4D Synchrotron X-Ray Multi Projection Imaging (XMPI) for studying multiphase flow dynamics and flow instabilities in porous networks

This paper demonstrates that synchrotron X-ray multi-projection imaging (XMPI) enables high-resolution, real-time 4D visualization of sub-second flow instabilities in porous media without the centrifugal artifacts of conventional tomography, thereby revealing critical limitations in current Lattice Boltzmann simulations regarding contact-line dynamics and boundary conditions.

The Gist

Imagine trying to watch a race car zoom around a track, but every time you try to take a photo, the car spins so fast it becomes a blur. Now, imagine that the "track" is a tiny, invisible maze made of glass, and the "car" is a drop of water trying to squeeze through it. This is the challenge scientists face when studying how liquids move through porous materials like soil, rock, or paper.

This paper introduces a revolutionary new way to watch this race in slow motion, in 3D, and in real-time, without spinning the track so fast that it breaks the rules of physics.

Here is the story of their discovery, broken down into simple concepts:

1. The Problem: The "Spinning Blur"

To see inside a solid object (like a rock or a piece of paper), scientists usually use X-ray tomography. Think of this like a CT scan at a hospital. To get a 3D picture, the object has to be rotated while X-rays take pictures from every angle.

However, the liquid moving inside these tiny pores moves incredibly fast—sometimes in just a few milliseconds. This is called a "Haines Jump." It's like a dam breaking: water builds up pressure at a narrow bottleneck, and then whoosh, it instantly floods the next chamber.

The Dilemma: To get a 3D picture of this, the old method required spinning the sample very fast. But spinning a wet sample that fast creates "centrifugal force" (like the force that pushes you to the side of a turning car). This force would actually push the water around, changing the very thing the scientists were trying to study. It's like trying to watch a dance by spinning the dancer so fast they fall over.

2. The Solution: The "Multi-Lens Camera"

The researchers, led by Patrick Wegele and Zisheng Yao, invented a new trick using a giant, super-powerful X-ray machine called a Synchrotron (think of it as the world's most powerful flashlight).

Instead of spinning the sample fast to get different angles, they used a clever optical trick called XMPI (X-ray Multi-Projection Imaging).

• The Analogy: Imagine you want to see a statue from the front and the side at the exact same time. Instead of walking around the statue, you hire two photographers standing at different angles, both snapping photos simultaneously.
• The Tech: They split the X-ray beam into two separate "beams" (like two flashlights) that hit the sample from different angles at the same time. Two high-speed cameras catch these images instantly.
• The Result: The sample only needs to rotate very slowly (like a lazy Susan). This means the water stays calm and moves naturally, but the scientists still get a full 3D movie of what's happening inside.

3. The Experiment: A "Glass City" of Water

To test this, they didn't use a messy rock. They used 3D printing to build a perfect, transparent city made of hollow glass balls connected by tiny tunnels.

• They pumped water into this city.
• They watched the water fight its way through the tunnels.
• They saw the "Haines Jumps" happen: the water would get stuck at a narrow throat, build up pressure, and then suddenly snap into the next room.

4. The "Computer vs. Reality" Showdown

The team also ran a computer simulation (a video game version of the experiment) to predict how the water would move. They used a famous physics model called the Shan-Chen Lattice Boltzmann method.

The Surprise:

• The Computer said: "The water will fill the rooms in this specific order, and it will happen very fast."
• The Real Experiment said: "Actually, the water filled the rooms in a slightly different order, and it took about 10 times longer."

Why the difference?
The computer model was too perfect. It assumed the walls of the tunnels were perfectly smooth. But in the real 3D-printed world, the walls had tiny bumps and roughness (like a real road vs. a smooth video game track). These tiny imperfections changed how the water stuck to the walls (contact angle) and how much pressure was needed to make the jump.

The computer also assumed the water supply was infinite, but in the real experiment, the water had to travel through a long, thin tube to get there, creating a "traffic jam" that slowed everything down.

5. Why This Matters

This study is a big deal for three reasons:

1. It sees the invisible: It allows us to watch "Haines Jumps" in 4D (3D space + time) without disturbing the flow.
2. It exposes the flaws: It shows us that our current computer simulations aren't perfect. They miss the tiny details of how water interacts with rough surfaces.
3. It bridges the gap: By combining this new "super-camera" with 3D printing, scientists can now build perfect test models to fix their computer simulations.

The Bottom Line:
This paper is like upgrading from a blurry, spinning security camera to a high-definition, multi-angle drone that can hover perfectly still. It lets us finally see the tiny, split-second battles between water and air inside porous materials, helping us build better fuel cells, cleaner oil recovery methods, and more efficient water filters.

Technical Summary

1. Problem Statement

Understanding multiphase flow dynamics in porous media (e.g., oil recovery, fuel cells, carbon storage) is critical, yet observing transient phenomena like Haines jumps (instantaneous pore filling events) remains a significant experimental challenge.

• Temporal Limitations: Haines jumps occur on sub-second to millisecond timescales. Conventional X-ray computed tomography (CT) requires sample rotation to acquire 3D data. To capture fast dynamics, high-speed rotation is needed, but this generates centrifugal forces that alter the fluid flow, rendering the experiment unrealistic.
• Resolution Trade-offs: Existing methods often sacrifice spatial resolution for temporal resolution or rely on assumptions of reversible flow (imbibition/drainage symmetry), which does not hold true for forced imbibition.
• Simulation Gaps: Numerical simulations (e.g., Lattice Boltzmann) often struggle to accurately capture contact-line dynamics and realistic boundary conditions, leading to discrepancies with experimental observations.

2. Methodology

The authors developed a novel experimental and computational framework to overcome these limitations.

A. Experimental Setup: Synchrotron XMPI

• Technique: The study utilizes Synchrotron X-ray Multi-Projection Imaging (XMPI) at the MAX IV Laboratory (ForMAX beamline).
• Principle: Instead of rotating the sample rapidly, the setup uses two angularly resolved X-ray beamlets (split from a single source using Si-111 and Ge-400 crystals) that illuminate the sample simultaneously from different angles (-17.0° and 30.7°).
• Sample Rotation: The sample undergoes only a slow, continuous rotation (12°/s). This minimizes centrifugal forces while providing the angular diversity needed for 4D reconstruction.
• Specimen: An additively manufactured (3D printed) homogeneous porous network consisting of hollow spheres (radius $r=0.100$ mm) connected by throats, fabricated from methacrylate-based resin.
• Flow Conditions: Forced imbibition of deionized water into an air-filled network at a constant flow rate ($Q=0.5$ ml/h), creating a creeping flow regime ($Re \approx 0.25$, $Ca \approx 5.0 \times 10^{-6}$).
• Imaging Specs: Two indirect X-ray microscopes capture data at 50 Hz with an effective pixel size of 1.3 µm.

B. Data Processing & 4D Reconstruction

• Preprocessing: Raw images undergo flat-field correction, stripe removal, and edge enhancement filtering to ensure consistency between the two cameras.
• Reconstruction Algorithm: The authors employed X-Hexplane, a deep-learning-based 4D reconstruction framework. Unlike traditional tomography requiring 180° scans per time step, X-Hexplane uses a tensorial representation and physics-informed projection approximations to reconstruct 3D dynamics at the same frame rate as the 2D acquisition (50 Hz) from ultra-sparse views.

C. Numerical Simulation

• Model: Multiphase Lattice Boltzmann (LB) simulations using the Shan-Chen model (D3Q19 lattice).
• Geometry: The simulation domain was generated directly from the binarized experimental synchrotron tomogram to capture printing defects and exact geometry.
• Boundary Conditions: Simulations were run with fixed pressure drops to match the experimental Reynolds and Capillary numbers, allowing for a direct comparison of filling sequences and timescales.

3. Key Contributions

1. Novel 4D Imaging Platform: Demonstrated the first successful application of XMPI to visualize non-repeatable, sub-second multiphase flow instabilities (Haines jumps) in opaque porous media without the artifacts caused by high-speed rotation.
2. High Spatiotemporal Resolution: Achieved 1.3 µm spatial resolution and 50 Hz temporal resolution (with potential for >10 kHz), enabling the observation of pore-scale events previously unresolvable in 3D.
3. Experimental vs. Simulation Benchmarking: Provided a rigorous comparison between real-world imbibition and Shan-Chen LB simulations, highlighting specific limitations in current simulation methods regarding contact-line dynamics and boundary conditions.
4. Deep Learning Reconstruction: Validated the use of X-Hexplane for reconstructing dynamic 3D flows from sparse, multi-projection data, bypassing the need for full angular scans per time step.

4. Results

• Flow Dynamics: The experiment successfully visualized the step-wise filling of pores (Haines jumps). The imbibition front progressed asymmetrically, starting from the sides (pores A6, A7) and moving inward.
• Timescale Discrepancy:
  • Simulation: Pore filling occurred extremely fast ($\sim$0.1 s for the first layer) due to the fixed pressure boundary condition.
  • Experiment: Filling took significantly longer ($\sim$1.6 s for the first layer). This was attributed to supply limitations (constant flow rate vs. fixed pressure) and the high advancing contact angle ($\theta \approx 84^\circ$), which reduced the driving capillary pressure.
• Filling Order: While both simulation and experiment showed a similar initial sidewise filling pattern, the subsequent sequence diverged. The simulation filled pores A9, A1, A2, A3 next, whereas the experiment filled A8, A4, A9 first. This was attributed to the binarization process removing micro-scale surface roughness and resin residues, altering local threshold pressures.
• Pressure Analysis: Calculations confirmed that during Haines jumps, capillary pressure drops ($\Delta p_c$) dominate viscous losses ($\Delta p_v$) by 2–4 orders of magnitude, consistent with theoretical expectations for intersecting hollow-sphere geometries.
• Event Duration: While some filling events approached the millisecond scale, the observed durations were often limited by the bulk liquid supply rate rather than intrinsic pore-scale dynamics.

5. Significance and Conclusion

This study establishes Synchrotron XMPI as a unique and powerful platform for bridging the gap between pore-scale experiments and simulations.

• Scientific Impact: It provides the first direct, non-invasive 4D visualization of Haines jumps in a controlled, homogeneous network, revealing the complex interplay between geometry, contact angle, and flow instabilities.
• Methodological Advance: It proves that high-fidelity 4D reconstruction is possible without the centrifugal artifacts of traditional high-speed CT, opening new avenues for studying fast transient phenomena in opaque media.
• Future Outlook: The authors identify that future iterations of the setup should incorporate reservoir-based designs to decouple supply limitations from pore-scale dynamics, allowing for the observation of intrinsic millisecond-scale Haines jumps. Additionally, refining simulation boundary conditions and capturing wall microstructure are essential for improving predictive accuracy.

In summary, the paper demonstrates that combining advanced synchrotron imaging, additive manufacturing, and deep learning reconstruction offers a transformative approach to understanding multiphase flow instabilities, providing critical data to validate and improve numerical models of porous media flow.