On the permeability of fractal tube bundles

The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability-porosity relationships represented by the Kozeny-Carman equations and Archie's law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The goal of this paper is an evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability-porosity relationships are derived analytically. Several examples of the tube bundles are constructed and relevance of the derived permeability-porosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literature.Comment: Short version of manuscript accepted for publication in Transport in Porous Medi

On the Permeability of Fractal Tube Bundles

The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions, and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability-porosity relationships represented by the Kozeny-Carman equations and Archie's law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The aim of this article is the evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability-porosity relationships are derived analytically. Several examples of the tube bundles are constructed, and the relevance of the derived permeability-porosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literatur

Quantitative Analysis of Evolved Gas in the Thermal Decomposition of a Tobacco Substrate

Thermogravimetry coupled to FTIR analysis of evolved gas was applied to the quantitative determination of key-components formed in the slow pyrolysis and thermal decomposition of tobacco samples. Eight keycomponents were selected for the study: carbon dioxide, carbon monoxide, water, acetaldehyde, glycerol, isoprene, nicotine, and phenol. Specific calibration techniques developed for FTIR evolved gas analysis were applied to carry out the quantitative analysis of evolved gases. Deconvolution techniques were applied to identify the contributions of the key-components of interest to the overall FTIR spectra. The results obtained allowed the characterization of evolution profiles of most of the key components of interest. Phenol and isoprene results were below the detection limits of the technique, while the calibration technique was not suitable for glycerol characterization due to condensation and decomposition phenomena during calibration runs. Quantitative data were obtained for carbon dioxide, carbon monoxide, water, acetaldehyde and nicotine evolution in pure nitrogen and dry air

Tomographic immersed boundary method for permeability prediction of realistic porous media: Simulation and experimental validation

In this paper we demonstrate the ability of a volume-penalizing immersed boundary method to predict pore-scale fluid transport in realistic porous media. A numerical experiment is designed that recreates the exact conditions of a real flow experiment through a fibrous porous medium. Under a constant volumetric flow rate air is forced through the porous sample and the pressure drop across its length is accurately measured. The exact pore geometry is obtained using highresolution micro-computed tomography, and the data is, after processing, directly inserted into the flow solver. Simulations are performed on a uniform Cartesian grid, spanning the entire physical domain (i.e., including both fluid and solid regions)— a feature which represents one of the major benefits of volume penalization. We demonstrate that the numerical results agree well with the experiment and that an error of approximately < 10% is attainable on a grid of 512×256×256 cells

Finding Lean Induced Cycles in Binary Hypercubes

Induced (chord-free) cycles in binary hypercubes have many applications in computer science. The state of the art for computing such cycles relies on genetic algorithms, which are, however, unable to per-form a complete search. In this paper, we propose an approach to find-ing a special class of induced cycles we call lean, based on an efficient propositional SAT encoding. Lean induced cycles dominate a minimum number of hypercube nodes. Such cycles have been identified in Systems Biology as candidates for stable trajectories of gene regulatory networks. The encoding enabled us to compute lean induced cycles for hypercubes up to dimension 7. We also classify the induced cycles by the num-ber of nodes they fail to dominate, using a custom-built All-SAT solver. We demonstrate how clause filtering can reduce the number of blocking clauses by two orders of magnitude

Finding Lean Induced Cycles in Binary Hypercubes

Induced (chord-free) cycles in binary hypercubes have many applications in computer science. The state of the art for computing such cycles relies on genetic algorithms, which are, however, unable to per-form a complete search. In this paper, we propose an approach to find-ing a special class of induced cycles we call lean, based on an efficient propositional SAT encoding. Lean induced cycles dominate a minimum number of hypercube nodes. Such cycles have been identified in Systems Biology as candidates for stable trajectories of gene regulatory networks. The encoding enabled us to compute lean induced cycles for hypercubes up to dimension 7. We also classify the induced cycles by the num-ber of nodes they fail to dominate, using a custom-built All-SAT solver. We demonstrate how clause filtering can reduce the number of blocking clauses by two orders of magnitude