NMR signal loss from turbulence: Models of time dependence compared with data

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Abstract
This paper reviews theoretical models of nuclear magnetic resonance signal loss due to turbulence in the presence of a magnetic gradient and presents measurements of signal loss from pipe flow as a function of echo time. The models all treat homogeneous turbulence as a random velocity superimposed on a steady velocity. Theoretical signal losses were calculated using previous hot wire anemometry data from dynamically similar air flow. Theoretical pipe cross sections were partitioned into nine concentric homogeneous regions with distinct turbulent diffusivities and intensities. Experimental pipes were 0.95 and 5.0 cm diameter with average water velocities of 1 m s−1 providing Reynolds numbers of 12 000 and 55 000. Magnetic gradient strengths ranged from 0.01 to 0.04 G cm−1; echo times ranged from 24 to 120 ms. The models that include the decay of the velocity autocorrelation with time (i.e., consider that turbulence appears more diffusive as the observation time increases) fit the data better than those that do not.