Real-time fluid transport characterization through direct acquisition of the averaged propagator

Brownian motion (diffusion) and coherent flow are fundamental for many natural and artificial processes. Therefore, its accurate measurement and description is highly desirable in many areas of science, engineering, and technology. Currently available methods commonly involve multiple experiments and substantial processing of acquired data. This contribution proposes a theoretical and experimental framework that 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 proposed method is based on a single instantaneous nuclear magnetic resonance measurement event. It also removes the need for data postprocessing by capturing the averaged propagator directly as the acquired signal, which enables the monitoring of diffusion and flow in real time.