🔬 condensed matter

The flow deep within granular piles

This study challenges the conventional view that flow in granular piles is confined to the surface by providing direct evidence of continuous plastic flow deep within conical piles, where the flow direction transitions smoothly from vertical at the center to parallel at the periphery.

Original authors: Aqib Khan, Prabhu R Nott

Published 2026-05-29

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Aqib Khan, Prabhu R Nott

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a pile of sand, gravel, or sugar cones sitting on a table. For a long time, scientists and engineers believed a simple story about how these piles behave: when you pour more grains on top, they only slide down the very outer skin, like water running down a hill. They thought the giant, heavy core of the pile underneath was completely frozen, static, and solid, like a block of ice.

This paper, by Aqib Khan and Prabhu R Nott, tells a different story. They discovered that the entire pile is actually moving, not just the surface.

Here is how they figured it out and what they found, explained simply:

The "Magic" Experiment

To see inside the pile, the researchers built a special setup. They placed a clear glass plate on the floor and poured grains onto it to form a cone. Because the floor was see-through, they could look up from underneath and watch the grains at the very bottom of the pile.

They did a clever visual trick:

First, they built a pile using black glass beads.
Then, they started pouring white glass beads on top.

If the old idea were true (that only the surface moves), the white beads would just sit on top of the black ones, and the black ones at the bottom would stay exactly where they were.

What actually happened?
The white beads didn't just sit on top. They pushed the black beads down and forced them to slide outward toward the edges of the pile. Over time, the black core shrank and was eventually replaced by the white grains. This proved that the "frozen" core was actually flowing, slowly but surely, all the way to the bottom.

The Flow Pattern: A Gentle Slide

The researchers found that the movement isn't chaotic. It's a smooth, organized flow:

In the very center: The grains move straight down, like a gentle waterfall.
As you move toward the edge: The flow smoothly turns sideways, sliding out toward the rim of the pile.
At the bottom: The grains are sliding outward in a circle.

Think of it like a slow-motion lava lamp or a very thick syrup pouring onto a plate. The center goes down, and the edges spread out.

How Fast is it Moving?

The flow is incredibly slow deep inside the pile.

The Surface: Moves fast (like a quick slide).
The Deep Core: Moves very slowly. The researchers measured speeds as tiny as a few millionths of a millimeter per second.

They found a rule for how fast it moves: The bigger the pile, the slower the flow at the bottom. If you double the size of the pile, the speed at the bottom drops by four times. It's like trying to push a giant, heavy carpet; the bigger it is, the harder it is to get the center to budge.

What Changes the Flow?

The team tested different things to see what made the flow faster or slower:

Roughness: If the floor under the pile is rough (like sandpaper), the grains get stuck more, and the flow slows down significantly.
Stickiness: If the grains are "stickier" or more frictional (like mustard seeds or sand compared to smooth glass beads), the flow slows down even more. However, even with these sticky grains, the flow still happens deep inside; it just takes much longer.

Why Does This Matter?

The paper argues that this changes how we understand granular materials (sand, grain, rocks).

No "Frozen" Cores: There is no such thing as a completely static core in a flowing pile. The whole thing is in a state of "plastic flow," meaning it's constantly rearranging itself, even if it looks solid.
Stress is Different: Because the whole pile is moving, the pressure at the bottom isn't just the weight of the pile sitting still; it's influenced by this slow, continuous movement.
Real World Connection: The authors mention this helps us understand things like landslides and avalanches. Just as a small disturbance can cause movement deep inside a grain pile, small tremors on a hillside might cause deep deformation that leads to a landslide, rather than just the surface sliding off.

The Bottom Line

The paper uses clear experiments and computer simulations to prove that when you pour grains onto a pile, the movement penetrates deep into the center. The entire pile is a slow, flowing river, not a solid mountain with a sliding skin. This discovery challenges old ideas and suggests that even "solid" piles of sand or grain are constantly shifting and adjusting deep beneath the surface.

Technical Summary: The Flow Deep Within Granular Piles

Problem Statement
Granular piles are ubiquitous in nature and industry, yet their internal mechanics remain partially misunderstood. The prevailing paradigm posits that when grains are deposited onto a conical pile, flow is confined to a thin, inertial layer at the free surface, while the bulk of the pile remains a static, solid-like core that grows through accretion. This assumption is supported by the observation that piles maintain their shape after deposition stops. However, this view is challenged by continuum plasticity theories, which suggest yield criteria are satisfied throughout the pile, and by experimental observations showing that the stress distribution at the base depends on the deposition method (e.g., funnel vs. distributed rain). Furthermore, geophysical phenomena such as landslides suggest that disturbances can induce deep deformation. While surface flow and quasi-two-dimensional sublayers have been studied, direct experimental evidence of flow deep within the bulk of three-dimensional conical piles has been lacking, primarily due to the opacity of granular materials and the limitations of non-invasive imaging.

Methodology
The authors employed a dual approach combining direct experimental imaging and particle dynamics simulations to investigate the kinematics of steady-flowing conical piles.

Experimental Setup: Experiments were conducted on piles formed by pouring grains (glass beads, mustard seeds, and beach sand) from a hopper onto a transparent acrylic disk of diameter $D$ . The system was allowed to reach a steady state where the inflow rate equaled the efflux rate at the periphery.
- Imaging: A video camera positioned beneath the transparent base captured the flow at the bottom of the pile.
- Visualization: To demonstrate displacement, piles were initially formed with grains of one color, followed by the deposition of contrasting colored grains.
- Quantification: Particle Image Velocimetry (PIV) was used on the recorded movies to extract radial velocity profiles ( $v_r$ ) at the base. Measurements were averaged over time and annular bins to ensure accuracy.
- Variables: The study varied the pile diameter ( $D$ ), hopper orifice diameter ( $\xi$ ), and grain properties (friction, size). Roughness of the base was also manipulated by creating spherical cap cavities in the acrylic disk.
Simulations: Discrete Element Method (DEM) simulations were performed using the LIGGGHTS package. The simulations utilized Hertz-Mindlin contact models with rolling friction to replicate the experimental conditions (glass beads). The simulations provided full 3D fields of velocity, stress, density (solids fraction), and the inertia number ( $I$ ).

Key Contributions and Results

Evidence of Deep Plastic Flow: The study provides the first unambiguous experimental evidence that flow penetrates the entire depth of a growing granular pile. The color-displacement experiments revealed that grains from the original pile are displaced radially outward and downward, reaching the base. This refutes the hypothesis of a static core.
Velocity Field Characteristics:
- Direction: The flow direction varies smoothly from vertical at the symmetry axis to parallel to the surface at the periphery, resembling a liquid jet impinging on a plate.
- Magnitude and Scaling: The radial velocity at the base ( $v_r$ ) is measurable across the entire radius, though it decreases significantly toward the center. The data suggests a scaling law where the velocity magnitude decreases as the inverse square of the pile diameter ( $D^{-2}$ ).
- Profile Structure: The scaled velocity profile exhibits three distinct regions: a sharp drop near the edge (Region I, corresponding to the surface layer impact), an exponential decay in the intermediate zone (Region II, characteristic of slow shearing), and a faster-than-exponential decay to zero at the core (Region III).
Influence of Friction and Roughness:
- Increasing grain friction (e.g., using mustard seeds or sand instead of glass beads) or base roughness reduces the magnitude of the velocity, particularly in the core. However, the qualitative nature of the flow field (the existence of deep flow) remains unchanged.
- Rougher bases increased the angle of repose and reduced slip, leading to lower velocities but preserving the flow structure.
Rheological Regime: Analysis of the inertia number ( $I$ ) from simulations indicates that, except for the thin inertial surface layer, the flow throughout the bulk is in the quasistatic regime ( $I \ll 1$ ). This implies that grain inertia is irrelevant to the subsurface dynamics.
Stress Implications: The simulations show that the basal stress profile during flow is nearly identical to that of a static pile, including the characteristic dip under the apex. This suggests that the stress state in static piles is plastic rather than elastic.

Significance and Claims
The authors claim that their findings fundamentally alter the understanding of granular kinematics by demonstrating that "solid-like" regions in granular piles are actually undergoing continuous plastic flow (creep). This has several specific implications:

Continuum Modeling: The presence of flow throughout the pile reinforces the necessity for non-local plasticity models to accurately describe granular rheology, as local models fail to capture the long-range correlations observed in the velocity fields.
Stress Transmission: The similarity between flow and static stress profiles suggests that stress transmission in gravity-deposited granular assemblies occurs in a plastic state, potentially resolving long-standing questions regarding the nature of stress in these systems.
Geophysical and Industrial Relevance: The results offer insight into geophysical phenomena like landslides and avalanches, where small surface disturbances can elicit responses deep within the medium. Similarly, the findings are relevant to industrial processes involving hoppers and bunkers, suggesting that flow may not be restricted to surface layers in these configurations either.

The paper concludes with a caveat that these results apply to non-cohesive granular media; cohesive forces (e.g., in moist sand) may weaken or eliminate this deep flow.