A study on pressure-driven gas transport in porous media: from nanoscale to microscale

Microfluidics and Nanofluidics, Nov 2016

Gas flow in porous media can be seen in various engineering devices such as catalytic converters and fuel cells. It is important to understand transport phenomena in porous media for improvement of the performance of such devices. Porous media with pores as small as the mean free path of gas molecules are used in such devices as proton exchange membrane fuel cells. It is difficult to measure molecular transport through such small pores in the experimental approach. In addition, even when using theoretical or numerical approaches, gas flow through nanoscale pores must be treated by the Boltzmann equation rather than the Navier–Stokes equations because it cannot be considered as a continuum. Thus, conventional analyses based on the continuum hypothesis are inadequate and the transport phenomena in porous media with nanoscale pores are not yet clearly understood. In this study, we represented porous media by randomly arranged solid spherical particles and simulated pressure-driven gas flow through the porous media by using the direct simulation Monte Carlo (DSMC) method based on the Boltzmann equation. DSMC simulations were performed for different porosities and different sizes of solid particles of porous media. It was confirmed that Darcy’s law holds even in the case of porous media with micro-/nanoscale pores. Using the obtained results, we constructed expressions to estimate the pressure-driven gas transport in porous media with micro-/nanoscale pores and porosity ranging from 0.3 to 0.5. The flow velocities estimated by using the constructed expressions agreed well with those obtained in the DSMC simulations.

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A study on pressure-driven gas transport in porous media: from nanoscale to microscale

Microfluid Nanofluid A study on pressure‑driven gas transport in porous media: from nanoscale to microscale Yoshiaki Kawagoe Tomoya Oshima Ko Tomarikawa Takashi Tokumasu Tetsuya Koido Shigeru Yonemura Gas flow in porous media can be seen in various engineering devices such as catalytic converters and fuel cells. It is important to understand transport phenomena in porous media for improvement of the performance of such devices. Porous media with pores as small as the mean free path of gas molecules are used in such devices as proton exchange membrane fuel cells. It is difficult to measure molecular transport through such small pores in the experimental approach. In addition, even when using theoretical or numerical approaches, gas flow through nanoscale pores must be treated by the Boltzmann equation rather than the Navier-Stokes equations because it cannot be considered as a continuum. Thus, conventional analyses based on the continuum hypothesis are inadequate and the transport phenomena in porous media with nanoscale pores are not yet clearly understood. In this study, we represented porous media by randomly arranged solid spherical particles and simulated pressure-driven gas flow through the porous media by using the direct simulation Monte Carlo (DSMC) method based on the Boltzmann equation. DSMC simulations were performed for different porosities and different sizes of solid particles of porous media. It was confirmed that Darcy's law holds even in the case of porous media with micro-/nanoscale pores. Using the obtained results, we constructed expressions to estimate the pressure-driven gas transport in porous media with micro-/nanoscale pores and porosity ranging from 0.3 to 0.5. The flow velocities estimated by using the constructed expressions agreed well with those obtained in the DSMC simulations. Porous media; Pressure-driven gas transport; Direct simulation Monte Carlo method; High Knudsen number flow; Rarefied gas dynamics 1 Introduction Gas flow in porous media can be observed in various engineering devices such as catalytic converters and fuel cells. Because of their large effective surface area, porous media are used to facilitate surface reactions such as dissociation of H2 in electrodes of proton exchange membrane fuel cells (PEMFCs). In order to improve the performance of such devices, it is important to understand transport phenomena in porous media. Gas flow through a porous medium is usually analyzed by using Darcy’s law (1856), which states that the discharge rate through a porous medium is proportional to the pressure gradient ∇p and the permeability K and is inversely proportional to the coefficient of viscosity μ of gas. Darcy’s law can be written as where p is the gas pressure and Us is the superficial velocity, which is defined as the volume flow rate through a unit cross-sectional area of the solid plus fluid of a porous medium (Bird et al. 2007). The superficial velocity Us is not the velocity of the gas traveling through the pores. The average velocity U of the gas traveling through the pores has the following relation with the superficial velocity Us: where ε is the porosity of the porous medium. In order to estimate gas flow rate through a porous medium, evaluating its permeability correctly is important. In previous studies, the following empirical models for permeability have been proposed: where dp is the effective average diameter of packed particles of the porous medium, KB−K, KC−K, and KR−G are the Blake–Kozeny model (Blake 1922; Kozeny 1927), the Carman–Kozeny model (Carman 1937, 1938, 1956; Kozeny 1927), and the Rumpf–Gupte model (Rumpf and Gupte 1971), respectively. The Blake–Kozeny and the Carman–Kozeny models were derived by regarding a porous medium as a bundle of capillary tubes and by considering laminar flow in tubes (Dullien 1979; Bird et al. 2007). The Rumpf–Gupte model was derived by finding the relationship between the friction factor of the porous medium and the porosity by dimensional analysis (Dullien 1979). The constants in these models were determined to fit experimental data on packed beds. In the derivation of these models, the effect of the mean free path of molecules in gaseous flow was neglected. The pores of porous media used in the above-mentioned devices may be in the micro-/ nanoscale range, e.g., those of porous media used for electrodes of PEMFCs may be as small as the mean free path of gas molecules. The Knudsen number of gas flow in such porous media is on the order of unity, and hence, the gas is in nonequilibrium because of a lack of intermolecular collisions. Such kind of gas flow is called “high Knudsen number flow” and cannot be treated as a continuum. Since the effect of the mean free path was neglected in the derivation of the above-mentioned permeability models, these models are not applicable to gas flow in such porous media with micro-/nanoscale pores. In the case where the pore size of porous media is much smaller than (...truncated)


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Yoshiaki Kawagoe, Tomoya Oshima, Ko Tomarikawa, Takashi Tokumasu, Tetsuya Koido, Shigeru Yonemura. A study on pressure-driven gas transport in porous media: from nanoscale to microscale, Microfluidics and Nanofluidics, 2016, pp. 162, Volume 20, Issue 12, DOI: 10.1007/s10404-016-1829-8