Real-time probing of granular dynamics with magnetic resonance

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Science Advances  15 Sep 2017:
Vol. 3, no. 9, e1701879
DOI: 10.1126/sciadv.1701879
  • Fig. 1 Enabling single-shot MRI of granular dynamics.

    (A) Concurrent detection of MR using an array of 16 RF coils placed closely around the region of interest. The varying spatial sensitivities of the coil allow for a reduced k-space sampling density below the Nyquist limit (see Materials and Methods). (B) Single-shot echo-planar imaging (EPI) readouts are applied to sample k-space time-efficiently within one spin coherence. Asymmetric partial Fourier sampling reduces the readout duration further. The green shaded area of k-space is acquired, whereas the gray shaded area is estimated in the algebraic image reconstruction (see Materials and Methods). (C) Photograph of tailored oil-filled agar particles (particle diameter dp = 1.02 ± 0.12 mm) with enhanced MR signal intensity and lifetime when compared to agricultural seeds provides sufficient signal throughout the single-shot readout duration of 4.6 ms. (D) k-space representation of the single-shot EPI readout trajectory (bold black dots). The light dashed line represents a conventional EPI sequence sampled according to the Nyquist limit. The zoomed area shows the applied reduction of sampling density. The pulse sequence properties for this readout trajectory are detailed in fig. S1A. (E) Algebraic image reconstruction exploiting varying spatial sensitivities of the 16 receive channels to correct for undersampled, asymmetric k-space information. (F) Reconstructed image obtained by single-shot MRI. The temporal and spatial resolution (Δx × Δy × Δz) of the acquisition was 7 ms and 3 mm × 5 mm × 10 mm, respectively, for a field of view of 200 mm × 300 mm.

  • Fig. 2 Real-time MRI of bubble dynamics inside a cylindrical 3D gas-solid fluidized bed.

    (A) Schematic of the imaging setup. Particles in a cylindrical bed were fluidized by air injected through a perforated distributor plate at the bottom of the bed. The MR receiver array was placed concentrically around the fluidized bed. (B) Instantaneous MR images reveal details of bubble dynamics in gas-solid fluidized beds (see also movie S1). The coalescence of two bubbles and the subsequent splitting of the merged bubble following an indentation from the top surface of the bubble can be observed. (C) The high temporal resolution of 7 ms allows tracking the position (shaded areas) and detecting the velocities (lines) of the bubbles involved in the coalescence process. The speed of the trailing bubble increases significantly once it enters the wake of the leading bubble. (D) A threshold is applied to the MR images to determine the centers of mass and the equivalent bubble diameters of the bubbles. (E) Spatial distribution of bubble centers of mass (position of colored dots) and their equivalent circular bubble diameter De (color and size of the dots). Larger bubbles are found toward the central upper part of the bed. The scribbled area at the top of the bed demarcates the eruption region which was omitted from the bubble size analysis.

  • Fig. 3 Measured and simulated granular flow around an isolated bubble in a fluidized bed.

    (A) MR phase-contrast velocimetry of an isolated air bubble (white) rising in a fluidized granular system. The temporal and spatial resolution (Δx × Δy × Δz) of the acquisition was 22.5 ms and 3 mm × 7 mm × 10 mm, respectively. The colors denote the magnitude |vxy|, the black arrows denote the direction, and the white lines denote streamlines of the in-plane particle velocity, vxy. The highest particle velocities occur in the central wake region of the bubble (red area). (B) Numerical simulation of potential flow around a similarly shaped bubble assuming impenetrable bubble walls and irrotational flow. Considerable differences are observable around the top and along the sides of the bubble (see text for discussion). (C) Vorticity ωxy = ∇ × vxy of the measured flow field. Significant vorticity is observed in the wake region and side regions. A region of inverted vorticity can be observed around the top of the bubble, which is probably caused by particles “raining” down through the bubble. See also movie S2.

  • Fig. 4 Response of a loosely packed granular material to the impact of a spherical intruder.

    (A) Three selected frames of an MR image series (B) showing the impact of a heavy intruder into a granular packing (Δt = 53 ms). The leftmost image in (A) shows an area of significant signal increase following the impact of the intruder compared to preimpact conditions. This bright area propagates concentrically from the point of impact, indicating a wave of coherent particle motion and acceleration. The signal increase is followed by a signal attenuation [dark concentric area around the sphere in the central image of (A)] caused by incoherent particle motion. This incoherent motion relaxes to an immobile state in the course of approximately 0.5 s (see also movie S3). (C) 1D spatiotemporal plot (Δt = 2.3 ms) of the same event allows for a detailed analysis of the granular response dynamics. The yellow band corresponds to the white fringe in (B). The slope of this band determines the propagation speed of the spherical wavefront. Signal fluctuations (f = 30 Hz) throughout large regions of the granular material can be observed following the impact of the intruder, yet dampen out within 1 s. To provide an in-depth analysis of this phenomenon, a detailed parametric study is required, which is, however, beyond the scope of the current work.

Supplementary Materials

  • Supplementary material for this article is available at

    fig. S1. Sequence diagrams and properties of the presented MRI pulse sequences.

    fig. S2. Mechanical and NMR relaxation properties of the engineered particles.

    movie S1. Particle position measurements.

    movie S2. Particle velocity measurements.

    movie S3. Granular shock wave measurements.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Sequence diagrams and properties of the presented MRI pulse sequences.
    • fig. S2. Mechanical and NMR relaxation properties of the engineered particles.

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1. (.mp4 format). Particle position measurements.
    • movie S2 (.mp4 format). Particle velocity measurements.
    • movie S3 (.mp4 format). Granular shock wave measurements.

    Files in this Data Supplement:

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