Granular clogging across gravities: a unified scaling

By identifying the granular Bond number as the key control parameter, this study unifies contradictory findings on granular clogging across different gravitational environments and establishes a predictive scaling law for flow behavior in low-gravity space missions.

The Gist

Imagine you are trying to pour a bag of sand through a small hole in the bottom of a bucket. On Earth, this is usually easy. The sand flows like water, and the bucket empties quickly. But what happens if you take that same bucket to the Moon, where gravity is much weaker?

For decades, scientists and engineers have been arguing about the answer. Some thought the sand would flow better in low gravity because it's lighter. Others thought it might get stuck. The truth, according to this new study, is a bit more surprising: The sand is much more likely to get stuck (clog) on the Moon than on Earth.

Here is the story of how the researchers solved this mystery, explained simply.

The Problem: The "Stuck Salt" Dilemma

We've all experienced this: you shake a salt shaker, and the salt just won't come out. It's because the tiny grains have formed a little "bridge" or arch over the hole, locking everything in place. This is called clogging.

On Earth, gravity is strong. It pulls the salt grains down hard, breaking those little bridges and keeping the flow going. But on the Moon, gravity is only 1/6th as strong. On Mars, it's about 1/3rd.

Scientists used to think: "If gravity is weaker, the grains are lighter, so they should flow easier."
But other scientists thought: "If gravity is weaker, the grains might stick together more easily."

The result? Confusing, contradictory data. Some experiments said low gravity helps flow; others said it stops it.

The Missing Piece: The "Stickiness" vs. "Weight" Battle

The researchers realized that looking at gravity alone was like trying to judge a tug-of-war by only looking at one team. You need to see both sides.

They introduced a new concept called the Granular Bond Number. Think of it as a scoreboard for a tug-of-war between two forces:

1. Gravity (The Puller): This tries to drag the grains down through the hole.
2. Cohesion (The Sticker): This is the "stickiness" between grains. It comes from tiny forces like static electricity, van der Waals forces (molecular attraction), or even tiny amounts of moisture.

The Analogy:
Imagine the grains are people holding hands.

• On Earth: The "Gravity" team is a giant pulling them down. Even if the people hold hands (stickiness), the giant pulls them apart easily. They flow.
• On the Moon: The "Gravity" team is now a small child. The "Stickiness" team (the people holding hands) is suddenly much stronger than the child. The grains stick together, form clumps, and block the hole.

The researchers found that on Earth, gravity usually wins. But on the Moon, stickiness often wins.

The Experiment: The "Space Elevator"

To test this, the team didn't just simulate gravity; they actually went to space (sort of). They used a special tower in Germany called the GraviTower.

Think of this tower as a giant elevator that shoots a capsule up and then drops it. But instead of just falling, the capsule is pushed and pulled by motors to create a "fake" gravity.

• They could make the inside of the capsule feel like it was on Earth.
• They could make it feel like it was on Mars.
• They could make it feel like it was on the Moon.

Inside this capsule, they built a special hourglass with a vacuum chamber (to remove air) and filled it with different types of "Moon dirt" (regolith simulants). They watched how fast the dirt flowed through holes of different sizes.

The Big Discovery

The results were dramatic.

• Basalt (Rough rocks): Flowed fine on Earth and the Moon. It wasn't very "sticky."
• JSC-1A (Fine Moon dirt): Flowed easily on Earth, but clogged constantly on the Moon.
• LHS-2E (Super fine dirt): Clogged on Earth, and clogged even worse on the Moon.

They found that in low gravity, the "critical size" of the hole needed to keep the sand flowing had to be 10 times larger than on Earth. If you have a hole that works perfectly on Earth, it will likely be a disaster on the Moon.

The Solution: A New Universal Rule

The researchers didn't just stop at "it gets stuck." They created a Universal Map (a state diagram).

Instead of asking, "How does gravity affect this?", they asked, "What is the ratio of Stickiness to Weight?"

By using their new "Bond Number" rule, they could take data from Earth and accurately predict what would happen on Mars or the Moon. It's like having a translation guide that turns "Earth Physics" into "Moon Physics."

Why Does This Matter?

This isn't just about sand in a bucket. It's about the future of space exploration.

• Mining: If we want to mine asteroids or the Moon for water or metals, we need to move the dirt. If our machines clog, the mission fails.
• Building: If we want to build habitats out of Moon dirt, we need to know how it flows.
• Safety: If a lander's fuel tank or life-support system relies on granular materials, we can't afford for them to jam.

The Takeaway

The next time you pour a bag of flour or sand, remember: Gravity isn't just a force; it's a referee. On Earth, the referee is strong and keeps the game moving. On the Moon, the referee is weak, and the players (the grains) start huddling together, stopping the game.

This paper gives us the rulebook to understand that huddle, ensuring that when we return to the Moon and Mars, our machines keep flowing and our astronauts stay safe.

Technical Summary

1. Problem Statement

Granular materials (e.g., planetary regolith) are ubiquitous in the Solar System and critical for future space exploration (landing, drilling, resource extraction). A fundamental challenge in granular processing is clogging: the spontaneous arrest of flow through a constriction (orifice) due to the formation of arch-like structures.

While clogging is well-studied on Earth, its behavior in low-gravity environments (Moon, Mars, asteroids) remains poorly understood and contradictory. Previous studies yielded conflicting results:

• Some suggested gravity has no significant effect on clogging probability ($P_c$).
• Others suggested low gravity increases clogging (due to cohesion dominance).
• A third line of reasoning suggested low gravity might decrease clogging (due to reduced packing density and confinement pressure).

The lack of a universal predictive law hinders the design of reliable space hardware (e.g., hoppers, hourglasses) for In Situ Resource Utilization (ISRU). The core issue is that gravity alone is not the appropriate control parameter; the competition between gravity and intrinsic material cohesion was previously unquantified in a scalable way.

2. Methodology

The authors conducted experiments using an active drop tower (GraviTower Bremen Pro) to simulate true reduced gravity environments.

• Experimental Setup: A quasi-2D hourglass was placed inside a vacuum chamber within the drop tower capsule. The hourglass featured two hopper angles ($\alpha = 60^\circ$ and $120^\circ$) and variable orifice diameters ($D$) ranging from 1 mm to 20 mm.
• Gravity Conditions: Experiments were performed under Earth gravity ($g_E$), simulated Mars gravity ($g_M \approx 0.38g_E$), and simulated Moon gravity ($g_L \approx 0.165g_E$). The drop tower provided stable partial gravity phases lasting ~2.3s (Moon) and ~2.9s (Mars).
• Materials: Three lunar regolith simulants were tested to represent varying degrees of cohesion and particle size:
  1. Crushed Basalt: Coarse, low cohesion ($d_{50} \approx 183 \, \mu m$).
  2. JSC-1A: Fine-grained simulant ($d_{50} \approx 57.3 \, \mu m$).
  3. LHS-2E: Highly cohesive fine-grained simulant ($d_{50} \approx 54.5 \, \mu m$).
• Characterization of Cohesion: To quantify the "missing" control parameter, the authors measured the Granular Bond Number ($B$). Instead of theoretical van der Waals calculations (which fail for heterogeneous, non-spherical particles), they used an in-bulk fluidization method:
  • They measured the pressure drop hysteresis ($\Delta P_{up} - \Delta P_{down}$) during fluidization.
  • This hysteresis represents the granular tensile strength ($\Sigma_t$), or the cohesive force required to break interparticle bonds.
  • $B$ was defined as the ratio of this cohesive stress to the weight of the fluidized portion of the bed: $B = \frac{\Sigma_t}{\delta(mg/A)}$.

3. Key Contributions

1. Identification of the Control Parameter: The paper establishes the Granular Bond Number ($B$) as the unifying dimensionless parameter governing granular clogging. $B$ quantifies the ratio of cohesive forces to gravitational forces.
2. Unified Scaling Law: The authors propose a scaling law that collapses data from different materials and gravitational environments into a single state diagram. This resolves previous contradictions by showing that clogging depends on the relative balance of cohesion and gravity, not gravity alone.
3. Experimental Validation in True Low Gravity: Unlike previous studies using 2D analogues or centrifuges, this study utilized true reduced gravity (Moon/Mars) in a vacuum environment, confirming that low gravity significantly alters flow dynamics for cohesive materials.

4. Key Results

• Increased Clogging in Low Gravity: Contrary to some previous predictions, the experiments revealed a substantial increase in clogging probability under reduced gravity. For a given material and orifice size, $P_c$ increased significantly as gravity decreased.
• Shift in Critical Orifice Size: The critical orifice-to-particle size ratio ($D/d_{50}$) below which clogging occurs shifted by approximately one order of magnitude between Earth and Moon gravity. Materials that flowed freely on Earth clogged on the Moon.
• Material Dependence: The magnitude of the shift depended on the intrinsic cohesion of the material:
  • Basalt (Low Cohesion): Showed minimal change in flow behavior between Earth and Moon.
  • JSC-1A (Medium Cohesion): Flowed on Earth but clogged frequently on the Moon.
  • LHS-2E (High Cohesion): Clogged on Earth and clogged even more severely on the Moon.
• The State Diagram: By plotting clogging probability ($P_c$) against the orifice-to-particle size ratio ($D/d_{50}$) and the Granular Bond Number ($B$), all data points collapsed onto a single curve.
  • The transition from free flow to clogging is modeled by a cumulative distribution function where the transition point ($P_{50}$) scales logarithmically with $B$: $P_{50}(B) = a \cdot \log_{10}(B) + b$.
  • A threshold exists around $B \approx 1$, where materials transition from gravity-dominated to cohesion-dominated behavior. In low gravity, this threshold is reached at larger particle diameters.

5. Significance

• Predictive Framework for Space Missions: The study provides a general framework for predicting granular flow behavior in any gravitational environment. This is critical for the design of future missions to the Moon, Mars, and asteroids, specifically for systems involving regolith handling, fueling, and construction.
• Resolution of Scientific Discrepancies: The paper explains why previous studies reported contradictory results: studies using non-cohesive or large particles (where $B \ll 1$ even in low gravity) saw no effect, while studies with fine/cohesive particles (where $B$ becomes significant in low gravity) observed increased clogging. The Bond number unifies these observations.
• Broader Applications: The methodology and scaling law are not limited to space. They offer a robust model for understanding highly cohesive granular materials in terrestrial industries such as pharmaceuticals, food processing, and construction, where flow stability is often compromised by cohesion.

In conclusion, the paper demonstrates that gravity reduction shifts the balance of forces, making cohesive interactions dominant. By rescaling Earth-based data using the Granular Bond Number, engineers can accurately predict and mitigate clogging risks in extraterrestrial environments.