solutions for the linearized Boltzmann equation ͑at a low pressure ratio͒ in a cylindrical tube over the entire flow regime. 20 The good agreement obtained in these comparisons shows that the model is valid for predicting mass flow rate and streamwise pressure distribution for gas flows up to the transitional regime and is potentially applicable over the full range of flow regimes.…”

Section: Introductionmentioning

confidence: 50%

“…As P becomes large, the entire curve shifts from left to right. Loyalka and Hamoodi's solutions of the linearized Boltzmann equation 20 are also plotted in the figure to compare the measured gas flow rates at an extremely small pressure ratio of P = 1.001, for which Knudsen number is almost constant throughout the tube. Although experimental data could only be obtained over some of the flow regimes, the good agreement between the solution of the linear-Boltzmann equation and the curve for P = 1.001 implies that Eq.…”

Section: A Mass Flow Ratementioning

confidence: 99%

“…To account for the collision integral, the Bhatnagar-Gross-Krook model 17 as well as the hardsphere and Maxwellian models 18,19 have been used extensively. Solutions of the Boltzmann equation have been obtained for a cylindrical geometry, 20 as well as for ducts of different cross sections. 18,21 Experimental studies of rarefied gas flows have advanced rapidly due to developments in micromachining and lithographic techniques.…”

Section: Introductionmentioning

confidence: 99%

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Rarefied gas flow in microtubes at different inlet-outlet pressure ratios

Yang

Garimella

2009

Physics of Fluids

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A model is developed for rarefied gas flow in long microtubes with different inlet-outlet pressure ratios at low Mach numbers. The model accounts for significant changes in Knudsen number along the length of the tube and is therefore applicable to gas flow in long tubes encountering different flow regimes along the flow length. Predictions from the model show good agreement with experimental measurements of mass flow rate, pressure drop, and inferred streamwise pressure distribution obtained under different flow conditions and offer a better match with experiments than do those from a conventional slip flow model.

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Section: A Mass Flow Ratesupporting

confidence: 81%

Section: Introductionmentioning

confidence: 50%

Section: A Mass Flow Ratementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rarefied gas flow in microtubes at different inlet-outlet pressure ratios

Yang

Garimella

2009

Physics of Fluids

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“…The mass-flow-rate data are obtained from a variety of sources, including our own simulations 47 computed using a version of lowvariance deviational simulation Monte Carlo (LVDSMC). 48 Additional mass-flow-rate data are procured from solutions of the linearized Boltzmann equation 49,50 to verify the accuracy of the LVDSMC results. For dilute gases, the slip length can be related to the mean free path k via g ¼ C s k, where C s ¼ 1.11 is the first-order slip coefficient for the hard-sphere model of gases with purely diffuse molecular reflection at walls.…”

Section: B Rarefied Gas Flowmentioning

confidence: 99%

Generalizing Murray's law: An optimization principle for fluidic networks of arbitrary shape and scale

Stephenson

Patronis

Holland

et al. 2015

Journal of Applied Physics

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Murray's law states that the volumetric flow rate is proportional to the cube of the radius in a cylindrical channel optimized to require the minimum work to drive and maintain the fluid. However, application of this principle to the biomimetic design of micro/nano fabricated networks requires optimization of channels with arbitrary cross-sectional shape (not just circular) and smaller than is valid for Murray's original assumptions. We present a generalized law for symmetric branching that (a) is valid for any cross-sectional shape, providing that the shape is constant through the network; (b) is valid for slip flow and plug flow occurring at very small scales; and (c) is valid for networks with a constant depth, which is often a requirement for lab-on-a-chip fabrication procedures. By considering limits of the generalized law, we show that the optimum daughter-parent area ratio C, for symmetric branching into N daughter channels of any constant cross-sectional shape, is C ¼ N À2=3 for large-scale channels, and C ¼ N À4=5 for channels with a characteristic length scale much smaller than the slip length. Our analytical results are verified by comparison with a numerical optimization of a two-level network model based on flow rate data obtained from a variety of sources, including Navier-Stokes slip calculations, kinetic theory data, and stochastic particle simulations.

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Numerical Simulation of Multiphase Flow in Nanoporous Organic Matter With Application to Coal and Gas Shale Systems

Song

et al. 2018

Water Resources Research

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Fluid flow in nanoscale organic pores is known to be affected by fluid transport mechanisms and properties within confined pore space. The flow of gas and water shows notably different characteristics compared with conventional continuum modeling approach. A pore network flow model is developed and implemented in this work. A 3‐D organic pore network model is constructed from 3‐D image that is reconstructed from 2‐D shale SEM image of organic‐rich sample. The 3‐D pore network model is assumed to be gas‐wet and to contain initially gas‐filled pores only, and the flow model is concerned with drainage process. Gas flow considers a full range of gas transport mechanisms, including viscous flow, Knudsen diffusion, surface diffusion, ad/desorption, and gas PVT and viscosity using a modified van der Waals' EoS and a correlation for natural gas, respectively. The influences of slip length, contact angle, and gas adsorption layer on water flow are considered. Surface tension considers the pore size and temperature effects. Invasion percolation is applied to calculate gas‐water relative permeability. The results indicate that the influences of pore pressure and temperature on water phase relative permeabilities are negligible while gas phase relative permeabilities are relatively larger in higher temperatures and lower pore pressures. Gas phase relative permeability increases while water phase relative permeability decreases with the shrinkage of pore size. This can be attributed to the fact that gas adsorption layer decreases the effective flow area of the water phase and surface diffusion capacity for adsorbed gas is enhanced in small pore size.

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Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation

Cited by 140 publications

References 11 publications

Rarefied gas flow in microtubes at different inlet-outlet pressure ratios

Rarefied gas flow in microtubes at different inlet-outlet pressure ratios

Generalizing Murray's law: An optimization principle for fluidic networks of arbitrary shape and scale

Numerical Simulation of Multiphase Flow in Nanoporous Organic Matter With Application to Coal and Gas Shale Systems

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