Velocity imaging

In this section, we will focus on the different types of motion and their experimental determination, and will not consider imaging itself Section 1.5 will then combine the two encodings of position and motion into velocity imaging sequences. 

Velocity maps of simple or complex liquids, emulsions, suspensions and other mixtures in various geometries provide valuable information about macroscopic and molecular properties of materials in motion. Two- and three-dimensional spin echo velocity imaging methods are used, where one or two dimensions contain spatial information and the remaining dimension or the image intensity contains the information of the displacement of the spins during an observation time. This information is used to calculate the velocity vectors and the dispersion at each position in the spatially resolved dimensions with the help of post-processing software. The range of observable velocities depends mainly on the time the spins... 

Fig. 2.8.6 (a) (i) I implementation of vertical cylindrical Couette cell using concentric glass tubes (ii) velocity image taken across a horizontal slice and (iii) velocity profile taken across the cell. Note that the marker fluid in the inner cylinder exhibits rigid body motion... 

Fig. 2.8.7 (a) Implementation of cone-and-plate device, (b) Velocity image taken across a vertical slice, (c) Velocity profile taken across the cell with 7° cone angle. Note the highly linear variation of velocity (adapted from Ref. [15]). 

The molecular translations are spatially resolved by combining the velocity encoding sequence with the conventional spatial imaging encodings. In this velocity imaging", the phase shift of the spins reflects the information about their displacement as well as the spatial position. In this work, a flow-compensation [25] is implemented in the velocity imaging pulse sequence to eliminate the actifacts due to fluid flow. 

An example of the spin-velocity density function is demonstrated in Figure 4.1.6. A velocity imaging experiment was performed on water flowing through a 6-mm diameter tube. The velocity density function was spatially resolved along the axial direction of the tube, denoted by z in the figure. It is observed that the velocity density function has a steep peak at zero velocity when the fluid is not flowing, but is shifted to a positive velocity when the flow rate was increased to 2.5 mL min-1. 

Fig. 4.2.5 Unaliased (A) and aliased (B) velocity images for a 0.6% aqueous carboxy-methylcellulose solution obtained by MRI. The vertical axes represent the data obtained in the velocity encoded direction and the horizontal axis represents data obtained in the spatially encoded direction. Aliasing is achieved by setting the velocity encode gradients so large that the maximum phase evolution of a given fluid element for a pulsed gradient step exceeds Ji or 2jt...

Velocity images and profiles at several selected heights are shown in Figure 4.3.6, where the noisy points in the images indicate the air space where a liquid signal was not detected. When the fluid is inside the glass pipette, the velocity profile is nearly Poiseuille and a non-slip boundary condition is almost achieved. This is consistent with one of the early tube flow reports that the 0.5% w/v solution of... 

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...

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. 

A more quantitative method is the so-called phase method, the phase being one of two parameters that an MRI image yields, the other being signal amplitude. We show below (Section 4.8.2.6) that the phase is correlated with the velocity of the sample, so a spatially resolved image of the signal phase can yield a velocity image. 

Tagging is not the method of choice for determining velocities because the calculation of the velocity is complex and the spatial resolution of the velocity information is only as good as the size of the grids. The best velocity images are made with the phase method, described below. However, tagging is a superb method to visualize flow. 

Typically, at least two different values of m1 (besides ml = 0) are used because there are invariably phase shifts that arise from various factors that do not depend on the gradient moments, resulting in a non-zero intercept of c > versus mx. Thus, a velocity image is time consuming because each set of measurements with a value of m1 is an image in itself. 

The instrumentation is also as varied as the variety of parameters to be measured. However, the choice is severely limited if the instrumentation needs to be of a turnkey variety. An obvious example is MRI instruments for clinical medicine that are technologically well suited for particle density imaging. MRI technicians in clinical MRI facilities are well trained to make standard images but, with rare exceptions, would not be able to make the more complex measurements needed, for example, for velocity imaging. Unfortunately, clinical MRI instruments are very expensive and also require expensive physical facilities to house them. Furthermore, medical facilities are usually not willing to divert the use of their expensive MRI instrument for purposes other than their needs, especially if instrument settings need to be changed. 

Fig. 5.3.5 Jo int spatial-velocity images of xenon undergoing Poiseuille flow in a pipe (id = 4 mm, DXe = 4.5 mm2 s-1, Vave =...

Fig. 5.3.6 j oint spatial-velocity images of xenon undergoing Poiseuille flow in a pipe (id = 4 mm, Vave = 27 mm s 1, D = 8 mm2 s 1) at 0.7 atm recorded with a protocol shown in Figure 5.3.4(A). Only particles at walls are selected by the edge enhancement filter . A modified imaging gradient time duration... 

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