2012
DOI: 10.1016/j.jmr.2011.11.020
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Emulsion droplet sizing using low-field NMR with chemical shift resolution and the block gradient pulse method

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Cited by 52 publications
(43 citation statements)
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“…(2) exists in which it is assumed that the duration of the applied magnetic field gradient, d, is equal to zero; since the use of the EFNMR requires the use of a comparatively very long value of d (up to 40 ms) we do not consider this method further in this work. More recently [20], we demonstrated the use of the block gradient pulse (bgp) approximation method to describe restricted diffusion inside spherical droplets (emulsion droplet sizing), with significantly improved accuracy compared to the assumption of a Gaussian phase distribution or an infinitely short d over all experimental parameter space considered. The bgp method is based on the generalised gradient waveform set of methods [21][22][23], in which an eigenfunction expansion is used to solve the Bloch-Torrey equation in the presence of a piecewise-constant gradient waveform [24].…”
Section: Pulsed Field Gradient Emulsion Droplet Sizingmentioning
confidence: 99%
See 1 more Smart Citation
“…(2) exists in which it is assumed that the duration of the applied magnetic field gradient, d, is equal to zero; since the use of the EFNMR requires the use of a comparatively very long value of d (up to 40 ms) we do not consider this method further in this work. More recently [20], we demonstrated the use of the block gradient pulse (bgp) approximation method to describe restricted diffusion inside spherical droplets (emulsion droplet sizing), with significantly improved accuracy compared to the assumption of a Gaussian phase distribution or an infinitely short d over all experimental parameter space considered. The bgp method is based on the generalised gradient waveform set of methods [21][22][23], in which an eigenfunction expansion is used to solve the Bloch-Torrey equation in the presence of a piecewise-constant gradient waveform [24].…”
Section: Pulsed Field Gradient Emulsion Droplet Sizingmentioning
confidence: 99%
“…Details regarding the derivation can be sourced from Grebenkov [25] and our implementation for emulsion droplet sizing, as is employed in the work presented here, is detailed in Ref. [20].…”
Section: Pulsed Field Gradient Emulsion Droplet Sizingmentioning
confidence: 99%
“…While it is common practice to avoid this regularization step when using benchtop NMR apparatuses by assuming a priori a log-normal distribution, this is not universally appropriate. In this work, the emulsion DSDs are extracted using Tikhonov regularization with general cross-validation (GCV) to choose the regularization parameter (see the studies by Hollingsworth and Johns 26 and Lingwood et al 39 for further details).…”
Section: ■ Introductionmentioning
confidence: 99%
“…An alternative derivation is the short gradient pulse (SGP) model which assumes the gradient pulse duration is negligible, d = 0, and hence that the diffusion that occurs during this period can be neglected. To overcome some of the drawbacks of the GPD and SGP approaches [36][37][38], Lingwood et al [39] im-…”
Section: Nuclear Magnetic Resonancementioning
confidence: 99%