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Shear alignment and tensorial Taylor--Aris dispersion of Brownian rods in a circular tube

T0 review · 1 major / 3 minor · reviewed 2026-05-19 · grok-4.3

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Pith's one-line read Shear alignment of Brownian rods in tube flow raises the Taylor-Aris dispersion coefficient by up to 30 percent in strong shear.

desk verdict The paper gives a tensorial Taylor-Aris closure for rods in circular Poiseuille flow that produces a 23-30% rise in the dispersion coefficient from shear alignment, with a clean decomposition of the diffusivity contributions. read the letter →

arxiv 2605.17614 v1 pith:4M7OV6QB submitted 2026-05-17 physics.flu-dyn

Jingsen Feng , Xu Chu This is my paper · ORCID
classification physics.flu-dyn
keywords BrownianrodsTaylor-ArisdispersionshearalignmentcirculartubePoiseuilleflowFokker-Planckequationanisotropicdiffusiontensorialtransport
checked against Foundation.AbsoluteFloorClosure
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper develops a tensorial Taylor-Aris theory for dilute Brownian rods in pressure-driven Poiseuille flow inside a circular tube. It solves the local steady orientation distribution from the Fokker-Planck equation on the three-dimensional orientation space and closes a conservative axisymmetric transport equation using the second moments of that distribution. The long-wave reduction isolates how each component of the anisotropic diffusion tensor contributes to the one-dimensional effective equation. Strong shear produces streamwise alignment in annular high-shear layers, which lowers radial diffusivity, moves the rods' long-time sampling toward slower streamlines, and enlarges the radial cell response that sets the Taylor coefficient. The same radial operator also supplies a Sturm-Liouville spectral description of the approach to the long-time regime from arbitrary radial starting positions.

What carries the argument

The long-wave reduction of the tensorial transport equation closed by the second moments of the local steady orientation distribution obtained from the Fokker-Planck problem.

What would settle it

Direct numerical simulation or laboratory measurement of the effective axial dispersion coefficient for rods with aspect ratio near 1000 in strong Poiseuille flow through a circular tube, compared against the classical scalar Taylor-Aris value, would confirm or refute the predicted 23 percent increase.

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Extended reading notes

Core claim

The central claim is that the streamwise alignment generated in high-shear annular layers reduces radial diffusivity there, shifts the long-time sampling of the velocity profile toward slower streamlines, and amplifies the radial cell response. In strong shear this raises the Taylor coefficient by about 23% for aspect ratio p=1000 and by about 30% in the infinitely slender limit, approaching the fully aligned bound. Direct simulations of the full tensorial equation validate the asymptotic coefficients.

Load-bearing premise

The long-wave reduction assumes that the local steady orientation distribution solved from the Fokker-Planck problem can be used to close the conservative axisymmetric transport equation without higher-order corrections from radial gradients of the orientation field.

Editorial extensions

If this is right

  • The Taylor coefficient increases by about 23 percent for aspect ratio p=1000 in strong shear.
  • The increase reaches about 30 percent in the infinitely slender limit and approaches the fully aligned bound.
  • Direct simulations of the full tensorial equation confirm the asymptotic coefficients.
  • The radial mixing operator supplies a Sturm-Liouville spectral model that tracks finite-time relaxation from different radial injections to the long-time Taylor regime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The tensorial closure may be useful for predicting transport of rod-like particles in microfluidic channels where shear varies radially.
  • Finite-time spectral models could guide design of injection protocols to accelerate or delay arrival at the asymptotic dispersion regime.
  • Similar moment closures might extend to non-dilute suspensions or to channels with non-circular cross sections.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 3 minor

Summary. The manuscript develops a tensorial Taylor-Aris dispersion theory for dilute Brownian rods in pressure-driven Poiseuille flow through a circular tube. It solves the local steady orientation distribution from the Fokker-Planck equation at each radius using the local shear rate, inserts the resulting second-moment diffusion tensor into a conservative axisymmetric transport equation, and performs a long-wave reduction to obtain an effective one-dimensional dispersion coefficient. The central result is that shear-induced alignment in high-shear annular regions reduces radial diffusivity, shifts long-time sampling toward slower streamlines, and raises the Taylor coefficient by ~23% for aspect ratio p=1000 and ~30% in the infinitely slender limit, approaching the fully aligned bound. Direct simulations of the full tensorial equation validate the asymptotic coefficients, and a Sturm-Liouville spectral model is derived for finite-time relaxation from radial injections.

Significance. If the central result holds, the work supplies a parameter-free (apart from p) extension of classical Taylor-Aris theory to anisotropic particles in cylindrical geometries with radially varying shear. The explicit decomposition of how each component of the diffusion tensor enters the one-dimensional limit, the quantitative enhancement due to alignment, and the direct-simulation validation constitute a solid, falsifiable contribution. The additional Sturm-Liouville model for transient relaxation broadens the practical utility for microfluidic applications.

major comments (1)
  1. [Long-wave reduction] Long-wave reduction (section describing the closure of the axisymmetric transport equation): the assumption that the local steady orientation distribution can be inserted directly without leading-order corrections from radial derivatives of the orientation field is load-bearing for the reported 23-30% enhancement. An explicit scaling estimate showing that these corrections remain O(ε²) or higher, where ε is the long-wave parameter, would confirm that the cell problem for the Taylor coefficient is unaffected at the order retained.
minor comments (3)
  1. [Numerical validation] The abstract and main text both state that direct simulations validate the asymptotic coefficients, but the manuscript does not specify the spatial discretization, time-stepping scheme, or convergence checks used for the full tensorial equation; adding a short paragraph on numerical validation would improve reproducibility.
  2. [Infinitely slender limit] In the discussion of the infinitely slender limit, the comparison to the 'fully aligned bound' is useful, but the precise definition of that bound (e.g., whether it corresponds to perfect alignment or the limiting diffusion tensor) should be stated explicitly with an equation reference.
  3. [Figures] Figure captions for the dispersion coefficient versus Péclet number or shear strength should include the precise definition of the normalized Taylor coefficient (e.g., relative to the isotropic case) to avoid ambiguity when comparing the 23% and 30% enhancements.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the work, and the constructive comment on the long-wave reduction. We address the point below and will incorporate the requested clarification in the revised manuscript.

read point-by-point responses

  1. Referee: [Long-wave reduction] Long-wave reduction (section describing the closure of the axisymmetric transport equation): the assumption that the local steady orientation distribution can be inserted directly without leading-order corrections from radial derivatives of the orientation field is load-bearing for the reported 23-30% enhancement. An explicit scaling estimate showing that these corrections remain O(ε²) or higher, where ε is the long-wave parameter, would confirm that the cell problem for the Taylor coefficient is unaffected at the order retained.

    Authors: We agree that an explicit scaling argument strengthens the presentation. In the derivation the orientation distribution is obtained from the local steady Fokker–Planck problem at each radius using the local shear rate. The long-wave parameter ε = a/L (tube radius over axial length scale) governs the slow radial transport. Radial derivatives of the orientation field therefore generate an O(ε) correction to the distribution. When this correction is substituted into the conservative axisymmetric transport equation and the long-wave reduction is performed, the resulting contribution to the effective one-dimensional dispersion coefficient enters only at O(ε²) and higher. Consequently the leading-order cell problem that determines the Taylor coefficient remains unchanged. We will add a short scaling paragraph immediately after the statement of the local-steady closure to make this estimate explicit. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in the derivation chain

full rationale

The paper solves the local steady Fokker-Planck equation for rod orientation distribution at each radius using the local shear rate from Poiseuille flow, extracts the second-moment diffusion tensor, and inserts it into a conservative axisymmetric transport equation whose long-wave reduction yields the effective Taylor-Aris coefficient via a standard cell problem. This is a conventional asymptotic closure procedure; the reported 23-30% enhancement of the dispersion coefficient is a computed numerical outcome of the alignment-induced shift in radial sampling of the velocity profile, not a quantity redefined in terms of the inputs. Direct simulations of the full tensorial equation are invoked for validation, and no load-bearing self-citations, uniqueness theorems, or fitted parameters renamed as predictions appear in the derivation. The long-wave assumption that radial gradients of orientation produce only higher-order corrections is an explicit modeling choice rather than a tautological reduction.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The model rests on the dilute-axisymmetric-rod assumption, the existence of a local steady orientation distribution, and the validity of the long-wave reduction; no new particles or forces are postulated.

free parameters (1)
  • aspect ratio p
    Input parameter that controls the strength of alignment and the magnitude of the reported 23% and 30% corrections.
assumptions (2)
  • domain assumption Local steady orientation distribution obtained from the Fokker-Planck equation can be inserted directly into the transport closure
    Invoked when the second moments of the orientation distribution are used to close the axisymmetric transport equation.
  • domain assumption Long-wave reduction remains valid when shear strength varies radially
    Required for the decomposition of radial, radial-axial, and axial diffusivity contributions into the one-dimensional limit.

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Cite this review

Pith. "Pith review of Shear alignment and tensorial Taylor--Aris dispersion of Brownian rods in a circular tube." pith.science (2026). https://pith.science/paper/4M7OV6QB

@misc{pith2026260517614,
  author       = {Pith},
  title        = {Pith review of: Shear alignment and tensorial Taylor--Aris dispersion of Brownian rods in a circular tube},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4M7OV6QB}},
  note         = {Machine review of arXiv:2605.17614}
}
abstract

Brownian rods disperse in pressure-driven flow through a coupling between axial shear, anisotropic translational diffusion and Jeffery--Brownian rotation. Classical tube Taylor--Aris theory treats transverse mixing as a scalar process, and existing passive-rod reductions have mainly addressed planar geometries. A circular tube adds two ingredients: the shear strength varies with radius and freely rotating rods sample a three-dimensional orientation space. We formulate a tensorial Taylor--Aris theory for dilute axisymmetric rods in Poiseuille flow by solving the local steady orientation Fokker--Planck problem and using its second moments to close a conservative axisymmetric transport equation. The long-wave reduction shows how each part of the diffusion tensor enters the one-dimensional limit. The radial diffusivity sets the invariant cross-sectional measure and the cell problem for the leading Taylor coefficient; the radial--axial component produces an inverse-P{\'e}clet correction to the migration speed; the axial component gives the direct diffusivity. The central mechanism is the streamwise alignment generated in high-shear annular layers. Alignment reduces radial diffusivity there, shifts the long-time sampling of the velocity profile toward slower streamlines, and amplifies the radial cell response. In strong shear this raises the Taylor coefficient by about \(23\%\) for aspect ratio \(p=1000\) and by about \(30\%\) in the infinitely slender limit, approaching the fully aligned bound. Direct simulations of the full tensorial equation validate the asymptotic coefficients. The same radial mixing operator also gives a Sturm--Liouville spectral model that tracks finite-time relaxation from different radial injections to the long-time Taylor regime.

Figures

Figures reproduced from arXiv: 2605.17614 by the authors.

Figure 1
Figure 1. Geometry of freely rotating rod-like particles in tube shear flow. The left part shows the axial velocity profile 𝑢(𝑟) and the radius-dependent shear rate 𝛾¤(𝑟). The middle part indicates the radial position 𝑟, tube radius 𝑅 and local shear parameter 𝑞 = 𝑃𝑒𝑟 𝑟/𝑅. The right inset gives the local orthonormal basis (𝒆ˆ𝑧 , 𝒆ˆ𝑟 , 𝒆ˆ𝜙), the shear plane and the rod-axis orientation 𝒑. The angle 𝜃 measures the in-plane incl… view at source ↗
Figure 2
Figure 2. Three-dimensional orientational bias induced by local shear. The parameters are 𝑝 = 1000, corresponding to 𝛽 = 0.999998, 𝐷∥ /𝐷¯ = 1.4013 and 𝐷⊥/𝐷¯ = 0.7993. Panel (a) shows the probability density 𝑔/𝑔0 in (𝜃, 𝜇) coordinates at 𝑞 = 0. Panel (b) shows the same density at 𝑞 = 103 . Panel (c) shows the same density at 𝑞 = 105 . Here 𝜇 = sin 𝜓 and 𝑔0 = 1/(4𝜋). Panel (d) shows the second-order orientation moments [PITH_F… view at source ↗
Figure 3
Figure 3. Variation of the local orientation-averaged transport tensor with shear parameter 𝑞. Panel (a) shows 𝐷 loc 𝑟𝑟 . Panel (b) shows 𝐷 loc 𝑧𝑧 . Panel (c) shows 𝐷 loc 𝜙𝜙. Panel (d) shows 𝐷 loc 𝑟 𝑧 . The superscript “loc” is omitted in the panel labels. Different curves correspond to different aspect ratios 𝑝. The spherical limit 𝑝 = 1 gives 𝐷𝑟𝑟 = 𝐷𝑧𝑧 = 𝐷𝜙𝜙 = 1 and 𝐷𝑟 𝑧 = 0. by about 20% at large 𝑞, whereas the peak value … view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Representative concentration field from the closed axisymmetric tensorial transport equation. The parameters are 𝑝 = 1000, 𝑃𝑒𝑟 = 104 and 𝑃𝑒 = 105 . The normalized moving coordinate is 𝜁 = (𝑧 − ⟨𝑧⟩)/𝜎𝑧, 𝑓 , where 𝜎𝑧, 𝑓 is the final-time axial standard deviation. Panel (…
Figure 5
Figure 5. Figure 5: Variation of long-time mean speed and Taylor dispersion coefficient with 𝑃𝑒𝑟 . Panel (a) shows the leading-order mean speed 𝑢 (0) 𝑚 . Panel (b) shows the Taylor dispersion coefficient normalized by the classical spherical value 𝜅𝑠 = 1/192; the dashed lines indicate est…
Figure 6
Figure 6. Figure 6: Variation of the normalized Taylor-dispersion enhancement factor 𝐸 with 𝑃𝑒𝑟 . Solid curves are calculated from the long-time theory in [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Radial tensor profiles and dispersion contribution density for fixed 𝑝 = 1000. Panel (a) shows 𝐷𝑟𝑟 (𝑟). Panel (b) shows 𝐷𝑧𝑧 (𝑟). Panel (c) shows 𝐷𝑟 𝑧 (𝑟). Panel (d) shows 𝑣 + 𝐷 (𝑟) = max[−𝐷 ′ 𝑟𝑟 (𝑟), 0], the positive part of the statistical drift associated with radial…
Figure 8
Figure 8. Figure 8: Radial mechanism of the dispersion change at fixed 𝑝 = 1000. Panel (a) shows the change in source relative to the spherical reference, 𝛥𝑆(𝑟) = 𝑆(𝑟) − 𝑆𝑠 (𝑟). Panel (b) shows the change in cell-function slope, 𝛥𝐺′ (𝑟) = 𝐺 ′ (𝑟) −𝐺 ′ 𝑠 (𝑟). Panel (c) shows the radial ori…
Figure 9
Figure 9. Figure 9: Radial–axial initial conditions used for full-time spectral validation. Panel (a) shows 𝑐0 (𝑟, 𝑧)/𝑐0,max, with the horizontal coordinate (𝑧 − 𝑧0)/𝜎𝑧0; the three rows correspond to uniform, centre-enriched and near￾wall-enriched initial conditions. Panel (b) shows the c…
Figure 10
Figure 10. Figure 10: Comparison between the full-time spectral model and the full axisymmetric tensorial equation. Panel (a) compares the axial variance 𝜎 2 𝑧 (𝑡). Panel (b) compares the time-dependent dispersion coefficient 𝜅(𝑡)/𝜅∞, where 𝜅∞ is the long-time spectral limit for the corres…
Figure 11
Figure 11. Figure 11: Comparison between the reduced-order spectral model and the full axisymmetric tensorial equation in power-law non-Newtonian background flow. Panel (a) compares the axial variance 𝜎 2 𝑧 (𝑡). Panel (b) compares the normalized time-dependent dispersion coefficient 𝜅(𝑡)/𝜅…

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Works this paper leans on

51 extracted references · 51 canonical work pages · cited by 1 Pith paper

  1. [1]

    and Shim, Suin and Gupta, Ankur and Stone, Howard A

    Alessio, B. M., Shim, S., Gupta, A. & Stone, H. A. 2022 Diffusio-osmosis-driven dispersion of colloids: a Taylor dispersion analysis with experimental validation. J. Fluid Mech. 942, A23. doi:10.1017/jfm.2022.321 https://doi.org/10.1017/jfm.2022.321

    work page doi:10.1017/jfm.2022.321 2022

  2. [2]

    & Dean, D

    Alexandre, A., Gu \'e rin, T. & Dean, D. S. 2021 Generalized Taylor dispersion for translationally invariant microfluidic systems. Phys. Fluids 33, 082004. doi:10.1063/5.0057584 https://doi.org/10.1063/5.0057584

    work page doi:10.1063/5.0057584 2021

  3. [3]

    Aminian, M., Bernardi, F., Camassa, R., Harris, D. M. & McLaughlin, R. M. 2016 How boundaries shape chemical delivery in microfluidics. Science 354, 1252--1256. doi:10.1126/science.aag0532 https://doi.org/10.1126/science.aag0532

    work page doi:10.1126/science.aag0532 2016

  4. [4]

    Proceedings of the Royal Society of London

    Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67--77. doi:10.1098/rspa.1956.0065 https://doi.org/10.1098/rspa.1956.0065

    work page doi:10.1098/rspa.1956.0065 1956

  5. [5]

    1974 Rheology of a dilute suspension of axisymmetric Brownian particles

    Brenner, H. 1974 Rheology of a dilute suspension of axisymmetric Brownian particles. Intl J. Multiphase Flow 1, 195--341. doi:10.1016/0301-9322(74)90018-4 https://doi.org/10.1016/0301-9322(74)90018-4

    work page doi:10.1016/0301-9322(74)90018-4 1974

  6. [6]

    V., Sun, K

    Chakrabarty, A., Konya, A., Wang, F., Selinger, J. V., Sun, K. & Wei, Q.-H. 2013 Brownian motion of boomerang colloidal particles. Phys. Rev. Lett. 111, 160603. doi:10.1103/PhysRevLett.111.160603 https://doi.org/10.1103/PhysRevLett.111.160603

    work page doi:10.1103/physrevlett.111.160603 2013

  7. [7]

    & Santiago, J

    Chang, R. & Santiago, J. G. 2023 Taylor dispersion in arbitrarily shaped axisymmetric channels. J. Fluid Mech. 976, A30. doi:10.1017/jfm.2023.504 https://doi.org/10.1017/jfm.2023.504

    work page doi:10.1017/jfm.2023.504 2023

  8. [8]

    Chilukuri, S., Collins, C. H. & Underhill, P. T. 2015 Dispersion of flagellated swimming microorganisms in planar Poiseuille flow. Phys. Fluids 27, 031902. doi:10.1063/1.4914129 https://doi.org/10.1063/1.4914129

    work page doi:10.1063/1.4914129 2015

Show all 51 references
  1. [9]

    A., Sardina, G., Ahmed, M., Bees, M

    Croze, O. A., Sardina, G., Ahmed, M., Bees, M. A. & Brandt, L. 2013 Dispersion of swimming algae in laminar and turbulent channel flows: consequences for photobioreactors. J. R. Soc. Interface 10, 20121041. doi:10.1098/rsif.2012.1041 https://doi.org/10.1098/rsif.2012.1041

    2013 doi

  2. [10]

    & Guasto, J

    Dehkharghani, A., Waisbord, N., Dunkel, J. & Guasto, J. S. 2019 Bacterial scattering in microfluidic crystal flows reveals giant active Taylor--Aris dispersion. Proc. Natl Acad. Sci. USA 116, 11119--11124. doi:10.1073/pnas.1819613116 https://doi.org/10.1073/pnas.1819613116

    2019 doi

  3. [11]

    & Saintillan, D

    Ezhilan, B. & Saintillan, D. 2015 Transport of a dilute active suspension in pressure-driven channel flow. J. Fluid Mech. 777, 482--522. doi:10.1017/jfm.2015.372 https://doi.org/10.1017/jfm.2015.372

    2015 doi

  4. [12]

    & Chen, G

    Guan, M. & Chen, G. 2024 Streamwise dispersion of soluble matter in solvent flowing through a tube. J. Fluid Mech. 980, A33. doi:10.1017/jfm.2024.34 https://doi.org/10.1017/jfm.2024.34

    2024 doi

  5. [13]

    & Lee, J

    Guan, M., Jiang, W., Tao, L., Chen, G. & Lee, J. H. W. 2024 Migration of confined micro-swimmers subject to anisotropic diffusion. J. Fluid Mech. 985, A44. doi:10.1017/jfm.2024.349 https://doi.org/10.1017/jfm.2024.349

    2024 doi

  6. [14]

    M., Nobili, M., Zhang, J., Lubensky, T

    Han, Y., Alsayed, A. M., Nobili, M., Zhang, J., Lubensky, T. C. & Yodh, A. G. 2006 Brownian motion of an ellipsoid. Science 314, 626--630. doi:10.1126/science.1130146 https://doi.org/10.1126/science.1130146

    2006 doi

  7. [15]

    & Yodh, A

    Han, Y., Alsayed, A., Nobili, M. & Yodh, A. G. 2009 Quasi-two-dimensional diffusion of single ellipsoids: aspect ratio and confinement effects. Phys. Rev. E 80, 011403. doi:10.1103/PhysRevE.80.011403 https://doi.org/10.1103/PhysRevE.80.011403

    2009 doi

  8. [16]

    Hinch, E. J. & Leal, L. G. 1972 The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52, 683--712. doi:10.1017/S002211207200271X https://doi.org/10.1017/S002211207200271X

    1972 doi

  9. [17]

    Hinch, E. J. & Leal, L. G. 1973 Time-dependent shear flows of a suspension of particles with weak Brownian rotations. J. Fluid Mech. 57, 753--767. doi:10.1017/S0022112073001990 https://doi.org/10.1017/S0022112073001990

    1973 doi

  10. [18]

    Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161--179. doi:10.1098/rspa.1922.0078 https://doi.org/10.1098/rspa.1922.0078

    1922 doi

  11. [19]

    & Chen, G

    Jiang, W. & Chen, G. 2019 Dispersion of active particles in confined unidirectional flows. J. Fluid Mech. 877, 1--34. doi:10.1017/jfm.2019.562 https://doi.org/10.1017/jfm.2019.562

    2019 doi

  12. [20]

    & Chen, G

    Jiang, W. & Chen, G. 2020 Dispersion of gyrotactic micro-organisms in pipe flows. J. Fluid Mech. 889, A18. doi:10.1017/jfm.2020.91 https://doi.org/10.1017/jfm.2020.91

    2020 doi

  13. [21]

    & Chen, G

    Jiang, W. & Chen, G. 2021 Transient dispersion process of active particles. J. Fluid Mech. 927, A11. doi:10.1017/jfm.2021.747 https://doi.org/10.1017/jfm.2021.747

    2021 doi

  14. [22]

    Khair, A. S. 2022 Taylor dispersion of elongated rods at small and large rotational P \'e clet numbers. Phys. Rev. Fluids 7, 014502. doi:10.1103/PhysRevFluids.7.014502 https://doi.org/10.1103/PhysRevFluids.7.014502

    2022 doi

  15. [23]

    J., Wittkowski, R., ten Hagen, B., Edmond, K

    Kraft, D. J., Wittkowski, R., ten Hagen, B., Edmond, K. V., Pine, D. J. & L \"o wen, H. 2013 Brownian motion and the hydrodynamic friction tensor for colloidal particles of complex shape. Phys. Rev. E 88, 050301. doi:10.1103/PhysRevE.88.050301 https://doi.org/10.1103/PhysRevE....

    2013 doi

  16. [24]

    H., Thomson, S

    Kumar, A. H., Thomson, S. J., Powers, T. R. & Harris, D. M. 2021 Taylor dispersion of elongated rods. Phys. Rev. Fluids 6, 094501. doi:10.1103/PhysRevFluids.6.094501 https://doi.org/10.1103/PhysRevFluids.6.094501

    2021 doi

  17. [25]

    D., Cheng, X., Ong, D

    Leahy, B. D., Cheng, X., Ong, D. C., Liddell-Watson, C. & Cohen, I. 2013 Enhancing rotational diffusion using oscillatory shear. Phys. Rev. Lett. 110, 228301. doi:10.1103/PhysRevLett.110.228301 https://doi.org/10.1103/PhysRevLett.110.228301

    2013 doi

  18. [26]

    D., Koch, D

    Leahy, B. D., Koch, D. L. & Cohen, I. 2015 The effect of shear flow on the rotational diffusion of a single axisymmetric particle. J. Fluid Mech. 772, 42--79. doi:10.1017/jfm.2015.186 https://doi.org/10.1017/jfm.2015.186

    2015 doi

  19. [27]

    Leal, L. G. & Hinch, E. J. 1971 The effect of weak Brownian rotations on particles in shear flow. J. Fluid Mech. 46, 685--703. doi:10.1017/S0022112071000788 https://doi.org/10.1017/S0022112071000788

    1971 doi

  20. [28]

    & Harris, D

    Lee, G., Luner, A., Marzuola, J. & Harris, D. M. 2021 Dispersion control in pressure-driven flow through bowed rectangular microchannels. Microfluid. Nanofluid. 25, 34. doi:10.1007/s10404-021-02436-9 https://doi.org/10.1007/s10404-021-02436-9

    2021 doi

  21. [29]

    & Alim, K

    Marbach, S. & Alim, K. 2019 Active control of dispersion within a channel with flow and pulsating walls. Phys. Rev. Fluids 4, 114202. doi:10.1103/PhysRevFluids.4.114202 https://doi.org/10.1103/PhysRevFluids.4.114202

    2019 doi

  22. [30]

    Nitsche, L. C. & Hinch, E. J. 1997 Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow. J. Fluid Mech. 332, 1--21. doi:10.1017/S0022112096003369 https://doi.org/10.1017/S0022112096003369

    1997 doi

  23. [31]

    Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157--199. doi:10.1017/S0022112094002326 https://doi.org/10.1017/S0022112094002326

    1994 doi

  24. [32]

    & Brady, J

    Peng, Z. & Brady, J. F. 2020 Upstream swimming and Taylor dispersion of active Brownian particles. Phys. Rev. Fluids 5, 073102. doi:10.1103/PhysRevFluids.5.073102 https://doi.org/10.1103/PhysRevFluids.5.073102

    2020 doi

  25. [33]

    2024 Rotational Taylor dispersion in linear flows

    Peng, Z. 2024 Rotational Taylor dispersion in linear flows. J. Fluid Mech. 997, A10. doi:10.1017/jfm.2024.856 https://doi.org/10.1017/jfm.2024.856

    2024 doi

  26. [34]

    1934 Mouvement brownien d'un ellipsoide

    Perrin, F. 1934 Mouvement brownien d'un ellipsoide. I. Dispersion di \'e lectrique pour des mol \'e cules ellipsoidales. J. Phys. Radium 5, 497--511. doi:10.1051/jphysrad:01934005010049700 https://doi.org/10.1051/jphysrad:01934005010049700

    1934 doi

  27. [35]

    1936 Mouvement Brownien d'un ellipsoide

    Perrin, F. 1936 Mouvement Brownien d'un ellipsoide. II. Rotation libre et d \'e polarisation des fluorescences. Translation et diffusion de mol \'e cules ellipsoidales. J. Phys. Radium 7, 1--11. doi:10.1051/jphysrad:01936007010100 https://doi.org/10.1051/jphysrad:01936007010100

    1936 doi

  28. [36]

    J., Armstrong, R

    Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A. L. & Abbott, J. R. 1992 A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A 4, 30--40. doi:10.1063/1.858498 https://doi.org/10.1063/1.858498

    1992 doi

  29. [37]

    M., Thomann, E

    Ramirez, J. M., Thomann, E. A., Waymire, E. C., Haggerty, R. & Wood, B. 2006 A generalized Taylor--Aris formula and skew diffusion. Multiscale Model. Simul. 5, 786--801. doi:10.1137/050642770 https://doi.org/10.1137/050642770

    2006 doi

  30. [38]

    Rusconi, R., Guasto, J. S. & Stocker, R. 2014 Bacterial transport suppressed by fluid shear. Nat. Phys. 10, 212--217. doi:10.1038/nphys2883 https://doi.org/10.1038/nphys2883

    2014 doi

  31. [39]

    & Camporeale, C

    Salerno, L., Cardillo, G. & Camporeale, C. 2020 Aris--Taylor dispersion in the subarachnoid space. Phys. Rev. Fluids 5, 043102. doi:10.1103/PhysRevFluids.5.043102 https://doi.org/10.1103/PhysRevFluids.5.043102

    2020 doi

  32. [40]

    Schiek, R. L. & Shaqfeh, E. S. G. 1997 Cross-streamline migration of slender Brownian fibres in plane Poiseuille flow. J. Fluid Mech. 332, 23--39. doi:10.1017/S0022112096003291 https://doi.org/10.1017/S0022112096003291

    1997 doi

  33. [41]

    A., Koch, D

    Stover, C. A., Koch, D. L. & Cohen, C. 1992 Observations of fibre orientation in simple shear flow of semi-dilute suspensions. J. Fluid Mech. 238, 277--296. doi:10.1017/S002211209200171X https://doi.org/10.1017/S002211209200171X

    1992 doi

  34. [42]

    Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186--203. doi:10.1098/rspa.1953.0139 https://doi.org/10.1098/rspa.1953.0139

    1953 doi

  35. [43]

    Tirado, M. M. & de la Torre, J. G. 1979 Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders. J. Chem. Phys. 71, 2581--2587. doi:10.1063/1.438613 https://doi.org/10.1063/1.438613

    1979 doi

  36. [44]

    M., Mart \'i nez, C

    Tirado, M. M., Mart \'i nez, C. L. & de la Torre, J. G. 1984 Comparison of theories for the translational and rotational diffusion coefficients of rod-like macromolecules. Application to short DNA fragments. J. Chem. Phys. 81, 2047--2052. doi:10.1063/1.447827 https://doi.org/1...

    1984 doi

  37. [45]

    & Bruus, H

    Vedel, S. & Bruus, H. 2012 Transient Taylor--Aris dispersion for time-dependent flows in straight channels. J. Fluid Mech. 691, 95--122. doi:10.1017/jfm.2011.444 https://doi.org/10.1017/jfm.2011.444

    2012 doi

  38. [46]

    & Bruus, H

    Vedel, S., Hovad, E. & Bruus, H. 2014 Time-dependent Taylor--Aris dispersion of an initial point concentration. J. Fluid Mech. 752, 107--122. doi:10.1017/jfm.2014.324 https://doi.org/10.1017/jfm.2014.324

    2014 doi

  39. [47]

    Wang, B., Jiang, W., Chen, G., Tao, L. & Li, Z. 2021 Vertical distribution and longitudinal dispersion of gyrotactic microorganisms in a horizontal plane Poiseuille flow. Phys. Rev. Fluids 6, 054502. doi:10.1103/PhysRevFluids.6.054502 https://doi.org/10.1103/PhysRevFluids.6.054502

    2021 doi

  40. [48]

    & Wang, P

    Wang, B., Jiang, W., Zeng, L., Wu, Z. & Wang, P. 2025 Taylor--Aris dispersion of active particles in oscillatory channel flows. J. Fluid Mech. 1021, A3. doi:10.1017/jfm.2025.10700 https://doi.org/10.1017/jfm.2025.10700

    2025 doi

  41. [49]

    & Stark, H

    Z \"o ttl, A. & Stark, H. 2012 Nonlinear dynamics of a microswimmer in Poiseuille flow. Phys. Rev. Lett. 108, 218104. doi:10.1103/PhysRevLett.108.218104 https://doi.org/10.1103/PhysRevLett.108.218104

    2012 doi

  42. [50]

    & Stark, H

    Z \"o ttl, A. & Stark, H. 2013 Periodic and quasiperiodic motion of an elongated microswimmer in Poiseuille flow. Eur. Phys. J. E 36, 4. doi:10.1140/epje/i2013-13004-5 https://doi.org/10.1140/epje/i2013-13004-5

    2013 doi

  43. [51]

    E., Balin, A

    Z \"o ttl, A., Klop, K. E., Balin, A. K., Gao, Y., Yeomans, J. M. & Aarts, D. G. A. L. 2019 Dynamics of individual Brownian rods in a microchannel flow. Soft Matter 15, 5810--5814. doi:10.1039/C9SM00903E https://doi.org/10.1039/C9SM00903E

    2019 doi

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