NMR velocity-imaging

In summary, we have commented briefly on the microscopic applications of NMR velocity imaging in complex polymer flows in complex geometries, where these applications have been termed Rheo-NMR [23]. As some of these complex geometries can be easily established in small scales, NMR velocimetry and visc-ometry at microscopic resolution can provide an effective means to image the entire Eulerian velocity field experimentally and to measure extensional properties in elastic liquids non-invasively. 

Our goal is to determine the permeability with millimeter resolution, approaching an intrinsic scale that corresponds to the minimum representative volume element. To do so, we first use NMR velocity-imaging experiments to determine the velocity distributions within a saturated porous medium undergoing a constant injection of water. Then, we solve an associated inverse problem to determine the permeability distribution. 

The key challenge for the successful use of NMR velocity-imaging techniques to characterize fluid flow properties is the interpretation of the measured parameters. Different experimental strategies provide information about flow processes at different spatial and dynamic scales in porous media. In principle, the flow velocity can be probed either as a local quantity with an image resolution below the pore level,2425 or as a macroscopic flow property corresponding to local volume and temporal averages of fluid molecular displacements.26 One must develop a suitable methodology to correctly determine the parameters that best describe the properties of interest. 

Mair RW, Callaghan PT (1996) Observation of shear banding in wormlike micelles by nmr velocity imaging. Eur Phys Lett 36(9) 719-724... 

Pulmonary arteries The retrosternal position of central pulmonary arteries makes it difficult to assess pulmonary blood flow by Doppler echocardiography, especially in the presence of skeletal or lung abnormalities. NMR velocity imaging is not... 

Fig. 4.3.6 Velocity maps and profiles at differ- mark the NMR foldbacks from the stationary ent heights of the Fano column. The dark ring fluid at the inner surface of the fluid reservoir, surrounding the pipe at z= 1.5 mm (larger In the velocity profiles, the solid curves are the white arrow) is due to a layer of stationary fluid calculated Poiseuille profiles in tube flow, adhering to the pipe exterior following the Velocity images are reprinted from Ref. [20], dipping of the pipe into the reservoir at the with permission from Elsevier, start of the experiment. The small white arrows...

Figure 13.. Comparison of theoretical analysis and empirical NMR imaging of fluid flow during extrusion. Limiting cases for theoretical analysis (a), the velocity profile as a function of position with no pressure gradient in the z-direction (b), the velocity profile as a function of position with no net flow through the extruder. Limiting cases for empirical analysis by NMR flow imaging (c), no pressure gradient in the z-direction (die open) (d), no net flow through the extruder (die closed).[Reproduced with permission from Ref.61].

Figure 7.1 Most modern NMR techniques are based on the fact, that the phase (p of the precessing transverse magnetisation M t) kann be measured. By use of the Fourier transformation the phase provides access to NMR spectra, images, and parameters of translational motion like velocity v and acceleration a. Spectroscopic parameters as well as components of translational velocity and acceleration can be used for generating contrast in NMR imaging. In the drawing the magnetisation M(t) has been generated from Mz by use of a 90° pulse of the B1 radio-frequency (rf) field in y direction...

RF transmission and reception of the NMR signal. For the stimulated pulse sequence, three hard pulses were used with the spin-warp sequence as discussed in Section 3.1. It is also necessary to obtain images corresponding to the porosity distribution as described in Section 2, in addition to the velocity images. This is because the images obtained in the velocity experiment are measures of the intrinsic velocity, the actual velocity of the fluid within the pore space. Darcy s law, however, is written in terms of the superficial velocity. The two velocities are simply related by the porosity ... 

NMR Methods. Altobelli et al. (82) and Sinton and Chow (83) studied solid velocity and concentration profiles of flowing slurries using NMR flow imaging techniques. These profiles were obtained from the displacement of a tagged slice oriented perpendicular to the flow direction using fast Fourier reconstruction algorithms (83). 

Callaghan PT (2006) Rheo-nmr and velocity imaging. Curr Opin Colloid Interface Sci 11(1) 13-18... 

Figure 5 Sequences using stimulated echoes for flow velocity imaging (A) and tor the measurement of the displacement distribution function without imaging (B). The use of stimulated echoes often proves very convenient since the NMR signal can be observed for longer delays A, limited only by the T, value. The pair of gradient pulses, when exactly matched, produce no phase shift for nonmoving spins, and for moving spins they induce a phase shift A(j> equal to the product of the wavevector q = yGd, by the displacement (r(A) - r(0)). For a uniform velocity field v, (r(A) - r(0)) = Av everywhere in space and v can be found from the phase-shift measurement at a given value of q (A). In more complex flow situations, the full displacement distribution can be obtained from a Fourier transform analysis of data acquired with incremented G, and thus q, values (B).

J. Gotz, K. Zick, C. Heinen, T. Konig 2002, (Visualisation of flow processes in packed beds with NMR imaging Determination of the local porosity, velocity vector and local dispersion coefficients), Chem. Eng. Process. 41 (7), 611-630. 

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