Investigation of cohesive particle deagglomeration in homogeneous isotropic turbulence using particle-resolved DNS

This study employs particle-resolved direct numerical simulations to investigate cohesive particle agglomerate deagglomeration in homogeneous isotropic turbulence, revealing that erosion-driven breakage is the dominant mechanism governed by strain-dominated flow structures and providing data to develop physics-informed breakup kernels for coarser simulation models.

The Gist

Imagine a giant, fluffy snowball made of thousands of tiny, sticky marbles. Now, imagine throwing this snowball into a violent, swirling storm of wind. What happens? Does it shatter instantly like glass? Does it slowly shed snowflakes one by one? Or does it just spin around and stay whole?

This is exactly what the researchers in this paper investigated, but instead of snow and wind, they studied microscopic dust clumps (agglomerates) and turbulent gas flows. They used a super-powerful computer simulation to watch these tiny clumps break apart in real-time, particle by particle.

Here is a simple breakdown of their journey and what they found:

1. The Setup: A Digital Wind Tunnel

The researchers built a virtual, invisible box filled with air that is churning chaotically—like a blender on high speed, but with no blades. Inside this box, they dropped a single, perfectly round clump made of 500 tiny, dry, sticky spheres.

• The "Sticky" Factor: These spheres stick together because of invisible molecular forces (called van der Waals forces), similar to how a piece of tape sticks to a wall. The researchers tested three levels of stickiness: slightly sticky, very sticky, and super-sticky.
• The "Storm" Factor: They also tested three different "wind speeds" (turbulence intensities) to see how hard the air pushed against the clump.

2. The Super-Method: Seeing the Invisible

Most computer models treat a clump of dust like a single, solid marble. They guess how the wind hits it. But this team did something different: Particle-Resolved Simulation.

Think of it like this:

• Old Way: Watching a car drive through a crowd from a helicopter. You see the car, but you can't see how individual people bump into the bumper or get pushed aside.
• This Paper's Way: Putting a camera on every single person in the crowd. They could see exactly how the wind squeezed between the tiny gaps of the clump, how it pushed one specific marble, and how that push rippled through the whole structure.

They found that the wind doesn't hit the clump evenly. It creates "hot spots" of high pressure and stretching in specific tiny gaps between the marbles.

3. What Actually Happens? (The Results)

A. It's a Slow Peel, Not a Smash
When the wind hit the clump, it didn't explode into a million pieces at once. Instead, it acted like a slow peeling. The wind would grab a few loose marbles on the outside and pull them off. Then, it would grab a few more.

• The "Erosion" Effect: The main way the clump broke was through erosion. The outer layers were worn away bit by bit, rather than the whole thing snapping in half.

B. The "Sticky" vs. The "Storm"

• Stronger Wind = Faster Breakup: When the turbulence was fiercer, the clump fell apart much faster.
• Stickier Clumps = Slower Breakup: When the marbles were super-sticky, the clump held together longer, even in strong winds.
• The Stretch: Interestingly, before breaking, the clump sometimes got stretched out like taffy by the wind, getting longer and thinner before finally snapping.

C. The Direction of the Break
This was a key discovery. When a piece of the clump finally broke off, where did it go?

• It didn't fly off randomly.
• It didn't fly off because the air was spinning (vortex).
• It flew off along the "Stretch Line." Imagine pulling a piece of taffy in two opposite directions. The break happens along the line where you are pulling. The researchers found that the broken pieces flew off along the specific plane where the wind was stretching and compressing the clump the most. It's like the clump knew exactly where it was weakest and broke there.

D. The "Sticky Number"
The researchers created a simple formula (a "power law") to predict how fast a clump would break.

• If you know how sticky the particles are and how rough the wind is, you can predict the breakup speed.
• The stickier the clump, the slower it breaks. The formula showed a clear, predictable relationship: More stickiness = Much slower breakup.

4. Why Does This Matter? (According to the Paper)

The paper doesn't talk about curing diseases or building new engines directly. Instead, it says this research is like writing a better instruction manual for other computer programs.

Currently, many engineers use simplified computer models that treat dust clumps as simple balls. These models often get the breakup wrong because they can't see the tiny gaps and forces.

• The Goal: By using this super-detailed simulation to understand exactly how and why the clumps break, the researchers can create better, simpler rules (called "kernels") for those other, faster computer programs.
• The Result: This will help engineers predict how dust behaves in things like dry powder inhalers (for medicine) or how aerosols move in the atmosphere, but only by making the underlying math more accurate.

Summary

The paper is a deep dive into how a ball of sticky marbles falls apart in a chaotic wind tunnel. They discovered that:

1. It breaks slowly by peeling off the outside (erosion), not by shattering.
2. It breaks along the lines where the wind is stretching it the most.
3. The stickier the marbles, the longer it takes to break.
4. This detailed view helps us write better, simpler rules for predicting dust behavior in the real world.

Technical Summary

Technical Summary: Investigation of Cohesive Particle Deagglomeration in Homogeneous Isotropic Turbulence

Problem Statement
Micrometer-sized particles suspended in gas flows frequently form agglomerates due to cohesive forces (e.g., van der Waals) that exceed gravitational forces. These structures are dynamic, subject to fragmentation by fluid stresses in natural and industrial processes, such as aerosol transport and pharmaceutical dry powder inhalation. While experimental studies exist, they often focus on integral quantities (e.g., outlet size distributions) rather than the detailed mechanics of individual breakup events due to the complexity of capturing fluid-particle and particle-particle interactions. Numerical simulations offer an alternative but face challenges: fully resolved methods are computationally prohibitive for many applications, while point-particle Euler–Lagrange approaches often rely on empirical constitutive models that may lack accuracy in dense, interacting particle systems like agglomerates. There is a need for high-fidelity data to inform and validate more efficient, coarse-grained breakup models.

Methodology
The study employs a Particle-Resolved Direct Numerical Simulation (PR-DNS) approach coupled with a Discrete Element Method (DEM). This framework resolves the fluid-particle interface and all turbulent scales without relying on point-particle approximations.

• Fluid Solver: An immersed boundary (fictitious domain) method is used within the OpenFOAM framework to solve the incompressible Navier-Stokes equations. A linear forcing term is applied to maintain statistically stationary homogeneous isotropic turbulence (HIT). The method includes dynamic local mesh refinement, ensuring the particle diameter is resolved by eight cells in each direction.
• Particle Solver: The LIGGGHTS solver tracks particle trajectories in a Lagrangian frame. Inter-particle interactions are modeled using a soft-sphere contact model (Hertzian elasticity, damping, tangential friction, and rolling friction) coupled with a van der Waals cohesion model based on the Hamaker constant.
• Setup: Simulations are conducted in a triply periodic box containing a single agglomerate composed of 500 monodisperse, spherical silica particles ($d_p \approx 0.97 \, \mu m$). The study varies three flow Reynolds numbers ($Re_\lambda = 30, 43, 64$) and three levels of particle cohesion (Hamaker constants $H$, $10H$, and $100H$), resulting in nine distinct cases.

Key Contributions

1. First PR-DNS of Agglomerate Deagglomeration in HIT: To the authors' knowledge, this is the first study to utilize particle-resolved DNS combined with DEM to investigate the breakup of cohesive agglomerates in forced homogeneous isotropic turbulence.
2. Mechanistic Insight into Breakage: The study provides detailed visualization and analysis of local flow structures (vortices, strain rates) and fluid stresses acting on individual particles, which are typically unresolved in point-particle models.
3. Validation of Breakup Kernels: The results offer high-fidelity data on fragment size distributions, breakup modes, and ejection directions, intended to inform the development of physics-informed breakup kernels for computationally efficient Euler–Lagrange and Euler–Euler simulations.

Results

• Breakup Mechanism: Analysis of local flow structures reveals that particle erosion initiates and propagates primarily in strain-dominated regions. The breakup process is characterized as erosion-driven, where the agglomerate gradually disintegrates into smaller fragments and single particles, rather than shattering into large, equally sized pieces.
• Influence of Parameters: Increasing the flow Reynolds number accelerates and intensifies fragmentation, while increasing the Hamaker constant (cohesion) suppresses it. The fragmentation ratio (FR) evolves from 0 to 1 depending on these parameters.
• Fragment Size Distribution: The cumulative distribution functions (CDFs) of fragment sizes show a continuous evolution from the initial large agglomerate to medium-sized clusters and finally to single primary particles. No significant differences in the temporal development of the distribution shape were found between cases where significant breakage occurred, only in the rate and extent.
• Ejection Direction: A novel analysis of fragment detachment reveals that the center-of-mass velocity vectors of detaching fragments align strongly with the local deformation plane spanned by the most extensional ($e_1$) and most compressive ($e_3$) eigenvectors of the strain-rate tensor. This indicates that breakage is governed by the interplay of flow stretching and compression, rather than rotational motion (vorticity).
• Breakage Rate: The time-averaged breakage rate exhibits an inverse relationship with the adhesion number ($Ad$). By introducing a modified adhesion number ($Ad/Re_p$), the authors establish a power-law decay relationship ($BR \propto (Ad/Re_p)^c$) that aligns with general trends in the literature.

Significance and Claims
The paper claims that the particle-resolved simulation framework successfully captures the complex interplay between turbulence-induced stresses and cohesive forces, providing a level of physical detail unattainable by point-particle approaches. The authors assert that the identified mechanisms—specifically the dominance of strain-driven erosion and the alignment of fragment ejection with the deformation plane—offer critical insights for developing more accurate breakup kernels. These kernels are essential for improving less-detailed, computationally efficient simulation methods (such as point-particle Euler–Lagrange or Euler–Euler approaches) where agglomerates are often simplified as effective spheres. The study does not propose new experimental setups or specific industrial applications beyond the general context of particle-laden flows but emphasizes its role in bridging the gap between fundamental fluid dynamics and practical modeling tools.