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Transport properties of supercritical fluids in mesoporous materials probed by pulsed field gradient NMR
556
Abstracts / Magnetic Resonance Imaging 25 (2007) 544 – 591
Assessment of the porous media structure based on fuzzy distance transform and its map ridge A. Darabi, F. Chandelier, G. Baroud Biomechanics Lab., Mechanical Eng. Dept., Universite´ de Sherbrooke, Quebec, Canada Introduction: Recently, lCT and lMRI images have been widely used to study the structure of porous media. The accuracy of the microstructure assessment of porous media not only depends on lCT and lMRI image resolution but also relates to its parameter computation methods. Although these images are intuitively fuzzy, most of the traditional methods of microstructure assessment of the porous media first convert these images to binary images for subsequent processing. The binary distance transform (DT) is one such computation method which deals with binary images to compute the shortest distance of object pixels/voxels (2D/3D) from non-object pixels. To overcome the limitations of binary-image processing in DT computation, fuzzy logic was introduced as an intelligent and powerful tool to segment and further process gray level images in recent years. Fuzzy image processing can generally result in simple and fast computation methods that are easy to implement in practice. Method: We have developed lately a fuzzy distance transform (FDT) method to compute the distance of object pixels from non-object pixels in the integer space. This method uses an S-shape membership function to fuzzify the input gray level images. Then, the FDT map is computed using fuzzy Min–Max operations as expressed in the following equations: LP ¼
l1 X
maxðlBVF ðpk Þ; lBVF ðpkþ1 ÞÞ þ dðpk ; pkþ1 ÞDf ð pÞ ¼
k¼1
min
Papathsð p;qÞ
LP
where L P is the length of path P, p k is the kth point on path P, and d( p k, p k+1) is the Euclidian distance between points p k and p k+1. There are many paths between an object point p and background point q. The FDT, D f, is defined as the shortest path length for all object points from the background. Results: To assess solid/cavity thickness, the skeleton of the FDT map should be extracted. The skeletonization of the FDT map is done in two steps. In the first step, we extract some of the FDT map ridge points using an adaptive filter based on a second derivative of the map. In the second step, we employ an uphill-climbing algorithm to complete the ridge-based skeleton. If all local maxima and saddle points are found in the first step, then our skeletonization method usually produces connectivity preserved skeleton. The following figures respectively show the bone and cavity thickness distributions for different trabecular bone samples. Conclusion: The first advantage of the assessment of porous media based on FDT and its ridges is the ability to segment images into objects and nonobjects while keeping the inherent properties of the objects within the images. Secondly, the stepwise function allows consequent data processing to be done in the integer number space, thus running the algorithm faster. The third advantage is the robustness of the algorithm regarding image noise and rotation. Finally, FDT ridge skeleton provides representative bone/cavity thicknesses that are close to human perception.
doi:10.1016/j.mri.2007.01.037
Transport properties of supercritical fluids in mesoporous materials probed by pulsed field gradient NMR M. Dvoyashkin a, R. Valiullin a, J. Ka¨rger a, W.-D. Einickeb, R. Gla¨serc a Fakulta¨t fu¨r Physik und Geowissenschaften, Universita¨t Leipzig, D-04103 Leipzig, Germany, bFakulta¨t fu¨r Chemie und Mineralogie, Universita¨t Leipzig, D-04103 Leipzig, Germany, cInstitut fu¨r Technische Chemie, Universita¨t Stuttgart, D-70550 Stuttgart, Germany Supercritical (SC) fluids are of considerable interest because of their unusual properties between those of typical gases and liquids. The possibility to tune these properties with only minor variations in temperature and pressure in the vicinity of the critical point has led to a wide range of SC fluid applications as environmentally benign solvents for separations and chemical conversions. A bulk fluid becomes supercritical at certain values of temperature and pressure, unique for a given substance. The interrelation of bulk fluid properties such as diffusivity, solubility or polarity on pressure and temperature near the critical region continues to be the subject of a large number of theoretical and experimental studies. Qualitatively another situation arises when fluids confined within porous materials are considered. The presence of additional factors, e. g., the liquid-pore wall interaction, may shift the SC conditions and affect the behavior of SC fluids significantly. This shift is reflected, e.g., in an alteration of the trajectory of the liquid–gas coexistence curve in the general phase diagram, and in a shift of the critical point with respect to the bulk fluid [1,2]. To date, the description of the transport properties of SC fluids under confinement in porous solids is rather limited to theoretical predictions and some indirect experimental methods. In this work, we exploit the pulsed field gradient (PFG) NMR method to provide direct information about diffusion processes of fluids in the bulk and within porous materials over a broad range of temperatures, including the SC region. It is found that the transition to the supercritical state is accompanied by a sharp jump in the diffusivities occurring at a certain temperature T CP, although in the subcritical region the diffusivities are well fitted to the Arrhenius equation. Also, the essential difference between the pore (T CP) and the bulk (T CB) critical temperatures has been obtained in good agreement with theoretical predictions. [1] Gelb LD, Gubbins KE, Radhakrishnan R, Sliwinska-Bartkowiak M. Rep Prog Phys 1999;62:1573 – 1659. [2] Thommes M, Ko¨hn R, Fro¨ba M. J Phys Chem B 2000;104: 7932 – 43.
doi:10.1016/j.mri.2007.01.038
Abstracts / Magnetic Resonance Imaging 25 (2007) 544 – 591
Assessment of the porous media structure based on fuzzy distance transform and its map ridge A. Darabi, F. Chandelier, G. Baroud Biomechanics Lab., Mechanical Eng. Dept., Universite´ de Sherbrooke, Quebec, Canada Introduction: Recently, lCT and lMRI images have been widely used to study the structure of porous media. The accuracy of the microstructure assessment of porous media not only depends on lCT and lMRI image resolution but also relates to its parameter computation methods. Although these images are intuitively fuzzy, most of the traditional methods of microstructure assessment of the porous media first convert these images to binary images for subsequent processing. The binary distance transform (DT) is one such computation method which deals with binary images to compute the shortest distance of object pixels/voxels (2D/3D) from non-object pixels. To overcome the limitations of binary-image processing in DT computation, fuzzy logic was introduced as an intelligent and powerful tool to segment and further process gray level images in recent years. Fuzzy image processing can generally result in simple and fast computation methods that are easy to implement in practice. Method: We have developed lately a fuzzy distance transform (FDT) method to compute the distance of object pixels from non-object pixels in the integer space. This method uses an S-shape membership function to fuzzify the input gray level images. Then, the FDT map is computed using fuzzy Min–Max operations as expressed in the following equations: LP ¼
l1 X
maxðlBVF ðpk Þ; lBVF ðpkþ1 ÞÞ þ dðpk ; pkþ1 ÞDf ð pÞ ¼
k¼1
min
Papathsð p;qÞ
LP
where L P is the length of path P, p k is the kth point on path P, and d( p k, p k+1) is the Euclidian distance between points p k and p k+1. There are many paths between an object point p and background point q. The FDT, D f, is defined as the shortest path length for all object points from the background. Results: To assess solid/cavity thickness, the skeleton of the FDT map should be extracted. The skeletonization of the FDT map is done in two steps. In the first step, we extract some of the FDT map ridge points using an adaptive filter based on a second derivative of the map. In the second step, we employ an uphill-climbing algorithm to complete the ridge-based skeleton. If all local maxima and saddle points are found in the first step, then our skeletonization method usually produces connectivity preserved skeleton. The following figures respectively show the bone and cavity thickness distributions for different trabecular bone samples. Conclusion: The first advantage of the assessment of porous media based on FDT and its ridges is the ability to segment images into objects and nonobjects while keeping the inherent properties of the objects within the images. Secondly, the stepwise function allows consequent data processing to be done in the integer number space, thus running the algorithm faster. The third advantage is the robustness of the algorithm regarding image noise and rotation. Finally, FDT ridge skeleton provides representative bone/cavity thicknesses that are close to human perception.
doi:10.1016/j.mri.2007.01.037
Transport properties of supercritical fluids in mesoporous materials probed by pulsed field gradient NMR M. Dvoyashkin a, R. Valiullin a, J. Ka¨rger a, W.-D. Einickeb, R. Gla¨serc a Fakulta¨t fu¨r Physik und Geowissenschaften, Universita¨t Leipzig, D-04103 Leipzig, Germany, bFakulta¨t fu¨r Chemie und Mineralogie, Universita¨t Leipzig, D-04103 Leipzig, Germany, cInstitut fu¨r Technische Chemie, Universita¨t Stuttgart, D-70550 Stuttgart, Germany Supercritical (SC) fluids are of considerable interest because of their unusual properties between those of typical gases and liquids. The possibility to tune these properties with only minor variations in temperature and pressure in the vicinity of the critical point has led to a wide range of SC fluid applications as environmentally benign solvents for separations and chemical conversions. A bulk fluid becomes supercritical at certain values of temperature and pressure, unique for a given substance. The interrelation of bulk fluid properties such as diffusivity, solubility or polarity on pressure and temperature near the critical region continues to be the subject of a large number of theoretical and experimental studies. Qualitatively another situation arises when fluids confined within porous materials are considered. The presence of additional factors, e. g., the liquid-pore wall interaction, may shift the SC conditions and affect the behavior of SC fluids significantly. This shift is reflected, e.g., in an alteration of the trajectory of the liquid–gas coexistence curve in the general phase diagram, and in a shift of the critical point with respect to the bulk fluid [1,2]. To date, the description of the transport properties of SC fluids under confinement in porous solids is rather limited to theoretical predictions and some indirect experimental methods. In this work, we exploit the pulsed field gradient (PFG) NMR method to provide direct information about diffusion processes of fluids in the bulk and within porous materials over a broad range of temperatures, including the SC region. It is found that the transition to the supercritical state is accompanied by a sharp jump in the diffusivities occurring at a certain temperature T CP, although in the subcritical region the diffusivities are well fitted to the Arrhenius equation. Also, the essential difference between the pore (T CP) and the bulk (T CB) critical temperatures has been obtained in good agreement with theoretical predictions. [1] Gelb LD, Gubbins KE, Radhakrishnan R, Sliwinska-Bartkowiak M. Rep Prog Phys 1999;62:1573 – 1659. [2] Thommes M, Ko¨hn R, Fro¨ba M. J Phys Chem B 2000;104: 7932 – 43.
doi:10.1016/j.mri.2007.01.038