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README
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Dataset for:
"Self-organization of bubbles into spatiotemporally regular patterns in vertically vibrated 3D gas-fluidized granular beds"

Authors:
Benjamin Rahimian1,2, Melis Özdemir1, Nick Hildebrandt3, Swantje Pietsch-Braune3, Stefan Benders1, Stefan Heinrich3, Alexander Penn1*

1 Institute of Process Imaging, Hamburg University of Technology, Hamburg, Germany
2 Centre for Nature-Inspired Engineering and Department of Chemical Engineering, University College London, London, United Kingdom
3 Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Hamburg, Germany

Benjamin Rahimian: benjamin.rahimian.24@ucl.ac.uk (ORCID: 0009-0007-6785-8887)
Melis Özdemir: melis.oezdemir@tuhh.de (ORCID: 0009-0006-6067-800X )
Nick Hildebrandt: nick.hildebrandt@tuhh.de (ORCID: 0009-0002-4837-1006 )
Swantje Pietsch-Braune: swantje.pietsch@tuhh.de (ORCID: 0000-0003-4459-4771)
Stefan Benders: stefan.benders@tuhh.de (ORCID: 0000-0002-9823-1928)
Stefan Heinrich: stefan.heinrich@tuhh.de (ORCID: 0000-0002-7901-1698)
*Corresponding author: Alexander Penn (alexander.penn@tuhh.de) (ORCID: 0000-0001-5596-6310)

DOI of this dataset      : https://doi.org/10.15480/882.17457
Data collected at        : Hamburg University of Technology (TUHH)

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1. GENERAL INFORMATION
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This dataset accompanies the publication listed above. It contains real-time MRI data of a vertically vibrated, 3D gas-fluidized granular bed, together with the processed data underlying the figures of the paper.

To keep the deposit at a manageable size, only one experimental condition is included (reconstructed MRI for three slices). The complete experimental dataset (all conditions) and the CFD-DEM simulation data are available from the corresponding author on request (see Sections 11 and 12).

The single condition deposited here is: H28dp_f6Hz 
Acquisition date of the deposited scans: 2026-01-08.

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2. DATA OVERVIEW
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For the single deposited condition, three slices are provided:
  - one horizontal (transversal) slice, and
  - two perpendicular central vertical slices.

For each slice, the dataset includes:
  - reconstructed MR images as PNG sequences (in MRI_Scans/), and
  - the scanner source files: raw k-space and reconstructed data (in MRI_Raw_Data/).
The PNGs in MRI_Scans/ are derived from the reconstructed (.rec) data in MRI_Raw_Data/.

In addition, the processed data underlying Figures 2 and 4 are included as spreadsheets.

CFD-DEM simulation data is large and is not included here; it is available on request (see Section 11).

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3. TOP-LEVEL CONTENTS
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  README.txt          : this file
  MRI_Scans/          : reconstructed images (PNG)
  MRI_Raw_Data/       : scanner source files (.log/.par/.rec/.raw) per slice
  Figure2_data.xlsx   : data for Figure 2a (bubble formation rate f_b, FFT)
  Figure4_data.xlsx   : data for Figure 4 (alternation coefficient alpha)
  MRI_bubble_pattern_analysis.m : MATLAB analysis script (FFT + alternation coefficient)

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4. DIRECTORY STRUCTURE
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MRI_Scans/
  HXdp_fYHz/                               (one folder per condition)
    Horizontal_Slice/
      HXdp_fYHz_horizontal_frames/         PNG sequence

    Vertical_Slice/
      HXdp_fYHz_vertical_1_frames/         PNG sequence, vertical plane 1

      HXdp_fYHz_vertical_2_frames/         PNG sequence, vertical plane 2

MRI_Raw_Data/                              (scanner source files for the same single deposited condition)
  HXdp_fYHz_horizontal_raw/
    H28dp_f6Hz_horizontal.par
    H28dp_f6Hz_horizontal.rec
 
 HXdp_fYHz_vertical_1_raw/
    H28dp_f6Hz_vertical1.par
    H28dp_f6Hz_vertical1.rec
  HXdp_fYHz_vertical_2_raw/
    H28dp_f6Hz_vertical2.par
    H28dp_f6Hz_vertical2.rec

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5. FOLDER AND FILE NAMING
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Folder naming: HXdp_fYHz
  X  = bed height in particle diameters dp
       (X = 28 -> H = 33.3 mm ; X = 47 -> H = 54.5 mm)
  Y  = vibration frequency in Hz (Y = 3 ... 9, in 1 Hz steps)

Slice labels:
  horizontal   = transversal slice
  vertical_1   = central vertical plane 1
  vertical_2   = central vertical plane 2 (perpendicular to plane 1)

PNG frames: 600 consecutive frames per measurement, in temporal order.

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6. MRI RAW DATA FILE TYPES (MRI_Raw_Data/)
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The files in MRI_Raw_Data/ are in the native Philips MR format, exactly as exported from the scanner. There are two file types:

  .rec  Philips REC file. Reconstructed image pixel data. The frames were later subtracted using a python code with numpy and OpenCV.
  .par  Philips PAR file. It lists the general scan parameters (sequence, field of view, acquisition matrix, TR/TE, flip angle, number of slices and dynamics, etc.)

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7. IMAGE / ACQUISITION DETAILS
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Format            : PNG (reconstructed images)
Slices            : one horizontal (transversal) slice; two perpendicular central vertical planes
Frame rate (real) : horizontal 33.3 fps ; vertical 30.2 fps 
Frames per run    : 600
Sequence          : gradient echo, CS-SENSE reconstruction
Scanner           : 3 T large-bore vertical MRI 
Signal detection hardware: 32-channel radiofrequency receive coil (24 mm diameter)

Horizontal slice:
  position    : 20 mm above distributor (H = 33.3 mm bed) ;
                    30 mm above distributor (H = 54.5 mm bed)
  FOV         : 150 x 150 mm
  slice thick : 10 mm
  recon res   : 2.34 x 2.34 mm (from 2.34 x 6 mm)
  TE/TR/angle : 1.1 ms / 2.24 ms / 15 deg

Vertical slices:
  FOV         : 116 x 340 mm
  slice thick : 10 mm
  recon res   : 1.93 x 1.93 mm (from 4.05 x 4 mm)
  TE/TR/angle : 1.1 ms / 2.14 ms / 15 deg

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8. FIGURE DATA FILES
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Both spreadsheets contain one row per condition and cover all measured conditions.

Figure2_data.xlsx  -- Bubble formation rate f_b from FFT analysis.
    Columns:
    Folder name                  : matching folder in MRI_Scans/ (HXdp_fYHz)
    Bed height H/dp (-)           : bed height in particle diameters
    f_vib (Hz)                    : vibration frequency
    FFT peak frequency f_b (Hz)   : bubble formation rate in Hz
    Frequency ratio f_b/f_vib (-) : ratio of bubble formation rate to vibration frequency (dimensionless)

Figure4_data.xlsx  -- Alternation coefficient alpha.
    Columns:
    Folder name        : matching folder in MRI_Scans/ (HXdp_fYHz)
    Bed height H/dp (-) : bed height in particle diameters
    f_vib (Hz)          : vibration frequency
    Alpha (-)           : mean alternation coefficient (dimensionless)
    Alpha STD (-)       : standard deviation of alpha (dimensionless)
    Pattern             : observed pattern (e.g. No Pattern, 2-2 Pattern)

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9. ANALYSIS SCRIPT (MATLAB)
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The MATLAB script used for the image analysis in the publication is
included in the top level of this deposit:

MRI_bubble_pattern_analysis.m

It computes the bubble formation rate f_b (FFT analysis, Figure 2a) and
the alternation coefficient alpha (Dice-based analysis, Figure 4) from
the PNG image series in MRI_Scans/. As deposited, it is preconfigured
for the included condition (horizontal slice of H28dp_f6Hz).

Requirements: MATLAB (tested with R2023b), Image Processing Toolbox

Full details on usage, data structure, and citation are given in the
header of the script itself. If you use this code, please cite the
original publication (see Section 13).

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10. CONSTANT EXPERIMENTAL CONDITIONS (details in paper)
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  Vessel        : PMMA cylinder, D = 94 mm
  Particles     : poppy seeds, d = 0.9-1.35 mm, rho_s = 1165 kg/m^3, U_mf = 0.3 m/s
  Gas velocity  : U = 1.3 U_mf
  Vib amplitude : A_vib = 6 mm (fixed) 

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11. SIMULATIONS (CFD-DEM) -- available on request
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Raw simulation data is large and is not included in this repository. It is available from the corresponding author on request (Section 12). Note: the paper shows only selected snapshots, not the full image sequences.

Description:
  Unresolved CFD-DEM simulations with D, H, U, f_vib, A_vib, and gas properties set to the MRI experimental values. DEM parameters calibrated against bulk experimental measurements (simplified particle shape and size distribution).
Vibration is modeled by an oscillating gravitational acceleration:
      g = 9.81 + (2*pi*f_vib)^2 * A_vib * sin(2*pi*f_vib*t)

Conditions simulated for the self-organization mechanism:
  2-2 pattern     : H = 28 dp, f_vib = 6 Hz
  1-1:f/2 pattern : H = 47 dp, f_vib = 4 Hz
  1-1:f/4 pattern : H = 47 dp, f_vib = 7 Hz

Additional conditions to probe the influence of initial conditions, by varying the onset time of the g-oscillation:
  H = 28 dp, f_vib = 4 Hz
  H = 28 dp, f_vib = 5 Hz
  H = 28 dp, f_vib = 6 Hz

Numerical setup:
  Codes         : OpenFOAM (CFD) + LIGGGHTS (DEM), coupled via CFDEMcoupling
  Coupling      : unresolved; solver cfdemSolverPiso (PISO)
  Drag model    : Gidaspow (Ergun + Wen & Yu)
  Contact model : Hertz-Mindlin, non-linear spring-dashpot; elastic-plastic rolling friction
  CFD time step : 2.5e-4 s (CFL < 1)
  DEM time step : 2.5e-6 s (~10% of Rayleigh time)
  Sim duration  : 10 s total 
  Particles     : 3 discrete size classes, d32 = 1.17 mm
  Gas           : rho_f = 1.2 kg/m^3, nu_f = 1.5e-5 m^2/s (air, 20 C, atm.)

Full numerical setup and calibrated DEM parameters (incl. material constants, restitution and friction coefficients) are identical to those in (geometry differs):
  N. Hildebrandt et al., "Three-dimensional CFD-DEM simulations of vibrated
  fluidized beds validated by real-time MRI," Powder Technology 477 (2026)
  122468. DOI: 10.1016/j.powtec.2026.122468

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12. CONTACT / DATA ON REQUEST
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The full experimental dataset (all conditions) and the CFD-DEM simulation data
are available from the corresponding author on reasonable request.

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13. USAGE RIGHTS AND CITATION
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The data is published under CC BY-NC-ND 4.0 license.
The dataset can be cited via the DOI provided by TORE.
By using this data in your work, you agree to cite the original publication.