- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Dominant-mode closure for transient Taylor dispersion of reduced Brownian-rod transport in plane power-law channels

Jingsen Feng and Xu Chu*

  • *Contact author: x.chu@exeter.ac.uk
PDF

Phys. Rev. Fluids 11, 104501 – Published 7 October, 2026

DOI: https://doi.org/10.1103/y447-xmgm

Abstract

Taylor-Aris and generalized Taylor dispersion theories characterize the long-time spreading reached after transverse homogenization in bounded shear. The present work considers the preasymptotic approach to that regime for anisotropic microstructures transported through finite channels with non-Newtonian carriers. We use an established single-exponential memory closure to connect the exact short-time sampled-velocity variance with the long-time Taylor enhancement, and carry this reduction into bounded shear with varying transverse geometry, non-Newtonian rheology, and Brownian orientational dynamics. For scalar unit-reference problems with invariant release, the ratio of these two anchors defines the integral correlation time whenever sampled-velocity memory is governed by one slow mode. For the reduced rod problem, the same construction is used as a Green-Kubo-motivated two-anchor approximation to the dominant shear-generated contribution under a uniform but generally nonequilibrium transverse injection. Exact spectral solutions for isotropic dispersion in plane and circular power-law Poiseuille geometries and Newtonian Brownian-rod calculations with independently supplied rod generalized Taylor dispersion coefficients provide controlled benchmarks for this extension. Applied to a reduced Brownian-rod model in power-law channels, the carrier rheology enters through the imposed velocity and shear fields while the reference particle-scale diffusivities remain fixed. Lattice Boltzmann simulations of the corresponding anisotropic advection-diffusion equation retain the full tensorial direct-diffusion contribution and resolve the transient moment evolution. Across flow indices and rotational Péclet numbers, alignment and rheology-dependent shear sampling shape the raw transients, and the reduced variables follow common master curves to the reported accuracy. The resulting characteristic and tolerance-based development measures connect the approach to Taylor transport with physical residence times and downstream lengths in finite channels.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (85)

  1. G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London A 219, 186 (1953).
  2. R. Aris, On the dispersion of a solute in a fluid flowing through a tube, Proc. R. Soc. London A 235, 67 (1956).
  3. W. N. Gill, A note on the solution of transient dispersion problems, Proc. R. Soc. London A 298, 335 (1967).
  4. P. C. Chatwin, The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe, J. Fluid Mech. 43, 321 (1970).
  5. R. Smith, The early stages of contaminant dispersion in shear flows, J. Fluid Mech. 111, 107 (1981).
  6. R. Smith, A delay-diffusion description for contaminant dispersion, J. Fluid Mech. 105, 469 (1981).
  7. N. G. Barton, On the method of moments for solute dispersion, J. Fluid Mech. 126, 205 (1983).
  8. M. D. Bryden and H. Brenner, Multiple-timescale analysis of Taylor dispersion in converging and diverging flows, J. Fluid Mech. 311, 343 (1996).
  9. M. Latini and A. J. Bernoff, Transient anomalous diffusion in Poiseuille flow, J. Fluid Mech. 441, 399 (2001).
  10. E. Taghizadeh, F. J. Valdés-Parada, and B. D. Wood, Preasymptotic Taylor dispersion: Evolution from the initial condition, J. Fluid Mech. 889, A5 (2020).
  11. B. M. Alessio, S. Shim, A. Gupta, and H. A. Stone, Diffusioosmosis-driven dispersion of colloids: A Taylor dispersion analysis with experimental validation, J. Fluid Mech. 942, A23 (2022).
  12. R. Chang and J. G. Santiago, Taylor dispersion in arbitrarily shaped axisymmetric channels, J. Fluid Mech. 976, A30 (2023).
  13. M. Guan and G. Chen, Streamwise dispersion of soluble matter in solvent flowing through a tube, J. Fluid Mech. 980, A33 (2024).
  14. C. J. Samuel, R. Chang, K. Ma, and J. G. Santiago, Taylor dispersion for coupled electroosmotic and pressure-driven flows in all time regimes, J. Fluid Mech. 1011, A36 (2025).
  15. E. M. Lungu and H. K. Moffatt, The effect of wall conductance on heat diffusion in duct flow, J. Eng. Math. 16, 121 (1982).
  16. V. Balakotaiah and H.-C. Chang, Dispersion of chemical solutes in chromatographs and reactors, Philos. Trans. R. Soc. London A 351, 39 (1995).
  17. L. Zhang, M. A. Hesse, and M. Wang, Transient solute transport with sorption in Poiseuille flow, J. Fluid Mech. 828, 733 (2017).
  18. T. Aquino, Equilibrium distributions under advection-diffusion in laminar channel flow with partially absorbing boundaries, J. Fluid Mech. 985, A16 (2024).
  19. G. Batôt, L. Talon, Y. Peysson, M. Fleury, and D. Bauer, Analytical and numerical investigation of the advective and dispersive transport in Herschel-Bulkley fluids by means of a lattice-Boltzmann two-relaxation-time scheme, Chem. Eng. Sci. 141, 271 (2016).
  20. J. Rana and P. Murthy, Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption, J. Fluid Mech. 793, 877 (2016).
  21. S. Singh and P. Murthy, Significance of skewness and kurtosis on the solute dispersion in pulsatile Carreau-Yasuda fluid flow in a tube with wall absorption, J. Fluid Mech. 962, A42 (2023).
  22. C. Teodoro, O. Bautista, and F. Méndez, Taylor dispersion analysis in a viscoelastic fluid through arbitrarily shaped axisymmetric channels, J. Fluid Mech. 1025, A9 (2025).
  23. G. Covarrubias, O. Bautista, J. Arcos, and F. Méndez, Taylor dispersion in a pulsatile flow of a viscoelastic fluid through an eccentric annular tube, J. Fluid Mech. 1030, A55 (2026).
  24. Y. Liu, W. Gong, H. Xiao, and M. Wang, Non-monotonic effect of compaction on longitudinal dispersion coefficient of porous media, J. Fluid Mech. 988, R2 (2024).
  25. Y. Liu, H. Xiao, T. Aquino, M. Dentz, and M. Wang, Scaling laws and mechanisms of hydrodynamic dispersion in porous media, J. Fluid Mech. 1001, R2 (2024).
  26. Y. Liu, Y. Wang, and M. Wang, Mechanism transition of superlinear scaling in hydrodynamic dispersion, J. Fluid Mech. 1031, A32 (2026).
  27. T. Le Borgne, M. Dentz, and E. Villermaux, The lamellar description of mixing in porous media, J. Fluid Mech. 770, 458 (2015).
  28. M. Dentz, D. R. Lester, T. Le Borgne, and F. P. J. de Barros, Coupled continuous-time random walks for fluid stretching in two-dimensional heterogeneous media, Phys. Rev. E 94, 061102(R) (2016).
  29. D. R. Lester, M. Dentz, T. Le Borgne, and F. P. J. de Barros, Fluid deformation in random steady three-dimensional flow, J. Fluid Mech. 855, 770 (2018).
  30. E. Villermaux, Mixing versus stirring, Annu. Rev. Fluid Mech. 51, 245 (2019).
  31. J. Feng, Y. Liu, and X. Chu, Realizable entropic lattice Boltzmann method for high-Péclet scalar transport, Phys. Rev. E 114, L013301 (2026).
  32. I. Frankel and H. Brenner, On the foundations of generalized Taylor dispersion theory, J. Fluid Mech. 204, 97 (1989).
  33. I. Frankel and H. Brenner, Generalized Taylor dispersion phenomena in unbounded homogeneous shear flows, J. Fluid Mech. 230, 147 (1991).
  34. I. Frankel and H. Brenner, Taylor dispersion of orientable Brownian particles in unbounded homogeneous shear flows, J. Fluid Mech. 255, 129 (1993).
  35. O. A. Croze, R. N. Bearon, and M. A. Bees, Gyrotactic swimmer dispersion in pipe flow: Testing the theory, J. Fluid Mech. 816, 481 (2017).
  36. R. Alonso-Matilla, B. Chakrabarti, and D. Saintillan, Transport and dispersion of active particles in periodic porous media, Phys. Rev. Fluids 4, 043101 (2019).
  37. L. Vennamneni, S. Nambiar, and G. Subramanian, Shear-induced migration of microswimmers in pressure-driven channel flow, J. Fluid Mech. 890, A15 (2020).
  38. L. R. Vennamneni, P. Garg, and G. Subramanian, Anomalous scaling of the dispersion of microswimmer populations, J. Fluid Mech. 1020, A12 (2025).
  39. B. Wang, W. Jiang, L. Zeng, Z. Wu, and P. Wang, Taylor-Aris dispersion of active particles in oscillatory channel flows, J. Fluid Mech. 1021, A3 (2025).
  40. S. A. Allison, C. Chen, and D. Stigter, The length dependence of translational diffusion, free solution electrophoretic mobility, and electrophoretic tether force of rigid rod-like model duplex DNA, Biophys. J. 81, 2558 (2001).
  41. A. Zöttl, K. E. Klop, A. K. Balin, Y. Gao, J. M. Yeomans, and D. G. A. L. Aarts, Dynamics of individual Brownian rods in a microchannel flow, Soft Matter 15, 5810 (2019).
  42. W. Liu, L. Zhang, Z. Dong, K. Liu, H. He, Y. Lu, W. Wu, and J. Qi, Rod-like mesoporous silica nanoparticles facilitate oral drug delivery via enhanced permeation and retention effect in mucus, Nano Res. 15, 9243 (2022).
  43. L. C. Nitsche and E. J. Hinch, Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow, J. Fluid Mech. 332, 1 (1997).
  44. M. Nagel, P.-T. Brun, H. Berthet, A. Lindner, F. Gallaire, and C. Duprat, Oscillations of confined fibres transported in microchannels, J. Fluid Mech. 835, 444 (2018).
  45. A. H. Kumar, S. J. Thomson, T. R. Powers, and D. M. Harris, Taylor dispersion of elongated rods, Phys. Rev. Fluids 6, 094501 (2021).
  46. A. S. Khair, Taylor dispersion of elongated rods at small and large rotational Péclet numbers, Phys. Rev. Fluids 7, 014502 (2022).
  47. A. N. Beris, J. S. Horner, S. Jariwala, M. J. Armstrong, and N. J. Wagner, Recent advances in blood rheology: A review, Soft Matter 17, 10591 (2021).
  48. M. Jory, D. Donnarumma, C. Blanc, K. Bellouma, A. Fort, I. Vachier, L. Casanellas, A. Bourdin, and G. Massiera, Mucus from human bronchial epithelial cultures: Rheology and adhesion across length scales, Interface Focus 12, 20220028 (2022).
  49. F. Del Giudice, S. Sathish, G. D'Avino, and A. Q. Shen, “From the edge to the center”: Viscoelastic migration of particles and cells in a strongly shear-thinning liquid flowing in a microchannel, Anal. Chem. 89, 13146 (2017).
  50. G. Zhu, B. van Gogh, L. Zhu, O. S. Pak, and Y. Man, Self-diffusiophoretic propulsion of a spheroidal particle in a shear-thinning fluid, J. Fluid Mech. 986, A39 (2024).
  51. H. U. Naseer, D. Izbassarov, Z. Ahmed, and M. Muradoglu, Lateral migration of a deformable fluid particle in a square channel flow of viscoelastic fluid, J. Fluid Mech. 996, A31 (2024).
  52. X. Hu, J. Lin, Z. Zhu, Z. Yu, Z. Lin, and X. Li, Elasto-inertial focusing and rotating characteristics of ellipsoidal particles in a square channel flow of Oldroyd-B viscoelastic fluids, J. Fluid Mech. 997, A32 (2024).
  53. S. Raut, M. K. Raihan, Y. Song, and X. Xuan, Fluid shear thinning effects on particle focusing in a spiral microchannel, Phys. Fluids 36, 112036 (2024).
  54. E. Boyko, M. Bercovici, and A. D. Gat, Flow of power-law liquids in a Hele–Shaw cell driven by non-uniform electro-osmotic slip in the case of strong depletion, J. Fluid Mech. 807, 235 (2016).
  55. E. Boyko and H. A. Stone, Flow rate–pressure drop relation for shear-thinning fluids in narrow channels: Approximate solutions and comparison with experiments, J. Fluid Mech. 923, R5 (2021).
  56. D. Gu and R. I. Tanner, The drag on a sphere in a power-law fluid, J. Non-Newtonian Fluid Mech. 17, 1 (1985).
  57. C. Datt and G. J. Elfring, Dynamics and rheology of particles in shear-thinning fluids, J. Non-Newtonian Fluid Mech. 262, 107 (2018).
  58. J. Férec, E. Bertevas, B. C. Khoo, G. Ausias, and N. Phan-Thien, The effect of shear-thinning behaviour on rod orientation in filled fluids, J. Fluid Mech. 798, 350 (2016).
  59. J. Domurath, G. Ausias, J. Férec, and M. Saphiannikova, Numerical investigation of dilute suspensions of rigid rods in power-law fluids, J. Non-Newtonian Fluid Mech. 280, 104280 (2020).
  60. S. A. Abtahi and G. J. Elfring, Jeffery orbits in shear-thinning fluids, Phys. Fluids 31, 103106 (2019).
  61. V. Anand and V. Narsimhan, Dynamics of spheroids in pressure-driven flows of shear thinning fluids, Phys. Rev. Fluids 8, 113302 (2023).
  62. P. Geißler, J. Domurath, G. Ausias, J. Férec, and M. Saphiannikova, Viscosity and dynamics of rigid axisymmetric particles in power-law fluids, J. Non-Newtonian Fluid Mech. 311, 104963 (2023).
  63. A. Awenlimobor and D. E. Smith, Effect of shear-thinning rheology on the dynamics and pressure distribution of a single rigid ellipsoidal particle in viscous fluid flow, Phys. Fluids 36, 123113 (2024).
  64. H. Issa, G. Natale, G. Ausias, and J. Férec, Modeling and numerical simulations of Brownian rodlike particles with anisotropic translational diffusion, Phys. Rev. Fluids 8, 033302 (2023).
  65. B. D. Leahy, D. L. Koch, and I. Cohen, The effect of shear flow on the rotational diffusion of a single axisymmetric particle, J. Fluid Mech. 772, 42 (2015).
  66. B. Chung and C. Cohen, Orientation and rheology of rodlike particles with strong Brownian diffusion in a second-order fluid under simple shear flow, J. Non-Newtonian Fluid Mech. 25, 289 (1987).
  67. J. Zhang, L. Yang, H.-X. Wang, J. Wang, and R.-Y. Dong, Cross-sectional effects on nanorod diffusion in polymer melts, Macromolecules 58, 4959 (2025).
  68. M.-R. Rokhforouz, D. D. Sin, S. Hedtrich, and J. J. Feng, Brownian dynamics simulation of the diffusion of rod-like nanoparticles in polymeric gels, Soft Matter 21, 5529 (2025).
  69. W. Sokołowski, H. Jamil, and K. Makuch, Diffusion of rod-like particles in complex fluids, Soft Matter 22, 3683 (2026).
  70. T. M. Squires and T. G. Mason, Fluid mechanics of microrheology, Annu. Rev. Fluid Mech. 42, 413 (2010).
  71. M. R. Bittermann, M. Grzelka, S. Woutersen, A. M. Brouwer, and D. Bonn, Disentangling nano- and macroscopic viscosities of aqueous polymer solutions using a fluorescent molecular rotor, J. Phys. Chem. Lett. 12, 3182 (2021).
  72. R. Zwanzig, Memory effects in irreversible thermodynamics, Phys. Rev. 124, 983 (1961).
  73. H. Mori, Transport, collective motion, and Brownian motion, Prog. Theor. Phys. 33, 423 (1965).
  74. E. Darve, J. Solomon, and A. Kia, Computing generalized Langevin equations and generalized Fokker-Planck equations, Proc. Natl. Acad. Sci. USA 106, 10884 (2009).
  75. M. S. Green, Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids, J. Chem. Phys. 22, 398 (1954).
  76. R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957).
  77. R. Smith, Multi-mode models of flow and of solute dispersion in shallow water. Part 1. General derivation, J. Fluid Mech. 283, 231 (1995).
  78. S. D. Watt and A. J. Roberts, The construction of zonal models of dispersion in channels via matched centre manifolds, J. Aust. Math. Soc. Series B, Appl. Math. 38, 101 (1996).
  79. Z. Wu and G. Q. Chen, Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe, J. Fluid Mech. 740, 196 (2014).
  80. S. Vedel, E. Hovad, and H. Bruus, Time-dependent Taylor-Aris dispersion of an initial point concentration, J. Fluid Mech. 752, 107 (2014).
  81. J. Feng and X. Chu, Shear alignment and tensorial Taylor-Aris dispersion of Brownian rods in a circular tube, arXiv:2605.17614.
  82. J. Feng and X. Chu, Transient and asymptotic Taylor-Aris dispersion of Brownian rods in arbitrary regular-polygonal ducts, arXiv:2605.22982.
  83. G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. London, Ser. A 102, 161 (1922).
  84. J. Feng, J. Leng, J. Jiang, and X. Chu, Entropic lattice Boltzmann method for general anisotropic advection-diffusion, arXiv:2605.01774.
  85. J. Feng and X. Chu, Data for “Dominant-mode closure for transient Taylor dispersion of reduced Brownian-rod transport in plane power-law channels,” https://doi.org/10.5281/zenodo.22167455.

Outline

Information

Phys. Rev. Fluids 11, 104501– Published 7 October, 2026
  • Received 17 April 2026
  • Accepted 28 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation