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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)