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Turbophoresis of inertial particles in inhomogeneous turbulence generated by oscillating grids

This study experimentally investigates turbophoresis in inhomogeneous turbulence generated by oscillating grids, demonstrating that inertial particles preferentially accumulate in regions of minimum turbulence intensity through measurements of particle spatial distributions normalized against noninertial tracers.

Original authors: Elad Elmakies, Oleg Shildkrot, Nathan Kleeorin, Avi Levy, Igor Rogachevskii

Published 2026-09-29

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CC BY 4.0

Original authors: Elad Elmakies, Oleg Shildkrot, Nathan Kleeorin, Avi Levy, Igor Rogachevskii

Original paper licensed under CC BY 4.0 (https://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

In the chaotic, churning world of fluid dynamics, invisible forces constantly sort and separate the tiny objects suspended within a flow. When a fluid moves smoothly, particles tend to drift with the current. But when that fluid becomes turbulent—filled with swirling eddies and unpredictable bursts of speed—things get complicated. One of the most intriguing phenomena in this realm is the way heavy, solid particles behave differently from the fluid itself. While the fluid might swirl everywhere, these heavier particles possess a kind of stubbornness due to their inertia. They cannot instantly change direction to match every rapid twist and turn of the surrounding air or water. This lag causes them to drift away from the most violent parts of the turbulence and settle into calmer zones. This process, known as turbophoresis, acts like a silent sorter, gathering particles into specific regions based on how rough the turbulence is nearby. Understanding this mechanism is vital for fields ranging from atmospheric science, where it helps explain how dust and pollutants spread, to astrophysics, where it influences how dust clumps together to form planets.

A team of researchers at Ben-Gurion University of the Negev set out to observe this sorting process directly in a controlled laboratory setting. They wanted to see if they could catch these inertial particles accumulating in the quiet spots of a turbulent flow, just as theory predicted. To do this, they built a large, transparent chamber filled with air and used a pair of oscillating grids—mesh-like structures that move back and forth—to generate a strong, uneven turbulence. They created two different scenarios: one with a single moving grid and another with two grids working in tandem. These grids stirred the air, creating a complex environment where the intensity of the turbulence varied significantly from one side of the chamber to the other. The researchers then introduced two types of tiny particles into this swirling air. The first type consisted of very light, non-inertial particles that acted as perfect tracers, following the air's every move. The second type was made of slightly heavier, hollow glass spheres that possessed enough mass to resist the rapid changes in the flow, making them the "inertial" subjects of the study.

Using high-speed cameras and laser sheets, the team mapped the speed of the air and the location of the particles with extreme precision. They measured the velocity of the air currents and tracked where the particles ended up after being dispersed throughout the chamber. The key to their discovery was a clever comparison. Because the air itself was moving and swirling, the researchers needed to separate the effect of the wind simply blowing the particles around from the specific effect of the turbulence sorting them. They achieved this by comparing the distribution of the heavy particles against the distribution of the light tracers under the exact same conditions. By normalizing the data in this way, they could isolate the unique behavior caused by the particles' inertia. The results were clear and consistent across both experimental setups. The heavy particles did not stay evenly spread out. Instead, they migrated away from the areas where the air was churning most violently and gathered in the regions where the turbulence was weakest.

This accumulation happened in the zones of minimum turbulent speed, confirming that the particles were indeed being pushed by the gradient of the turbulence itself. The researchers found that this effect was not a fluke of a single setup; it appeared in both the single-grid and double-grid configurations, despite the differences in how the turbulence was structured in each case. In the two-grid setup, where the turbulence was more symmetric, the particles still found their way to the calmest pockets of air. The study also carefully ruled out other potential causes for this gathering. They showed that the particles were not simply settling to the bottom due to gravity, as their downward drift was far too slow to account for the observed patterns. Nor were they being trapped by dead zones where the air stopped moving entirely; the accumulation occurred in the bulk of the flow, driven by the large-scale differences in turbulence intensity. The findings provide direct experimental evidence that turbophoresis is a robust mechanism for organizing particles in turbulent environments, offering a clearer picture of how nature sorts matter in everything from storm clouds to the early stages of star formation.

Technical Summary: Turbophoresis of Inertial Particles in Inhomogeneous Turbulence Generated by Oscillating Grids

Problem Statement
The transport of inertial particles in turbulent flows remains a complex area of study, particularly regarding the formation of large-scale, nonuniform particle number density distributions in spatially inhomogeneous turbulence. While theoretical and numerical studies have identified two primary mechanisms for such accumulation—turbulent thermal diffusion (in temperature-stratified flows) and turbophoresis (in spatially inhomogeneous isothermal flows)—direct experimental evidence of turbophoresis in nearly unbounded turbulent flows remains limited. Most prior experimental work has focused on wall-bounded flows where mean shear and boundary effects complicate the isolation of turbophoretic transport. This study addresses the gap in experimental verification by investigating whether inertial particles in laboratory-generated, strongly inhomogeneous isothermal turbulence accumulate preferentially in regions of minimum turbulence intensity, as predicted by theory and Direct Numerical Simulations (DNS).

Methodology
The researchers conducted experiments in a rectangular transparent chamber using air flows generated by one and two oscillating grids. The grids, consisting of square arrays of bars, oscillated sinusoidally to produce inhomogeneous turbulence with relatively weak mean flow. Two distinct configurations were tested: a single-grid setup and a double-grid setup, which differed in turbulence intensity distribution, anisotropy, and integral length scales.

Key experimental techniques included:

Particle Image Velocimetry (PIV): A Nd-YAG laser and CCD camera were used to measure the turbulent velocity fields. The system captured 530 independent velocity maps to ensure statistical convergence of mean and root-mean-square (r.m.s.) velocities, shear, anisotropy, and integral length scales.
Particle Injection and Imaging: Two types of particles were utilized:
- Noninertial tracers: Incense smoke particles (mean diameter 0.7 µm) with a Stokes number ( $St$ ) of $\approx 10^{-5}$ , used to map the fluid flow and establish a baseline distribution unaffected by inertia.
- Inertial particles: Borosilicate hollow glass spheres (mean diameter 10 µm) with $St$ ranging from $6.7 \times 10^{-3}$ to $1.57 \times 10^{-2}$ .
Normalization Strategy: To isolate turbophoretic accumulation from mean flow effects or injection inhomogeneities, the spatial distribution of inertial particles was normalized pointwise by the distribution of noninertial tracer particles measured under identical flow conditions. This yielded a relative particle density field ( $n_{in}/n_{nin}$ ).
Data Analysis: Mie scattering measurements were used to determine particle number densities. The study focused on the relationship between the normalized particle density and the normalized turbulence intensity ( $\langle u^2 \rangle / \langle u^2 \rangle_{max}$ ).

Key Contributions and Results
The study provides direct laboratory evidence of large-scale turbophoretic transport in isothermal turbulence away from solid boundaries. The primary findings include:

Confirmation of Turbophoretic Accumulation: In both the one-grid and two-grid configurations, inertial particles were observed to accumulate preferentially in regions of minimum mean-square turbulent velocity. This behavior aligns with the theoretical expectation that turbophoresis drives particles toward low-turbulence intensity zones.
Quantitative Trends: The relationship between the normalized inertial particle concentration and normalized turbulence intensity was analyzed. The results showed a clear inverse correlation: as turbulence intensity decreased, the normalized concentration of inertial particles increased.
- In the one-grid configuration, the trend exhibited a moderate slope generally, with a significantly steeper slope in the region of very low turbulence intensity, indicating heightened sensitivity of particle accumulation in these zones.
- In the two-grid configuration, the data formed two symmetric branches corresponding to the decay of turbulence away from each grid. Both branches displayed consistent negative slopes, confirming that the accumulation trend is robust across different spatial structures of inhomogeneity.
Differentiation from Mean Flow Effects: The study demonstrated that the observed accumulation is driven by turbulence intensity gradients rather than mean flow stagnation points. The regions of maximum particle accumulation were spatially distinct from the mean flow stagnation points, and the normalization process effectively removed common mean-flow transport effects.
Negligible Gravitational Settling: Under the experimental conditions, the terminal fall velocity of the 10 µm particles was significantly lower than the characteristic turbulent and mean flow velocities. Consequently, the observed large-scale patterns were attributed to turbophoresis rather than gravitational sedimentation.

Significance and Claims
The paper claims to provide robust experimental validation of the turbophoretic transport mechanism in strongly inhomogeneous, non-stratified turbulence. By utilizing oscillating grids to create controlled, unbounded-like turbulent environments, the authors successfully isolated the turbophoretic effect from other transport mechanisms that typically dominate in wall-bounded flows.

The authors state that their results are consistent with analytical estimates and DNS findings, specifically confirming that the competition between turbophoretic drift and turbulent diffusion leads to the formation of large-scale particle concentrations in regions of minimum turbulence intensity. The study does not attempt to derive a precise quantitative value for the turbophoretic coefficient ( $\kappa_{turboph}$ ) due to the complexity of fully characterizing the anisotropic, inhomogeneous turbulence tensor; instead, it focuses on validating the qualitative spatial trend. The authors conclude that these findings offer a foundational experimental basis for understanding particle transport in geophysical, planetary, and astrophysical turbulent flows, with further parametric studies suggested as a subject for future investigation.

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