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Salvatore Torquato - One of the best experts on this subject based on the ideXlab platform.
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Predicting transport characteristics of hyperuniform porous media via rigorous microstructure-property relations
Advances in Water Resources, 2020Co-Authors: Salvatore TorquatoAbstract:Abstract This paper is concerned with the estimation of the effective transport characteristics of Fluid-saturated porous media via rigorous microstructure-property relations. We are particularly interested in predicting the formation factor F , mean survival time τ, principal NMR (diffusion) relaxation time T1, principal viscous relaxation time Θ1, and Fluid Permeability k. To do so, we employ rigorous methods to estimate the Fluid Permeability and these other transport properties of “hyperuniform” and nonhyperuniform models of porous media from microstructural information. Disordered hyperuniform materials are exotic amorphous states of matter that have attracted great attention in the physical, mathematical and biological science but little is known about their Fluid transport characteristics. In carrying out this investigation, we not only draw from ideas and results of the emerging field of hyperuniformity, but from homogenization theory, statistical geometry, differential equations (spectrum of Laplace and Stokes operators), and the covering and quantizer problems of discrete geometry. Among other results, we derive a Fourier representation of a classic rigorous upper bound on the Fluid Permeability that depends on the spectral density to infer how the permeabilities of hyperuniform porous media perform relative to those of nonhyperuniform ones. We find that the velocity fields in nonhyperuniform porous media are generally much more localized over the pore space compared to those in their hyperuniform counterparts, which has implications for their permeabilities. Rigorous bounds on transport properties suggest a new approximate formula for the Fluid Permeability that provides reasonably accurate Permeability predictions of a certain class of hyperuniform and nonhyperuniform porous media. These comparative studies shed new light on the microstructural characteristics that determine the transport properties of general porous media. Our findings also have implications for the design of porous materials with desirable transport properties.
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Fluid Permeabilities of Triply Periodic Minimal Surfaces
arXiv: Soft Condensed Matter, 2006Co-Authors: Y. Jung, Salvatore TorquatoAbstract:It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. The multifunctionality of such two-phase systems has been further established by demonstrating that they are also extremal when a competition is set up between the effective bulk modulus and electrical (or thermal) conductivity of the bicontinuous composite. Here we compute the Fluid permeabilities of these and other triply periodic bicontinuous structures at a porosity $\phi=1/2$ using the immersed boundary finite volume method. The other triply periodic porous media that we study include the Schoen gyroid (G) minimal surface, two different pore-channel models, and an array of spherical obstacles arranged on the sites of a simple cubic lattice. We find that the Schwartz P porous medium has the largest Fluid Permeability among all of the six triply periodic porous media considered in this paper. The Fluid permeabilities are shown to be inversely proportional to the corresponding specific surfaces for these structures. This leads to the conjecture that the maximal Fluid Permeability for a triply periodic porous medium with a simply connected pore space at a porosity $\phi=1/2$ is achieved by the structure that globally minimizes the specific surface.
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Fluid permeabilities of triply periodic minimal surfaces.
Physical Review E, 2005Co-Authors: Y. Jung, Salvatore TorquatoAbstract:It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. The multifunctionality of such two-phase systems has been further established by demonstrating that they are also extremal when a competition is set up between the effective bulk modulus and electrical (or thermal) conductivity of the bicontinuous composite. Here we compute the Fluid permeabilities of these and other triply periodic bicontinuous structures at a porosity $\ensuremath{\phi}=1∕2$ using the immersed-boundary finite-volume method. The other triply periodic porous media that we study include the Schoen gyroid (G) minimal surface, two different pore-channel models, and an array of spherical obstacles arranged on the sites of a simple cubic lattice. We find that the Schwartz P porous medium has the largest Fluid Permeability among all of the six triply periodic porous media considered in this paper. The Fluid permeabilities are shown to be inversely proportional to the corresponding specific surfaces for these structures. This leads to the conjecture that the maximal Fluid Permeability for a triply periodic porous medium with a simply connected pore space at a porosity $\ensuremath{\phi}=1∕2$ is achieved by the structure that globally minimizes the specific surface.
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Optimal Bounds on the Trapping Constant and Permeability of Porous Media
Physical Review Letters, 2004Co-Authors: Salvatore Torquato, D. C. PhamAbstract:We derive exact expressions for so-called "void" bounds on the trapping constant gamma and Fluid Permeability k for coated-sphere and coated-cylinder models of porous media. We find that in some cases the bounds are optimal. In these instances, exact expressions are obtained for the relevant length scale that arises in the void bounds, which depends on a two-point correlation function that characterizes the porous medium. This is the first time that model microstructures have been found that exactly realize bounds on either the trapping constant or Fluid Permeability.
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Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis
Journal of Geophysical Research: Solid Earth, 1996Co-Authors: David A. Coker, Salvatore Torquato, John H. DunsmuirAbstract:We present a study of the morphology and bulk physical properties of a Fontainebleau sandstone via an X ray tomographic analysis. Synchrotron-based X ray tomographic techniques provide us with a high-resolution (7.5 μm), three-dimensional digitized representation of the sandstone that leaves the sample intact and unaltered. To estimate a wide spectrum of bulk properties of the Fontainebleau sandstone specimen, we extract from this image a number of different correlation functions that statistically characterize the pore-space morphology and relevant pore-space length and time scales. These statistical measures are obtainable from lineal, plane, and/or volume measurements and include the porosity, specific surface, two-point and three-point probability functions, lineal-path function, chord-length distribution function, pore-size distribution function, and coarseness. The pore-size distribution function, in particular, contains a certain level of connectedness information and accordingly can only be obtained from a three-dimensional representation of the sample. Many bulk properties of the sandstone, such as the mean survival time τ (obtainable from Nuclear Magnetic Resonance relaxation studies), Fluid Permeability k, effective electrical and thermal conductivities, and effective elastic moduli, can be estimated using the aforementioned statistical correlation functions. Specifically, the electrical conductivity (or, equivalently, the formation factor F), mean survival time, and Fluid Permeability are determined using rigorous bounds. The mean survival time and Fluid Permeability are also found using direct simulation techniques and cross-property relations, respectively. One such cross-property relation for k depending on τ and F gives a Permeability estimate that is within a factor of 2 of the experimental result.
Frédéric Skoczylas - One of the best experts on this subject based on the ideXlab platform.
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Corrigendum to “Unified determination of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials” [Cem. Concr. Res. 67 (2015) 300–309]
Cement and Concrete Research, 2016Co-Authors: Chunsheng Zhou, Chen Wei, Wei Wang, Frédéric SkoczylasAbstract:In the published paper [1], an error has been made in the formulation of the capacity function C (Sw). In Equation (21) of that paper, the capacity function C (Sw) should be given as, C(SW)=θdSWdϕc(SW) in which θ denotes the capillary porosity for cement-based material. In accordance, after adopting the Zhou model Equation (24) to quantify the water retention characteristics, the capacity function C (Sw) in Equation (25) should be formulated as, C(SW)=βθSW[1+(α−1)SW],C(SW=1)=αβθ These above modifications have no further implications for the remaining part of the published paper [1]. The authors apologize for the naive errors they have made. Reference [1] C. Zhou, W. Chen, W. Wang, F. Skoczylas, Unified determina tion of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials, Cem. Concr. Res., 67 (2015), pp. 300–309
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Corrigendum to “Unified determination of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials” [Cem. Concr. Res. 67 (2015) 300–309]
Cement and Concrete Research, 2016Co-Authors: Chunsheng Zhou, Wei Chen, Wei Wang, Frédéric SkoczylasAbstract:International audienceIn the published paper [1], an error has been made in the formulation of the capacity function C (Sw). In Equation (21) of that paper, the capacity function C (Sw) should be given as,C(SW)=θdSWdϕc(SW)in which θ denotes the capillary porosity for cement-based material. In accordance, after adopting the Zhou model Equation (24) to quantify the water retention characteristics, the capacity function C (Sw) in Equation (25) should be formulated as,C(SW)=βθSW[1+(α−1)SW],C(SW=1)=αβθThese above modifications have no further implications for the remaining part of the published paper [1]. The authors apologize for the naive errors they have made.Reference [1] C. Zhou, W. Chen, W. Wang, F. Skoczylas, Unified determina tion of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials, Cem. Concr. Res., 67 (2015), pp. 300–30
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Unified determination of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials
Cement and Concrete Research, 2015Co-Authors: Chunsheng Zhou, Wei Chen, Wei Wang, Frédéric SkoczylasAbstract:From conductivity theory, general models for relative molecular diffusivity and Fluid Permeability are first derived with unknown tortuosity function and modification coefficient, which can be respectively deduced from hydraulic diffusivity and water retention curve (WRC). Based on empirical laws for hydraulic diffusivity and WRC of cement-based material, unified models for relative molecular diffusivity and Fluid Permeability are further formulated with only two measurable parameters. Because of practical difficulty for measuring water Permeability and pure gaseous molecular diffusivity, only relative gas Permeability and relative chloride diffusivity models are verified by the reported data. It is found that the predicted relative gas Permeability agrees with measured values and exponential law is a little more preferable than power law for quantifying hydraulic diffusivity. Moreover, relative chloride diffusivity from the unified model also agrees well with experimental data derived via Nernst–Einstein Equation. However, the unified model doesn't capture the possibly overestimated relative chloride diffusivity from Fick's law.
H Montazerian - One of the best experts on this subject based on the ideXlab platform.
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Permeability and mechanical properties of gradient porous PDMS scaffolds fabricated by 3D-printed sacrificial templates designed with minimal surfaces.
Acta Biomaterialia, 2019Co-Authors: H Montazerian, Mohamed G. A. Mohamed, M. Mohaghegh Montazeri, Sina Kheiri, Abbas S Milani, Mina HoorfarAbstract:Abstract In the present study, polydimethylsiloxane (PDMS) porous scaffolds are designed based on minimal surface architectures and fabricated through a low-cost and accessible sacrificial mold printing approach using a fused deposition modeling (FDM) 3D printer. The effects of pore characteristics on compressive properties and Fluid Permeability are studied. The results suggest that radially gradient pore distribution (as a potential way to enhance mechanically-efficient scaffolds with enhanced cell/scaffold integration) has higher elastic modulus and Fluid Permeability compared to their uniform porosity counterparts. Also, the scaffolds are fairly strain-reversible under repeated loading of up to 40% strain. Among different triply periodic minimal surface pore architectures, P-surface was observed to be stiffer, less permeable and have lower densification strain compared to the D-surface and G-surface-based pore shapes. The biocompatibility of the created scaffolds is assessed by filling the PDMS scaffolds using mouse embryonic fibroblasts with cell-laden gelatin methacryloyl which was cross-linked in situ by UV light. Cell viability is found to be over 90% after 4 days in 3D culture. This method allows for effectively fabricating biocompatible porous organ-shaped scaffolds with detailed pore features which can potentially tailor tissue regenerative applications. Statement of Significance Printing polymers with chemical curing mechanism required for materials such as PDMS is challenging and impossible to create high-resolution uniformly cured structures due to hard control on the base polymer and curing process. An interconnected porous mold with ordered internal architecture with complex geometries were 3D printed using low-cost and accessible FDM technology. The mold acted as a 3D sacrificial material to form internally architected flexible PDMS scaffolds for tissue engineering applications. The scaffolds are mechanically stable under high strain cyclic loads and provide enough pore and space for viably integrating cells within the gradient architecture in a controllable manner.
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Fluid Permeability of Graded Porosity Scaffolds Architectured with Minimal Surfaces
ACS Biomaterials Science & Engineering, 2019Co-Authors: Masoud Zhianmanesh, Mostafa Varmazyar, H MontazerianAbstract:The natural local porosity variation in the native tissue can be replicated by graded porosity scaffolds. Scaffolds with radial porosity distribution can be a solution to improve both mechanical and biological functions of the biomimetic scaffolds. In the present study, Fluid Permeability as a quantitative indicator of biological performance is studied numerically and experimentally for different pore shapes and porosity distribution patterns in the scaffolds designed on the basis of triply periodic minimal surfaces (TPMSs). Among the uniform porosity scaffolds, those designed on the basis of P* (P surface) and Y** (G surface) showed the highest Permeability. In the radially graded porosity scaffolds with linear porosity distribution, Permeability was found to be about twice more sensitive to the peripheral porosity than the porosity at the center. The results suggest that the Permeability-gradient parameter relationships can follow different trends depending on the pore shape as opposed to the convention...
I Song - One of the best experts on this subject based on the ideXlab platform.
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One‐dimensional Fluid diffusion induced by constant‐rate flow injection: Theoretical analysis and application to the determination of Fluid Permeability and specific storage of a cored rock sample
Journal of Geophysical Research: Solid Earth, 2004Co-Authors: I Song, S C Elphick, Ian Main, Bryne T Ngwenya, Nicholas Odling, Noel F SmythAbstract:[1] We describe the conceptual design and first application of a new method for simultaneously measuring the Fluid Permeability and specific storage of a rock sample. In our laboratory tests, a constant flow rate single-stroke piston pump injects Fluid into a cored rock specimen placed between two reservoirs in which Fluid pressure is recorded. For this geometry we have derived a new analytic solution of the governing diffusion equation describing the one-dimensional Fluid flow. This new analytic solution in the time domain consists of two parts: an asymptotic linear function of time, and a transient part which decays to zero as time increases. The model predicts that the Fluid pressures of the upstream and downstream reservoirs both increase linearly with time after the initial transient vanishes. The slope of the linear pressure variation depends on the specific storage of the rock sample for a given test condition, and the differential pressure between the two reservoirs is related to the Permeability. If the downstream pressure is not recorded, the Permeability can be calculated from the zero intercept of the linear upstream Fluid pressure variation. This calculation is quite straightforward and no tedious history curve matching is required. We applied our new method to measure Fluid Permeability and specific storage of Westerly granite. The measured values of the Permeability are consistent with those published in the literature. The main advantages of our method are the reliability of the testing method, its economy of time, and the flexibility in adapting the system parameters to tests at different conditions.
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one dimensional Fluid diffusion induced by constant rate flow injection theoretical analysis and application to the determination of Fluid Permeability and specific storage of a cored rock sample
Journal of Geophysical Research, 2004Co-Authors: I Song, S C Elphick, Ian Main, Bryne T Ngwenya, Nicholas Odling, Noel F SmythAbstract:[1] We describe the conceptual design and first application of a new method for simultaneously measuring the Fluid Permeability and specific storage of a rock sample. In our laboratory tests, a constant flow rate single-stroke piston pump injects Fluid into a cored rock specimen placed between two reservoirs in which Fluid pressure is recorded. For this geometry we have derived a new analytic solution of the governing diffusion equation describing the one-dimensional Fluid flow. This new analytic solution in the time domain consists of two parts: an asymptotic linear function of time, and a transient part which decays to zero as time increases. The model predicts that the Fluid pressures of the upstream and downstream reservoirs both increase linearly with time after the initial transient vanishes. The slope of the linear pressure variation depends on the specific storage of the rock sample for a given test condition, and the differential pressure between the two reservoirs is related to the Permeability. If the downstream pressure is not recorded, the Permeability can be calculated from the zero intercept of the linear upstream Fluid pressure variation. This calculation is quite straightforward and no tedious history curve matching is required. We applied our new method to measure Fluid Permeability and specific storage of Westerly granite. The measured values of the Permeability are consistent with those published in the literature. The main advantages of our method are the reliability of the testing method, its economy of time, and the flexibility in adapting the system parameters to tests at different conditions.
Chunsheng Zhou - One of the best experts on this subject based on the ideXlab platform.
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Corrigendum to “Unified determination of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials” [Cem. Concr. Res. 67 (2015) 300–309]
Cement and Concrete Research, 2016Co-Authors: Chunsheng Zhou, Chen Wei, Wei Wang, Frédéric SkoczylasAbstract:In the published paper [1], an error has been made in the formulation of the capacity function C (Sw). In Equation (21) of that paper, the capacity function C (Sw) should be given as, C(SW)=θdSWdϕc(SW) in which θ denotes the capillary porosity for cement-based material. In accordance, after adopting the Zhou model Equation (24) to quantify the water retention characteristics, the capacity function C (Sw) in Equation (25) should be formulated as, C(SW)=βθSW[1+(α−1)SW],C(SW=1)=αβθ These above modifications have no further implications for the remaining part of the published paper [1]. The authors apologize for the naive errors they have made. Reference [1] C. Zhou, W. Chen, W. Wang, F. Skoczylas, Unified determina tion of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials, Cem. Concr. Res., 67 (2015), pp. 300–309
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Corrigendum to “Unified determination of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials” [Cem. Concr. Res. 67 (2015) 300–309]
Cement and Concrete Research, 2016Co-Authors: Chunsheng Zhou, Wei Chen, Wei Wang, Frédéric SkoczylasAbstract:International audienceIn the published paper [1], an error has been made in the formulation of the capacity function C (Sw). In Equation (21) of that paper, the capacity function C (Sw) should be given as,C(SW)=θdSWdϕc(SW)in which θ denotes the capillary porosity for cement-based material. In accordance, after adopting the Zhou model Equation (24) to quantify the water retention characteristics, the capacity function C (Sw) in Equation (25) should be formulated as,C(SW)=βθSW[1+(α−1)SW],C(SW=1)=αβθThese above modifications have no further implications for the remaining part of the published paper [1]. The authors apologize for the naive errors they have made.Reference [1] C. Zhou, W. Chen, W. Wang, F. Skoczylas, Unified determina tion of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials, Cem. Concr. Res., 67 (2015), pp. 300–30
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Unified determination of relative molecular diffusivity and Fluid Permeability for partially saturated cement-based materials
Cement and Concrete Research, 2015Co-Authors: Chunsheng Zhou, Wei Chen, Wei Wang, Frédéric SkoczylasAbstract:From conductivity theory, general models for relative molecular diffusivity and Fluid Permeability are first derived with unknown tortuosity function and modification coefficient, which can be respectively deduced from hydraulic diffusivity and water retention curve (WRC). Based on empirical laws for hydraulic diffusivity and WRC of cement-based material, unified models for relative molecular diffusivity and Fluid Permeability are further formulated with only two measurable parameters. Because of practical difficulty for measuring water Permeability and pure gaseous molecular diffusivity, only relative gas Permeability and relative chloride diffusivity models are verified by the reported data. It is found that the predicted relative gas Permeability agrees with measured values and exponential law is a little more preferable than power law for quantifying hydraulic diffusivity. Moreover, relative chloride diffusivity from the unified model also agrees well with experimental data derived via Nernst–Einstein Equation. However, the unified model doesn't capture the possibly overestimated relative chloride diffusivity from Fick's law.