Diffusion in pore networks: Effective medium theory and smooth field approximation

Burganos, Vasilis N.; Sotirchos, Stratis V.

doi:10.1002/aic.690331011

Cited by 143 publications

(98 citation statements)

References 22 publications

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“…It relates the pore structure (pore-size distribution, connectivity and porosity) to its transporting capacity, which is typically expressed in terms of effective diffusion coefficients (Burganos and Sotirchos, 1987;Sahimi, 1992;Hollewand, 1992;Sahimi, 1995). The basic setup is the same as for the bond-percolation model described above, with open or closed bonds connecting neighbouring sites in a lattice.…”

Section: Pore-network Modellingmentioning

confidence: 99%

“…The meso to macro transition is more challenging, however, pore-network modelling can accurately predict effective properties based on the pore structure (pore size distribution, connectivity and porosity) (Burganos and Sotirchos, 1987;Sahimi, 1992;Hollewand, 1992;Sahimi, 1995). The outcome of such an analysis typically is an effective diffusion coefficient D eff (or D ′ , see Sec.…”

Section: Drug Release As a Multiscale Processmentioning

confidence: 99%

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Modelling drug release from inert matrix systems: From moving-boundary to continuous-field descriptions

Frenning

2011

International Journal of Pharmaceutics

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The purpose of this review is to provide a comprehensive overview of mathematical procedures that can be used to describe the release of drugs from inert matrix systems. The review focuses on general principles rather than particular applications. The inherent multiscale nature of the drug-release process is pointed out and multiscale modelling is exemplified for inert porous matrices. Although effects of stagnant layers and finite volumes of release media are briefly discussed, the systematic analysis is restricted to systems under sink conditions. When the initial drug loading exceeds the drug solubility in the matrix, Higuchi-type moving-boundary descriptions continue to be highly valuable for obtaining approximate analytical solutions, especially when coupled with integralbalance methods. Continuous-field descriptions have decisive advantages when numerical solutions are sought. This is because the mathematical formulation reduces to a diffusion equation with a nonlinear source term, valid over the entire matrix domain. Solutions can thus be effortlessly determined for arbitrary geometries by using standard numerical packages.

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Section: Pore-network Modellingmentioning

confidence: 99%

Section: Drug Release As a Multiscale Processmentioning

confidence: 99%

Modelling drug release from inert matrix systems: From moving-boundary to continuous-field descriptions

Frenning

2011

International Journal of Pharmaceutics

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“…These correspond to a cathode microstructure of LSM and YSZ powders [43] and an anode microstructure of Ni and YSZ powders [59]. Earlier work [43,59] was confined to quantification of the geometric properties of the electrodes. The present study extends previous work in terms of obtaining results for the effective transport properties of the cathode and anode reconstructions.…”

Section: Sofc Electrodes Applicationsmentioning

confidence: 99%

Effective transport properties of the porous electrodes in solid oxide fuel cells

Choi

Berson

Pharoah

et al. 2011

Proceedings of the Institution of Mechanical Engineers, Part A:

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This article presents a numerical framework for the computation of the effective transport properties of solid oxide fuel cells (SOFCs) porous electrodes from three-dimensional (3D) constructions of the microstructure. Realistic models of the 3D microstructure of porous electrodes are first constructed from measured parameters such as porosity and particle size distribution. Then each phase in the model geometries is tessellated with a computational grid. Three different types of grids are considered: Cartesian, octree, and body-fitted/cut-cell with successive levels of surface refinement. Finally, a finite volume method is used to compute the effective transport properties in the three phases (pore, electron, and ion) of the electrode. To validate the numerical approach, results obtained with the finite volume method are compared to those calculated with a random walk simulation for the case of a body-centred cubic lattice of spheres. Then, the influence of the sample size is investigated for random geometries with monosized particle distributions. Finally, effective transport properties are calculated for model geometries with polydisperse particle size distributions similar to those observed in actual SOFC electrodes.

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“…The latter go back to the seminal work of Maxwell Garnett (Garnett 1904) and have been adapted to diffusivity upscaling by Burganos and Sotirchos (1987). However, quoting from (Levy and Stroud 1997), effective medium approaches are "useful when one of the components can be considered as a host in which inclusions of the other components are embedded."…”

Section: Discussionmentioning

confidence: 99%

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

et al. 2017

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Chloride ingress into concrete is a major cause for material degradation, such as cracking due to corrosion-induced steel reinforcement expansion. Corresponding transport processes encompass diffusion, convection, and migration, and their mathematical quantification as a function of the concrete composition remains an unrevealed enigma. Approaching the problem step by step, we here concentrate on the diffusivity of cement paste, and how it follows from the microstructural features of the material and from the chloride diffusivity in the capillary pore spaces. For this purpose, we employ advanced self-consistent homogenization theory as recently used for permeability upscaling, based on the resolution of the pore space as pore channels being oriented in all space directions, resulting in a quite compact analytical relation between porosity, pore diffusivity, and the overall diffusivity of the cement paste. This relation is supported by experiments and reconfirms the pivotal role that layered water most probably plays for the reduction of the pore diffusivity, with respect to the diffusivity found under the chemical condition of a bulk solution.Keywords Diffusion · Homogenization · Chlorides · Multiscale modeling · Layered water List of Symbols Mathematical operators divDivergence operator, applied to a vector field div Divergence operator, applied to a second-order tensor field grad Gradient operator on the microscopic observation scale of pore space

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Diffusion in pore networks: Effective medium theory and smooth field approximation

Cited by 143 publications

References 22 publications

Modelling drug release from inert matrix systems: From moving-boundary to continuous-field descriptions

Modelling drug release from inert matrix systems: From moving-boundary to continuous-field descriptions

Effective transport properties of the porous electrodes in solid oxide fuel cells

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

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