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The contribution presents a modified method of stochastic reconstruction of two porous stainless-steel filters. The description of their microstructures was based on a combination of the two-point probability function for the void phase and the lineal-path functions for the void and solid phases. The method of stochastic reconstruction based on simulated annealing was capable of reproducing good connectivity of both phases, which was confirmed by calculating descriptors of the local porosity theory. Theoretical values of permeability were compared with their experimental counterparts measured by means of quasi-stationary permeation of four inert gases.

Porous metal filters are fabricated by sintering of compacted metal powder particles. Their primary applications are as permeable barriers in purifiers, heat exchangers, catalyst reactors or oil burners. To optimize processes taking place in these devices, knowledge of transport and mechanical properties of the filters is necessary. A quantitative description of their microstructure, particularly geometry and topology of pore space, is required for reliable prediction of fluid transport in pore space. There are well-established ways to reproduce 3D microstructures of macroporous media such as serial tomography [

Another way to do this involves 3D stochastic reconstruction [

This contribution presents an application of stochastic reconstruction of stainless-steel filter microstructures. Two samples were reconstructed and their percolation properties were analyzed. Theoretical values of permeability of both porous replicas were compared with their experimental counterparts measured by means of quasi-steady state permeation of four inert gases.

The replicas of porous metal filters were obtained by means of stochastic reconstruction based on simulated annealing method. Three reference microstructural descriptors used in the objective function

3D reconstructed microstructure (replica) of filter F1 as a subregion of 200 × 200 × 200 voxels (0.5 micron/voxel). Pore orifices are yellow, pore-metal interface is blue, and metal phase is transparent.

Here, the presented method delivered the replicas almost free of isolated clusters. Isolated porosity only formed a small fraction of total porosity, indicating good percolation properties. The quantitative analysis using the local porosity theory [

Permeability in the Knudsen region expressed as the effective pore size, κ_{cal}, was determined using random-walk simulation whilst permeation in the region of continuum, β_{cal}, was deduced from solutions of the Stokes equations in the reconstructed pore space [_{cal }and β_{cal} were estimated from first principles.

Experimental and calculated effective transport properties of porous metal filters.

Sample | κ_{exp} (nm) |
β_{exp} (µm^{2}) |
_{cal} (nm) |
_{cal} (µm^{2}) |
---|---|---|---|---|

F1 media grade 0.5 | 67 ± 8 | 0.0527 ± 0.0008 | 67.1 | 0.0533 |

F2 media grade 0.2 | 51 ± 2 | 0.0241 ± 0.0004 | 55.1 | 0.0324 |

Porous metal filters were purchased from Mott Corporation (Farmington, CT, USA). The flat thin discs had diameter of 19 mm and thickness of 1.5 mm. They were made of stainless-steel 316L SS by process of axial compaction and sintering. Two samples of porous metal filter, differing in porosity and specific surface area, were studied. Their basic properties were obtained using standard methods—helium pycnometry (AccuPyc1330), mercury porosimetry (AutoPore III), and physical adsorption of krypton (ASAP 2010M), all instruments from Micromeritics (Norcross, GA, USA), (see

Physical properties of porous metal filters.

Sample | Porosity | Bulk density (g·mL^{−1}) |
Specific surface area (μm^{−1}) |
Median pore diameter (μm) |
---|---|---|---|---|

F1 media grade 0.5 | 0.178 | 6.377 | 0.089 | 3.55 |

F2 media grade 0.2 | 0.201 | 6.255 | 0.110 | 2.70 |

SEM image of porous metal filter.

For preparation of cross-sections of porous metal filters, the samples were impregnated with epoxy resin under low pressure. Epoxy resin (Araldite, Struers, GmbH, Germany) was found to be suitable for filling of pores because of its low viscosity, good adhesion to the material, and little shrinking after hardening. The impregnated porous samples (casts) were exposed to the pressurized nitrogen (~10 MPa, laboratory temperature) in an autoclave, to fill all pores perfectly before hardening. Then, the casts were treated at mild temperature (~40 °C) five hours. The hardened blocks were cut using a diamond saw in arbitrary direction, lapped, and polished. The procedure of cutting, lapping and polishing was repeated several times to collect images from different polished sections.

The polished sections were observed in a scanning electron microscope (SEM JSM−5500LV, JEOL, Tokyo, Japan). The polished cross-sections were sputtered with a slight layer of platinum, to take away the electrical charge from their surface. The spatial resolution enhancement and microscope response were also maximized. Series of back-scatter electron (BSE) images of uniform size of 1280 × 960 pixels were obtained from statistically representative parts of the porous media. The raw intensity images (256 grey levels) revealed the excellent contrast and resolution (

The selected microstructural descriptors, particularly total porosity, ϕ, two-point probability function, _{2}(^{p}^{m}^{p}^{m}_{2}(^{p}^{m}_{2}(_{2}(^{p}^{m}

Part of back-scatter electron (BSE) image of the porous filter F1 (magnification 200×, cut size 480 × 480 pixel, 0.5 micron/pixel). (

(

Stochastic reconstruction of porous metal filters was carried out by means simulated annealing method [_{2}(^{p}^{m}^{p}

Permeability of porous metal filter was simulated in the Knudsen region, in which the frequency of gas molecule-pore walls collisions is much higher then number of intermolecular collisions. In the calculations, random walk of gas molecules in the 3D reconstructed microstructure using Monte Carlo algorithm was applied. The relationship between the mean squared displacement,

where _{cal}, represents the permeability of the porous metal filter.

The effective gas permeability β_{cal}, when intermolecular collisions prevail over molecule-pore walls collisions (viscous flow regime), was derived by solving of the Stokes equation and equation of continuity under boundary conditions and the prescribed pressure difference across the opposite walls of reconstructed microstructure. The public domain “permsolver” from [_{cal}.

Effective permeability of both metal filters was measured in quasi-stationary permeation cell within the total pressure range from 1 to 25 kPa [

Macroscopically one-dimensional transport of a pure inert gas (hydrogen, nitrogen, helium, and argon) through the filters under laboratory conditions was considered. The transport parameters, κ_{exp} and β_{exp}, were evaluated from repeated pressure responses using the constitutive equation:

where ^{0.5} denotes the mean arithmetic velocity of a gas, _{exp}) and viscous flow (β_{exp}).

Quasi-stationary permeation cell. (

This contribution presents a specific method developed for the reconstruction of a microstructure, based on the limited statistical information from 2D BSE images, of two real porous metal samples. The 3D reconstruction of porous materials was provided by applying a simulated annealing technique, utilizing low-order pore-space information (microstructural descriptors): total porosity, two-point probability function, lineal path functions for porous and metal phases derived from processed image sets.

The porous and metal phases formed large clusters in the 3D reconstructed porous metal replicas, whereas non-percolating clusters took only negligible fractions of both phases. The method used in this study was capable of reproducing good connectivity of both phases. The microstructure of replicas here described was characterized by using 3D microstructural descriptors capturing long-range pore connectivity, particularly total fraction of percolating cells. Theoretical values of permeability of both porous replicas were compared with their experimental counterparts measured by means of quasi-steady state permeation of four inert gases through the real filters. A good correspondence between both values was found.

The reconstruction method proposed in [

The authors are greatly appreciated for financial support from the Czech Science Foundation, grant projects No. 203/09/1353, and P204/11/1206. We also thank L. Brabec for imaging the polished sections.

The authors declare no conflict of interest.