Two-Dimensional PFG NMR for Encoding Correlations of Position, Velocity, and Acceleration in Fluid Transport
✍ Scribed by Song-I Han; Siegfried Stapf; Bernhard Blümich
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 290 KB
- Volume
- 146
- Category
- Article
- ISSN
- 1090-7807
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✦ Synopsis
A generalized approach to obtain two-dimensional maps of spatial particle coordinates and their derivatives with respect to time by PFG-NMR employing multiple gradient pulses is presented. A sequence of n magnetic field gradient pulses makes it possible, after independent stepping of each pulse and subsequent Fourier transformation, to plot the spin density distribution in coordinate space at n times and along the respective directions of the gradient pulses. In particular, two gradient pulses of effective area k 1 and k 2 separated by a time interval ⌬ lead to a plot of the combined two-time probability density, W 2 (r 1 , 0; r 2 , ⌬), to find a particle at a coordinate r 1 at t ؍ 0 and at r 2 at t ؍ ⌬. A conventional experiment for measuring transport properties by simultaneous stepping of the gradients under the condition k 1 ؍ ؊k 2 is equivalent to a projection onto the secondary diagonal in the [r 1 , r 2 ] plot. The main diagonal represents an average position between the two timepoints t ؍ 0 and t ؍ ⌬, so that a rotation of the coordinate plot by an angle of 45°allows one to correlate the displacement R ؍ r 2 ؊ r 1 with the averaged position r parallel to the gradient direction. While an average velocity during the time interval ⌬ can be defined as v v ؍ R/⌬, an extension toward acceleration and higher order derivatives is straightforward by modification of the pulse sequence. We discuss this concept by application to flow through a circular and a narrowing pipe (confusor), respectively, the experimental results of which are compared to numerical simulations.