Fractal approach is used to derive a power law relation between effective diffusion coefficient of solute in porous media and the geometry parameter characterizing the media. The results are consistent with the empiri...Fractal approach is used to derive a power law relation between effective diffusion coefficient of solute in porous media and the geometry parameter characterizing the media. The results are consistent with the empirical equations analogous to Archie`s law and are expected to be applied to prediction of effective diffusion coefficient. Key words: diffusion; effective diffusion coefficient; fractal; porous media.展开更多
Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Fick' s diffusion, and its mea...Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Fick' s diffusion, and its mean-squared displacement follows fractal scaling law. The model of particle diffusion in pore fractal by means of the statistics method of stochastic process is structured and some fractal characteristics and non-Markov property are proved.展开更多
The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusio...The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity Φ>0.4, while there is a linear and slow decrease in pressure difference for high porosity.展开更多
A flux equation of diffusion for bi-disperse porous catalyst pellets was proposed by modifying the previously developed model equation over fractal trajectories. The proposed fractal model equation considered the same...A flux equation of diffusion for bi-disperse porous catalyst pellets was proposed by modifying the previously developed model equation over fractal trajectories. The proposed fractal model equation considered the same tortuous degree for both micro-and macro-pores. The experimental data of diffusion over a bi-disperse Ni/gamma-alumina pellet were obtained with a standard Wicke-Kallenbach diffusion cell for both carbon monoxide- ethylene and carbon dioxide-ethylene binary mixtures. The fitting between experimental results and the fractal model equation leads to a fractal dimension of 1.11. The prediction of diffusion flux over the bi-disperse Ni/gamma- alumina pellet by the proposed fractal model equation is much better than the traditional tortuosity-based model equation by comparison with the measured flux through the pellet.展开更多
文摘Fractal approach is used to derive a power law relation between effective diffusion coefficient of solute in porous media and the geometry parameter characterizing the media. The results are consistent with the empirical equations analogous to Archie`s law and are expected to be applied to prediction of effective diffusion coefficient. Key words: diffusion; effective diffusion coefficient; fractal; porous media.
文摘Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Fick' s diffusion, and its mean-squared displacement follows fractal scaling law. The model of particle diffusion in pore fractal by means of the statistics method of stochastic process is structured and some fractal characteristics and non-Markov property are proved.
基金Project(2015CB060200)supported by the National Basic Research Program of ChinaProject supported by the R-D Program of Gangxi Province of ChinaProject(201622ts093)supported by the Fundamental Research Funds for the Central Universities,China
文摘The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity Φ>0.4, while there is a linear and slow decrease in pressure difference for high porosity.
基金Supported by the National Natural Science Foundation of China (No. 50228203 and No. 20476076)
文摘A flux equation of diffusion for bi-disperse porous catalyst pellets was proposed by modifying the previously developed model equation over fractal trajectories. The proposed fractal model equation considered the same tortuous degree for both micro-and macro-pores. The experimental data of diffusion over a bi-disperse Ni/gamma-alumina pellet were obtained with a standard Wicke-Kallenbach diffusion cell for both carbon monoxide- ethylene and carbon dioxide-ethylene binary mixtures. The fitting between experimental results and the fractal model equation leads to a fractal dimension of 1.11. The prediction of diffusion flux over the bi-disperse Ni/gamma- alumina pellet by the proposed fractal model equation is much better than the traditional tortuosity-based model equation by comparison with the measured flux through the pellet.
