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arxiv: 2602.22008 · v3 · pith:KEP7SAAYnew · submitted 2026-02-25 · ⚛️ physics.flu-dyn · physics.ao-ph

Experimental study of turbulent thermal diffusion of inertial particles in a convective turbulence forced by oscillating grids

E. Elmakies , O. Shildkrot , N. Kleeorin , A. Levy , I. Rogachevskii This is my paper

Pith reviewed 2026-05-15 19:18 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.ao-ph
keywords turbulent thermal diffusioninertial particlesconvective turbulenceparticle clusteringoscillating gridsparticle image velocimetrytemperature distributioneffective drift velocity
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The pith

Inertial particles form larger clusters near the mean temperature minimum than smaller particles because turbulent thermal diffusion produces a stronger effective drift velocity for them.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates through laboratory measurements that solid particles suspended in convective air turbulence driven by oscillating grids accumulate into large-scale clusters at locations of minimum mean temperature. This accumulation arises from turbulent thermal diffusion, an effect that creates a non-diffusive particle flux directed opposite the temperature gradient. The experiments find that the resulting drift velocity is 1.5 to 2.5 times larger for particles of 10 micrometer diameter than for 0.7 micrometer particles, with the ratio depending on turbulence intensity. A reader would care because the mechanism governs size-dependent separation and concentration of particles in any turbulent flow that also carries temperature variations, such as atmospheric clouds, industrial mixers, or combustion chambers.

Core claim

Measurements of temperature and particle number density spatial distributions have demonstrated the formation of large-scale clusters of inertial particles in the vicinity of the mean temperature minimum due to turbulent thermal diffusion. In the experiments, the effective drift velocity caused by turbulent thermal diffusion that results in the formation of large-scale clusters of inertial particles (having the diameter 10 μm) is in 1.5 -- 2.5 times larger than that for noninertial particles (having the diameter 0.7 μm) depending on the level of turbulence. This is in agreement with the theoretical predictions.

What carries the argument

Turbulent thermal diffusion, which generates an effective drift velocity of particles directed opposite to the gradient of mean fluid temperature and whose magnitude increases with particle inertia via the Stokes and Reynolds numbers.

If this is right

  • Large-scale clusters of inertial particles form in the vicinity of the mean temperature minimum.
  • The effective drift velocity is 1.5 to 2.5 times larger for 10-micrometer particles than for 0.7-micrometer particles, with the exact ratio set by turbulence intensity.
  • The size dependence of the drift velocity matches existing theoretical predictions for inertial particles in turbulent thermal diffusion.
  • The clustering effect strengthens or weakens directly with changes in the level of convective turbulence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The mechanism could produce preferential accumulation of larger particles in atmospheric layers that maintain stable temperature gradients.
  • Industrial particle separation processes could exploit controlled temperature profiles to enhance size-based sorting without additional mechanical filters.
  • In vertical flows the thermal drift may couple with gravitational settling to alter net sedimentation rates in a size-dependent manner.

Load-bearing premise

The measured particle clustering and size-dependent drift velocities arise exclusively from turbulent thermal diffusion rather than from gravitational settling, wall interactions, or nonuniform forcing by the oscillating grids.

What would settle it

A controlled repeat of the same grid-driven setup in which the mean temperature gradient is deliberately removed while particle inertia and turbulence level are held fixed would eliminate the observed size-dependent clustering if turbulent thermal diffusion is the sole cause.

Figures

Figures reproduced from arXiv: 2602.22008 by A. Levy, E. Elmakies, I. Rogachevskii, N. Kleeorin, O. Shildkrot.

Figure 1
Figure 1. Figure 1: FIG. 1. Experimental setup with the convective turbulence forced by one oscillating grid (left panel) and by two oscillating [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Distributions of the mean velocity field [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Distributions of the mean velocity shear [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Distributions of the turbulent velocity [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Distributions of the ratio [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Distributions of the anisotropy of turbulent velocity field [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Dependencies of the turbulent velocity [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Dependencies of the turbulent velocity [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Dependencies of the horizontal integral turbulence scale [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Dependencies of the vertical integral turbulence scale [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Distributions of the Reynolds number Re= ( [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Distributions of the anisotropy of turbulent time [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Distributions of the mean temperature [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Distributions of the normalized mean particle number density [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Dependencies of the parameter [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗
read the original abstract

We investigate the phenomenon of turbulent thermal diffusion of inertial solid particles in laboratory experiments with convective turbulence forced by one or two oscillating grids in the air. Turbulent thermal diffusion causes a non-diffusive contribution to turbulent flux of particles described in terms of an effective drift velocity directed opposite to the gradient of the mean fluid temperature. For inertial particles, this effective drift velocity depends on the Stokes and Reynolds numbers. In the experiments, fluid velocity and spatial distribution of inertial particles are measured using a Particle Image Velocimetry (PIV) system, and the temperature field is measured in many locations by a temperature probe equipped with 12 thermocouples. Measurements of temperature and particle number density spatial distributions have demonstrated the formation of large-scale clusters of inertial particles in the vicinity of the mean temperature minimum due to turbulent thermal diffusion. In the experiments, the effective drift velocity caused by turbulent thermal diffusion that results in the formation of large-scale clusters of inertial particles (having the diameter $10 \mu m$) is in 1.5 -- 2.5 times larger than that for noninertial particles (having the diameter $0.7 \mu m$) depending on the level of turbulence. This is in agreement with the theoretical predictions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript reports laboratory experiments investigating turbulent thermal diffusion of inertial solid particles in convective turbulence generated by one or two oscillating grids in air. Fluid velocity and particle spatial distributions are measured via PIV, while temperature fields are obtained from a 12-thermocouple probe. The central result is the observation of large-scale particle clustering near the mean temperature minimum, with the effective drift velocity for 10 μm inertial particles being 1.5–2.5 times larger than for 0.7 μm noninertial particles (depending on turbulence level), in agreement with theoretical predictions that incorporate Stokes and Reynolds number dependence.

Significance. If the turbulent thermal diffusion mechanism can be isolated from confounding effects, the work supplies quantitative experimental data on the Stokes-number enhancement of the effective drift velocity in a convective setup. This would constitute a useful validation point for models of inertial particle transport in inhomogeneous turbulence, with potential relevance to atmospheric aerosol dynamics and industrial mixing processes.

major comments (1)
  1. [Experimental setup and results] The terminal settling velocity for 10 μm particles is ~0.3 cm/s (non-negligible relative to typical rms velocities in the grid-forced cell), while it is negligible for 0.7 μm particles. The manuscript does not report zero-mean-temperature-gradient control runs at identical grid forcing to subtract any gravitational or mean-flow contribution from the measured drift velocities. Without such isolation, the reported 1.5–2.5× enhancement cannot be unambiguously assigned to turbulent thermal diffusion alone (see abstract and results description of drift velocity extraction).
minor comments (3)
  1. [Data analysis] The methods description lacks explicit details on error propagation for particle number density fields and the subsequent drift velocity estimates; inclusion of uncertainty bands on the reported factors would strengthen the quantitative claims.
  2. [Experimental setup] Particle material and density are not stated, preventing independent verification of the Stokes numbers used in the comparison with theory.
  3. [Figures] Figure captions should specify the Reynolds numbers or grid oscillation parameters corresponding to each turbulence level shown.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting an important issue regarding the isolation of the turbulent thermal diffusion effect. We address the major comment below and will revise the manuscript to incorporate additional discussion and clarification.

read point-by-point responses

  1. Referee: The terminal settling velocity for 10 μm particles is ~0.3 cm/s (non-negligible relative to typical rms velocities in the grid-forced cell), while it is negligible for 0.7 μm particles. The manuscript does not report zero-mean-temperature-gradient control runs at identical grid forcing to subtract any gravitational or mean-flow contribution from the measured drift velocities. Without such isolation, the reported 1.5–2.5× enhancement cannot be unambiguously assigned to turbulent thermal diffusion alone (see abstract and results description of drift velocity extraction).

    Authors: We agree that the terminal settling velocity of the 10 μm particles (~0.3 cm/s) is non-negligible relative to the rms velocities in the grid-forced turbulence, while it remains negligible for the 0.7 μm particles. The manuscript does not include control runs with zero mean temperature gradient at the same grid forcing conditions. This represents a genuine limitation in unambiguously separating gravitational settling or residual mean-flow effects from the turbulent thermal diffusion contribution to the measured effective drift velocity. The oscillating-grid setup is intended to produce nearly zero-mean-flow conditions, and the observed particle clustering occurs specifically at the location of the mean temperature minimum, consistent with the direction predicted by turbulent thermal diffusion theory. The reported 1.5–2.5 factor enhancement matches the Stokes- and Reynolds-number dependence derived in the theory for inertial particles. In the revised manuscript we will add a dedicated paragraph in the results section that (i) estimates the possible gravitational contribution to the drift velocity using the measured terminal velocities and (ii) explains why the differential clustering between the two particle sizes, under identical flow conditions, supports attribution to the inertial enhancement of turbulent thermal diffusion. We will also expand the description of how the effective drift velocity is extracted from the particle number-density profiles. These textual revisions will make the limitations and supporting arguments explicit. revision: partial

Circularity Check

0 steps flagged

Experimental results independent of any derivation chain

full rationale

The paper reports laboratory experiments measuring fluid velocity with PIV, temperature with thermocouples, and particle distributions. The formation of clusters and the effective drift velocity are directly observed and quantified from these measurements. The statement of agreement with theoretical predictions does not make the experimental findings circular, as the data stands on its own. No self-definitional steps, fitted predictions, or load-bearing self-citations are present in the derivation of the main claims. The analysis is self-contained based on empirical observations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The experimental claim relies on standard assumptions of fluid dynamics and particle tracking; no new free parameters are introduced, no invented entities are postulated, and no ad-hoc axioms are invoked beyond conventional definitions of Stokes and Reynolds numbers.

axioms (1)
  • domain assumption Turbulent thermal diffusion produces an effective drift velocity opposite to the mean temperature gradient
    Invoked in the abstract as the mechanism under study; treated as established from prior theory.

pith-pipeline@v0.9.0 · 5539 in / 1339 out tokens · 41040 ms · 2026-05-15T19:18:49.278091+00:00 · methodology

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Turbophoresis of inertial particles in inhomogeneous turbulence produced by oscillating grids

    physics.flu-dyn 2026-05 unverdicted novelty 4.0

    Inertial particles concentrate in regions of lower turbulence intensity in oscillating-grid experiments, confirmed by normalizing their density against noninertial tracers.

  2. Turbophoresis of inertial particles in inhomogeneous turbulence produced by oscillating grids

    physics.flu-dyn 2026-05 unverdicted novelty 3.0

    Experiments confirm inertial particles concentrate in lower-turbulence regions of oscillating-grid flows, consistent with turbophoretic velocity predictions.

  3. Turbophoresis of inertial particles in inhomogeneous turbulence produced by oscillating grids

    physics.flu-dyn 2026-05 unverdicted novelty 3.0

    Inertial particles preferentially accumulate in regions of lower turbulence intensity in oscillating-grid flows, as confirmed by normalized PIV density measurements.