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Brownian motion (diffusion) and coherent flows are fundamental processes in nature. Therefore, their accurate measurement and description is highly desirable in many areas of science, engineering and technology. Here we describe a theoretical and experimental framework which enables one to directly examine the dynamics of fluid matter subject to diffusion and flow through the acquisition of the so-called averaged propagator. This statistical function holds all information on particle mobility due to flow and diffusion averaged over the observed fluid. The method is based on a single instantaneous nuclear magnetic resonance (NMR) measurement event. It also removes the need of data post processing by capturing the averaged propagator directly as the acquired signal which enables the monitoring of diffusion and flow in real time. When the propagator is acquired multiple times within one NMR experiment the real time measurement of surface-to-volume ratios in porous materials become possible. (In parts reprinted with permission from [W. Kittler, M. Hunter and P. Galvosas, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2015, 92, 023016] Copyright (2015) by the American Physical Society and from W. C. Kittler, P. Galvosas and M. W. Hunter, Parallel acquisition of q space using second order magnetic fields for single-shot diffusion measurements, J. Magn.Reson., 244, 46–52, Copyright (2014), with permission from Elsevier.)

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