Effect of Reynolds number on triboelectric particle charging in turbulent channel flow

This study introduces **triboFoam**, an open-source OpenFOAM-based solver, to demonstrate that increasing the Reynolds number in turbulent channel flows enhances both near-wall particle concentration and triboelectric charging rates, ultimately providing an empirical correlation to predict these charging behaviors.

The Gist

The Spark in the Pipe: Why Dust Gets "Electric"

Imagine you are working in a massive factory where fine powders—like flour, sugar, or even pharmaceutical medicine—are being zoomed through giant pipes using high-speed air. It looks like a smooth, invisible river of dust. But underneath that calm surface, a tiny, invisible war is happening. Every time a grain of dust bumps into another grain or hits the side of the pipe, it swaps a tiny bit of electricity.

This is called triboelectric charging (basically, "friction electricity"). If too much of this charge builds up, it’s like a ticking time bomb: the dust can stick to everything, clog up the machines, or—worst of all—cause a massive dust explosion.

Scientists want to know: How much does the speed of the air (the "turbulence") change how much electricity these particles collect?

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The Problem: The "Windy Hallway" Dilemma

Think of a hallway filled with thousands of ping-pong balls being blown by a giant fan.

• If the fan is on low, the balls drift lazily. They might bump into the walls occasionally, but it’s a gentle tap.
• If the fan is on high, the balls are flying wildly. They aren't just moving; they are slamming into the walls and each other like tiny, frantic bumper cars.

The researchers wanted to know if that "high-speed bumper car" effect makes the particles much more electric, or if it just makes them move faster without changing the total charge.

The Tool: The "Digital Wind Tunnel" (triboFoam)

Since you can't easily stick a tiny voltmeter inside a high-speed industrial pipe without breaking it, the researchers built a super-advanced digital simulator called triboFoam.

Think of triboFoam as a hyper-realistic video game. In most games, if a ball hits a wall, it just bounces. In triboFoam, the "physics engine" is so detailed that it calculates the exact microscopic "spark" that happens during every single tiny collision. It even simulates how the electricity itself creates a tiny magnetic-like pull that drags particles back toward the walls.

The Discovery: The Speed-Up Effect

By running these "digital experiments" at different speeds (what scientists call Reynolds numbers), they found three big things:

1. Faster Air = More Sparks
As the air gets more turbulent (the fan gets higher), the particles don't just move more; they hit the walls with much more "oomph." Because they are slamming harder, they transfer more electricity per hit. It’s like the difference between rubbing two balloons together gently versus slapping them together—the harder the impact, the more static you get.

2. The "Small Particle" Chaos
Small particles (like fine mist) are like tiny feathers in a storm; they follow every single swirl and gust of the wind. Because they are so light, the turbulent "swirls" keep throwing them back against the walls over and over again. This creates a "rebounding" effect where they keep hitting the wall, picking up more and more charge.

3. The "Big Particle" Limit
Surprisingly, the biggest particles (like grains of sand) don't follow the same rule. Because they are heavy, they have a lot of "momentum." At very high speeds, the chaotic wind actually starts to push them away from the walls more effectively, which can actually slow down how much charge they collect.

Why does this matter to you?

The researchers created a mathematical "cheat sheet" (an empirical correlation). This is like a recipe: if an engineer knows how fast their air is moving and how big their dust particles are, they can plug those numbers into this formula to predict exactly how much "static electricity" will build up.

The bottom line: This helps engineers design safer factories, preventing clogs and explosions by knowing exactly how much "electric chaos" is happening inside the pipes.

Technical Summary

Technical Summary: Effect of Reynolds Number on Triboelectric Particle Charging in Turbulent Channel Flow

1. Problem Statement

Triboelectric (frictional) charging in particle-laden flows is a critical phenomenon in industrial processes involving powders (e.g., pharmaceuticals, food, polymers). Excessive electrostatic charge can lead to severe hazards, including particle segregation, pipe blockages, and catastrophic dust explosions. While it is known that flow velocity (Reynolds number, $Re_\tau$) significantly influences charging, existing research presents contradictory findings. Previous studies have been limited by:

• Computational Constraints: Most Direct Numerical Simulations (DNS) are restricted to low Reynolds numbers ($Re_\tau \leq 180$).
• Resolution Issues: Large-Eddy Simulations (LES) often fail to resolve the viscous sublayer, where turbulence intensities and velocity gradients are highest.
• Inconsistent Results: Discrepancies exist between RANS, DEM, and LES models regarding whether increasing $Re_\tau$ increases or decreases charge.

2. Methodology

The authors introduce triboFoam, a new open-source CFD-DEM solver built on the OpenFOAM framework. The methodology follows a hierarchical validation and investigation approach:

• Solver Development: triboFoam couples Eulerian fluid dynamics with Lagrangian particle tracking. It implements a hybrid electrostatic force model (combining Gauss’s and Coulomb’s laws) and two charging models: the deterministic Condenser Model and the stochastic Stochastic Scaling Model (SSM).
• Validation (DNS): The solver was validated against the existing open-source solver pafiX using DNS of a fully developed turbulent channel flow at $Re_\tau = 180$. Validation focused on fluid velocity profiles, particle concentration distributions, and temporal charge build-up.
• Parametric Study (LES): To explore higher Reynolds numbers, the authors employed LES with the WALE (Wall Adapting Local Eddy-viscosity) subgrid-scale model. This setup allowed for a fully resolved viscous sublayer. The study varied:
  • Friction Reynolds numbers ($Re_\tau$): From 180 to 550.
  • Particle diameters ($d_p$): 25 $\mu$m, 50 $\mu$m, and 100 $\mu$m.
  • Coupling Complexity: 1-way (fluid $\to$ particle), 2-way (momentum feedback), and 4-way (particle-particle collisions and electrostatic interactions).

3. Key Contributions

• New Computational Tool: The release of triboFoam, an open-source, high-fidelity tool capable of simulating triboelectric charging in complex geometries and turbulent flows.
• Systematic $Re_\tau$ Investigation: The first study to systematically quantify how increasing Reynolds numbers affect both particle distribution and charging rates using resolved LES.
• Empirical Correlations: The derivation of two symbolic regression-based mathematical models to predict the average particle charging rate as a function of $Re_\tau$ and $d_p$.

4. Results and Discussion

• Charging Trends: The study confirms that higher Reynolds numbers lead to increased charging rates. This is driven by intensified turbulent fluctuations that increase both the collision frequency and the impact velocities of particles against the walls.
• Particle Size Effects:
  • Small particles ($d_p = 25 \mu$m): Show a massive increase in charging rate (up to two orders of magnitude) as $Re_\tau$ increases. This is attributed to an "electrostatic mechanism" where the grounded wall creates an image charge that attracts particles, leading to recurring collisions.
  • Large particles ($d_p = 100 \mu$m): Show a much weaker dependence on $Re_\tau$. Interestingly, for very large particles at high $Re_\tau$, the charging rate may actually decrease due to a reduction in near-wall particle concentration (lower turbophoretic drift).
• Coupling Effects: 4-way coupling significantly alters particle distribution. For larger particles, particle-particle collisions push particles away from the wall, reducing near-wall concentration but increasing the average impact velocity, which can paradoxically enhance the charging rate.
• Predictive Modeling: The authors proposed two correlations. The more complex version (Eq. 4.3) successfully captures the non-monotonic behavior (the tendency for charging rates to peak and then decrease at very high $Re_\tau$ for larger particles).

5. Significance

This work bridges the gap between fundamental micro-scale collision mechanics and macro-scale industrial fluid dynamics. By providing a validated, open-source tool and predictive empirical formulas, the study enables engineers to better assess the safety and efficiency of pneumatic conveying systems. It clarifies previous scientific contradictions by demonstrating that the resolution of small-scale turbulent structures is paramount to accurately predicting electrostatic phenomena.