- Email: [email protected]
Two-phase flow in a flexible porous medium
550
Abstracts / Magnetic Resonance Imaging 25 (2007) 544 – 591
Fig. 1 Profiles of velocity (VX), normalized by its respective value at the entry. These slices, which are taken at different levels of the bone, show the nonuniformities in the flow profile. on validated Lattice Boltzmann code, which has been previously used to study Newtonian flow in packing of glass beads. The 3D trabecular bone skeleton was reconstructed using the microscans. The simulation was conducted for a small Reynolds number of 0.0 to 1, which is characteristic for the flow process of this medical procedure. Results: Trabecular bone showed a well-organized 3-D structure and a very high porosity. In the case of healthy bone, its porosity is in the range of 80% but increases up to 96% for bone suffering from osteoporosis. Fig. 1 shows the velocity profile within the cavities of osteoporotic bone. It shows that the velocity and volume flow rate vary substantially depending on the size of the cavity and, more importantly and very substantially, because of the nonuniform cavity structure and distribution throughout the sample. Discussion: This study presented a microscale flow model of Newtonian flow through the trabecular bone cavities. Micro CT scanning provides representative geometric data and, if combined with the simulation, both seem to be adequate to address the question posed. Future directions will examine geometrically larger models and physically more adequate nonNewtonian models of the fluid, in addition to understanding the local velocities, flow patterns and pressure drop in the bone cavities. This research may provide understanding on the role of the length scale in passing from the pore scale phenomenon to the macroscopic scale, which will likely make the computation more efficient in the long run. doi:10.1016/j.mri.2007.01.023 AxCaliber: an MRI method to measure the diameter distribution and density of axons in neuronal tissue P.J. Bassera, T. Blumenfeldb, G. Levinb, Y. Yovel b, Y. Assaf b a STBB/LIMB/NICHD, NIH, bDepartment of Neurobiochemistry, Tel Aviv University The experimental determination of the diameter distribution, p(d), of emulsions and droplets has long been studied using NMR methods (see Refs. [1,2]). In these experiments, p(d) is estimated from PFG data by assuming a model of restricted diffusion within spheres. We have adapted this approach to estimate the diameter distribution within cylindrical nerve fascicles — a pack or array of nerve axons — by assuming that axons contain a restricted pool of water within their intracellular spaces. A composite hindered and restricted model of diffusion (CHARMED) within axons was first elaborated and tested in Ref. [3], and then applied clinically in Ref. [4]. The AxCaliber framework presented here extends CHARMED by providing an estimate of p(d) directly from diffusion-weighted (DW) MR data. In this implementation, a Gamma distribution is assumed to describe the axon diameter distribution. Parameters of this distribution are then estimated from the PFG data in optic nerve (ON) and sciatic nerve (SN) bundles. The estimated p(d) using AxCaliber (above right) is compared with measurements obtained from histological analysis (above left). MR experiments were performed using a 7-T scanner (Bruker, Germany) on fixed porcine nerve tissue. High b-value DWIs were acquired with a
stimulated echo DWI sequence with the following parameters: TR/ TE = 3000/166 ms, d = 2.5 ms, G max = 120 G/cm, no. of averages = 8, with the diffusion time, D, chosen from 20 to 150 ms in eight increments. Diffusion gradients were applied only perpendicular to the nerves’ axes in 16 gradient amplitude increments for each D. The entire acquisition consisted of 128 DW spectra acquired in 51 min. Histological analysis was performed using conventional myelin basic protein (MBP) stains along with particle sizing software used on the histological sections. Agreement between MR and histology data is excellent, suggesting the possibility for measuring p(d) in vivo using DW-MRI data. The marriage between MRI and porous media theory with biology and medicine is generating promising new applications. AxCaliber is one such example of a growing discipline of virtual in vivo tissue biopsy. [1] Packer KJ, Rees C. Pulsed NMR studies of restricted diffusion 1. Droplet size distributions in emulsions. J Colloid Interface Sci 1972;40(2):206–18. [2] McDonald PJ, Ciampi E, Keddie JL, Heidenreich M, Kimmich R. Magnetic-resonance determination of the spatial dependence of the droplet size distribution in the cream layer of oil-in-water emulsions: Evidence for the effects of depletion flocculation. Phys Rev E 1999;59(1):874–84. [3] Assaf Y, Freidlin RZ, Rohde GK, Basser PJ. New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn Reson Med 2004;52(5): 965–78. [4] Assaf Y, Basser PJ. Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain. NeuroImage 2005;27(1):48–58. doi:10.1016/j.mri.2007.01.024 Two-phase flow in a flexible porous medium D.A. Beauregard a, M.D. Mantlea, A.J. Sedermana, L.F. Gladdena, M. Bakerb, N. Shawb a Magnetic Resonance Research Centre, Department of Chemical Engineering, University of Cambridge, Cambridge CB3 0HE, bUnilever Research and Development Port Sunlight, Wirral CH63 3JW, UK Flow in porous media composed of rigid materials or arrays of rigid components, such as porous rock or packed beds, is now studied routinely using MR [1,2]. Acquisition schemes have been developed that achieve high spatial and/or temporal resolution and which further lend themselves to the study of flexible porous media, which may be deformed by the application of flow. The deformations may be temporally stable or unstable, and examples of these porous media are filtration materials, hollow-fibre bioreactors, and fibres presented as arrays used in the textile industry. Here, we report on the characteristics of two-phase flow in a flexible porous medium constructed from parallel fibres anchored in a cylinder. The aim was to map flow for different densities of fibres, in order to assess the ability of the medium to alter its porosity, trap the liquid phase and alter flow properties of the liquid phase.
Abstracts / Magnetic Resonance Imaging 25 (2007) 544 – 591
Fig. 1 Cross section of fibre array, showing wet fibres: (A) lower density, no flow; (B) lower density, flow rate 14 mm/s; (C) higher density, no flow; and (D) higher density, flow rate 14 mm/s. The method was to present a flow of deionised water (flow rate, 6 mm/s) to the top of a perspex column of internal diameter 26 mm in which was suspended either 16 or 29 g of fibre. The column was positioned within an imaging coil contained within a 4.7-T magnet, and spin-echo and snapshot FLASH acquisitions were made. The former were at high spatial resolution (0.10.11 mm3) to map the position of fibre in the absence of flow (Fig. 1 A and C), and the latter were at high temporal resolution (129 ms/acquisition, 150 acquisitions made consecutively in 19 s) to capture flow characteristics (Fig. 1B and D). The results indicated that (i) at low-fibre density, a temporally variable flow pattern developed in which a cylinder of wetted fibre was associated with the wall of the column with a central air channel (Fig. 1B). At higher fibre density, a temporally variable flow pattern developed, but which was not so strongly associated with the cylinder wall (Fig. 1D). (ii) The proportion of the liquid phase that was trapped within the porous medium and hence flowing slowly was correlated with fibre density in the cylinder, but the correlation was not linear. The conclusions were that flow characteristics in a flexible porous medium could be analysed using MR techniques, and that the flexibility of the medium resulted in different flow geometries according to the packing of the medium. [1] Proceedings of the Seventh International Conference on Recent Advances in MR Applications to Porous Media Magnetic Resonance Imaging 2005;23(2):121–444. [2] MD Mantle, AJ Sederman. Dynamic MRI in chemical process and reaction engineering Progress in Nuclear Magnetic Resonance Spectroscopy 2003;43:3–60.
551
Self-diffusion coefficients have been thoroughly measured using the B1 gradient method (so as to overcome problems associated with short relaxation times). We have observed a decrease of the apparent diffusion coefficient as a function of the diffusion interval, until the tortuosity plateau is reached. This behaviour has been interpreted in terms of mean square displacement. Finally, we shall present preliminary measurements performed on a micro PEM fuel cell under operation, specially built for being studied in a NMR mini-imager. doi:10.1016/j.mri.2007.01.026 Magnetic resonance imaging of flow distributed oscillations in a packed bed reactor M.M. Brittona,b, A.J. Sedermanb, A.F. Taylorc, S.K. Scott c, L.F. Gladdenb a School of Chemistry, University of Birmingham, Birmingham, UK, b Department of Chemical Engineering, University of Cambridge, Cambridge, UK, cSchool of Chemistry, University of Leeds, Leeds, UK The formation of bflow distributed oscillationQ (FDO) patterns in a manganese-catalysed Belousov-Zhabotinsky (BZ) reaction is studied using magnetic resonance imaging (MRI) [1]. FDO patterns [2] occur when chemical reaction-diffusion systems are coupled with flow, producing stationary chemical waves. A plug flow reactor is used, consisting of a packed bed of glass beads, and is fed constantly by a continuous stirred tank reactor (CSTR), in which reactant concentrations are kept constant. MRI is used to probe the formation and complete structure of the stationary wave. MRI image contrast is produced through changes in the ratio of the oxidized (Mn3+) to reduced (Mn2+) form of the manganese catalyst, which change the relaxation times of protons in the surrounding water molecules. The formation, 3-D structure and development of these waves were studied. A typical 2-D image taken through the centre of a stationary wave is shown in Fig. 1A; a 3-D rendering from a matrix of 2-D vertical slice images through a stationary wave is shown in Fig. 1B. Images were obtained using a fast imaging sequence [3], which could take a single 2-D image on the order of a few seconds and was able to take multiple-slice images through the width of the bead pack, at regular timings. This allowed the 3-D structure of the wave to be probed and the dynamics of the wave to be monitored, over time, as it formed. Images of
doi:10.1016/j.mri.2007.01.025 Water motional properties in proton exchange membrane of fuel cell (PEMFC) by NMR (spin relaxation and translational diffusion) J. Bedet a,b, S. Leclerca, D. Stemmelena, O. Lottina, C. Moynea, P. Mutzhenhardt b, D. Canetb a Laboratoire d’E´nerge´tique et de Me´canique The´orique et Applique´e (UMR 7563 CNRS-INPL-Universite´ Henri Poincare´-Nancy 1), France, bMe´thodologie RMN (UMR 7565 CNRS-Universite´ Henri Poincare´-Nancy 1), France Proton exchange membrane of fuel cells (PEMFCs) are particularly attractive as efficient pollution-free power generators for stationary or mobile applications. They are notably considered for replacing internal combustion engine in electric vehicles. Indeed, fuel cells are devices that use hydrogen (or hydrogen-rich fuel) and oxygen (or air) to produce electricity. PEMFCs use perfluorosulfonic acid membranes (Nafion for example) as solid electrolyte which is proton conductor and electron insulator. The performance of these fuel cells is strongly influenced by the state of hydration of the membrane. As a consequence, precise knowledge of water distribution inside the membrane and of its transport properties (diffusion and electroosmosis) is a crucial issue. NMR applied to the Nafion membrane reveals a relationship between water content and chemical shift on the one hand, and between water content and longitudinal relaxation on the other hand. It turns out that the longitudinal relaxation time is much more sensitive to water uptakes than the chemical shift. It can therefore be used reliably to determine in situ the water content.
Fig. 1 (A) Two-dimensional image of a chemical wave associated with a Mn-catalysed BZ reaction, pumped at a flow rate of 0.1 cm3 s1 through a 17-mm-id tube packed with 1 mm beads. (B) Three-dimensional render of a stationary wave, in a 12-mm-id tube packed with 1-mm beads pumped at a flow rate of 0.06 cm3 s1, taken from a series of 0.8-mm-thick 2-D images, at intervals of 0.8 mm.
Abstracts / Magnetic Resonance Imaging 25 (2007) 544 – 591
Fig. 1 Profiles of velocity (VX), normalized by its respective value at the entry. These slices, which are taken at different levels of the bone, show the nonuniformities in the flow profile. on validated Lattice Boltzmann code, which has been previously used to study Newtonian flow in packing of glass beads. The 3D trabecular bone skeleton was reconstructed using the microscans. The simulation was conducted for a small Reynolds number of 0.0 to 1, which is characteristic for the flow process of this medical procedure. Results: Trabecular bone showed a well-organized 3-D structure and a very high porosity. In the case of healthy bone, its porosity is in the range of 80% but increases up to 96% for bone suffering from osteoporosis. Fig. 1 shows the velocity profile within the cavities of osteoporotic bone. It shows that the velocity and volume flow rate vary substantially depending on the size of the cavity and, more importantly and very substantially, because of the nonuniform cavity structure and distribution throughout the sample. Discussion: This study presented a microscale flow model of Newtonian flow through the trabecular bone cavities. Micro CT scanning provides representative geometric data and, if combined with the simulation, both seem to be adequate to address the question posed. Future directions will examine geometrically larger models and physically more adequate nonNewtonian models of the fluid, in addition to understanding the local velocities, flow patterns and pressure drop in the bone cavities. This research may provide understanding on the role of the length scale in passing from the pore scale phenomenon to the macroscopic scale, which will likely make the computation more efficient in the long run. doi:10.1016/j.mri.2007.01.023 AxCaliber: an MRI method to measure the diameter distribution and density of axons in neuronal tissue P.J. Bassera, T. Blumenfeldb, G. Levinb, Y. Yovel b, Y. Assaf b a STBB/LIMB/NICHD, NIH, bDepartment of Neurobiochemistry, Tel Aviv University The experimental determination of the diameter distribution, p(d), of emulsions and droplets has long been studied using NMR methods (see Refs. [1,2]). In these experiments, p(d) is estimated from PFG data by assuming a model of restricted diffusion within spheres. We have adapted this approach to estimate the diameter distribution within cylindrical nerve fascicles — a pack or array of nerve axons — by assuming that axons contain a restricted pool of water within their intracellular spaces. A composite hindered and restricted model of diffusion (CHARMED) within axons was first elaborated and tested in Ref. [3], and then applied clinically in Ref. [4]. The AxCaliber framework presented here extends CHARMED by providing an estimate of p(d) directly from diffusion-weighted (DW) MR data. In this implementation, a Gamma distribution is assumed to describe the axon diameter distribution. Parameters of this distribution are then estimated from the PFG data in optic nerve (ON) and sciatic nerve (SN) bundles. The estimated p(d) using AxCaliber (above right) is compared with measurements obtained from histological analysis (above left). MR experiments were performed using a 7-T scanner (Bruker, Germany) on fixed porcine nerve tissue. High b-value DWIs were acquired with a
stimulated echo DWI sequence with the following parameters: TR/ TE = 3000/166 ms, d = 2.5 ms, G max = 120 G/cm, no. of averages = 8, with the diffusion time, D, chosen from 20 to 150 ms in eight increments. Diffusion gradients were applied only perpendicular to the nerves’ axes in 16 gradient amplitude increments for each D. The entire acquisition consisted of 128 DW spectra acquired in 51 min. Histological analysis was performed using conventional myelin basic protein (MBP) stains along with particle sizing software used on the histological sections. Agreement between MR and histology data is excellent, suggesting the possibility for measuring p(d) in vivo using DW-MRI data. The marriage between MRI and porous media theory with biology and medicine is generating promising new applications. AxCaliber is one such example of a growing discipline of virtual in vivo tissue biopsy. [1] Packer KJ, Rees C. Pulsed NMR studies of restricted diffusion 1. Droplet size distributions in emulsions. J Colloid Interface Sci 1972;40(2):206–18. [2] McDonald PJ, Ciampi E, Keddie JL, Heidenreich M, Kimmich R. Magnetic-resonance determination of the spatial dependence of the droplet size distribution in the cream layer of oil-in-water emulsions: Evidence for the effects of depletion flocculation. Phys Rev E 1999;59(1):874–84. [3] Assaf Y, Freidlin RZ, Rohde GK, Basser PJ. New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn Reson Med 2004;52(5): 965–78. [4] Assaf Y, Basser PJ. Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain. NeuroImage 2005;27(1):48–58. doi:10.1016/j.mri.2007.01.024 Two-phase flow in a flexible porous medium D.A. Beauregard a, M.D. Mantlea, A.J. Sedermana, L.F. Gladdena, M. Bakerb, N. Shawb a Magnetic Resonance Research Centre, Department of Chemical Engineering, University of Cambridge, Cambridge CB3 0HE, bUnilever Research and Development Port Sunlight, Wirral CH63 3JW, UK Flow in porous media composed of rigid materials or arrays of rigid components, such as porous rock or packed beds, is now studied routinely using MR [1,2]. Acquisition schemes have been developed that achieve high spatial and/or temporal resolution and which further lend themselves to the study of flexible porous media, which may be deformed by the application of flow. The deformations may be temporally stable or unstable, and examples of these porous media are filtration materials, hollow-fibre bioreactors, and fibres presented as arrays used in the textile industry. Here, we report on the characteristics of two-phase flow in a flexible porous medium constructed from parallel fibres anchored in a cylinder. The aim was to map flow for different densities of fibres, in order to assess the ability of the medium to alter its porosity, trap the liquid phase and alter flow properties of the liquid phase.
Abstracts / Magnetic Resonance Imaging 25 (2007) 544 – 591
Fig. 1 Cross section of fibre array, showing wet fibres: (A) lower density, no flow; (B) lower density, flow rate 14 mm/s; (C) higher density, no flow; and (D) higher density, flow rate 14 mm/s. The method was to present a flow of deionised water (flow rate, 6 mm/s) to the top of a perspex column of internal diameter 26 mm in which was suspended either 16 or 29 g of fibre. The column was positioned within an imaging coil contained within a 4.7-T magnet, and spin-echo and snapshot FLASH acquisitions were made. The former were at high spatial resolution (0.10.11 mm3) to map the position of fibre in the absence of flow (Fig. 1 A and C), and the latter were at high temporal resolution (129 ms/acquisition, 150 acquisitions made consecutively in 19 s) to capture flow characteristics (Fig. 1B and D). The results indicated that (i) at low-fibre density, a temporally variable flow pattern developed in which a cylinder of wetted fibre was associated with the wall of the column with a central air channel (Fig. 1B). At higher fibre density, a temporally variable flow pattern developed, but which was not so strongly associated with the cylinder wall (Fig. 1D). (ii) The proportion of the liquid phase that was trapped within the porous medium and hence flowing slowly was correlated with fibre density in the cylinder, but the correlation was not linear. The conclusions were that flow characteristics in a flexible porous medium could be analysed using MR techniques, and that the flexibility of the medium resulted in different flow geometries according to the packing of the medium. [1] Proceedings of the Seventh International Conference on Recent Advances in MR Applications to Porous Media Magnetic Resonance Imaging 2005;23(2):121–444. [2] MD Mantle, AJ Sederman. Dynamic MRI in chemical process and reaction engineering Progress in Nuclear Magnetic Resonance Spectroscopy 2003;43:3–60.
551
Self-diffusion coefficients have been thoroughly measured using the B1 gradient method (so as to overcome problems associated with short relaxation times). We have observed a decrease of the apparent diffusion coefficient as a function of the diffusion interval, until the tortuosity plateau is reached. This behaviour has been interpreted in terms of mean square displacement. Finally, we shall present preliminary measurements performed on a micro PEM fuel cell under operation, specially built for being studied in a NMR mini-imager. doi:10.1016/j.mri.2007.01.026 Magnetic resonance imaging of flow distributed oscillations in a packed bed reactor M.M. Brittona,b, A.J. Sedermanb, A.F. Taylorc, S.K. Scott c, L.F. Gladdenb a School of Chemistry, University of Birmingham, Birmingham, UK, b Department of Chemical Engineering, University of Cambridge, Cambridge, UK, cSchool of Chemistry, University of Leeds, Leeds, UK The formation of bflow distributed oscillationQ (FDO) patterns in a manganese-catalysed Belousov-Zhabotinsky (BZ) reaction is studied using magnetic resonance imaging (MRI) [1]. FDO patterns [2] occur when chemical reaction-diffusion systems are coupled with flow, producing stationary chemical waves. A plug flow reactor is used, consisting of a packed bed of glass beads, and is fed constantly by a continuous stirred tank reactor (CSTR), in which reactant concentrations are kept constant. MRI is used to probe the formation and complete structure of the stationary wave. MRI image contrast is produced through changes in the ratio of the oxidized (Mn3+) to reduced (Mn2+) form of the manganese catalyst, which change the relaxation times of protons in the surrounding water molecules. The formation, 3-D structure and development of these waves were studied. A typical 2-D image taken through the centre of a stationary wave is shown in Fig. 1A; a 3-D rendering from a matrix of 2-D vertical slice images through a stationary wave is shown in Fig. 1B. Images were obtained using a fast imaging sequence [3], which could take a single 2-D image on the order of a few seconds and was able to take multiple-slice images through the width of the bead pack, at regular timings. This allowed the 3-D structure of the wave to be probed and the dynamics of the wave to be monitored, over time, as it formed. Images of
doi:10.1016/j.mri.2007.01.025 Water motional properties in proton exchange membrane of fuel cell (PEMFC) by NMR (spin relaxation and translational diffusion) J. Bedet a,b, S. Leclerca, D. Stemmelena, O. Lottina, C. Moynea, P. Mutzhenhardt b, D. Canetb a Laboratoire d’E´nerge´tique et de Me´canique The´orique et Applique´e (UMR 7563 CNRS-INPL-Universite´ Henri Poincare´-Nancy 1), France, bMe´thodologie RMN (UMR 7565 CNRS-Universite´ Henri Poincare´-Nancy 1), France Proton exchange membrane of fuel cells (PEMFCs) are particularly attractive as efficient pollution-free power generators for stationary or mobile applications. They are notably considered for replacing internal combustion engine in electric vehicles. Indeed, fuel cells are devices that use hydrogen (or hydrogen-rich fuel) and oxygen (or air) to produce electricity. PEMFCs use perfluorosulfonic acid membranes (Nafion for example) as solid electrolyte which is proton conductor and electron insulator. The performance of these fuel cells is strongly influenced by the state of hydration of the membrane. As a consequence, precise knowledge of water distribution inside the membrane and of its transport properties (diffusion and electroosmosis) is a crucial issue. NMR applied to the Nafion membrane reveals a relationship between water content and chemical shift on the one hand, and between water content and longitudinal relaxation on the other hand. It turns out that the longitudinal relaxation time is much more sensitive to water uptakes than the chemical shift. It can therefore be used reliably to determine in situ the water content.
Fig. 1 (A) Two-dimensional image of a chemical wave associated with a Mn-catalysed BZ reaction, pumped at a flow rate of 0.1 cm3 s1 through a 17-mm-id tube packed with 1 mm beads. (B) Three-dimensional render of a stationary wave, in a 12-mm-id tube packed with 1-mm beads pumped at a flow rate of 0.06 cm3 s1, taken from a series of 0.8-mm-thick 2-D images, at intervals of 0.8 mm.