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REVIEW 3 major objections 4 minor 34 references

Inertia-driven propulsion of asymmetric spinner-dimers at moderate Reynolds numbers

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Inertia turns purely rotating asymmetric sphere pairs into self-propelling dimers, with direction tunable by aspect ratio and Reynolds number.

desk verdict Solid LBM study with a genuinely new reversal result; the critical aspect ratio needs dimer-specific convergence checks before it is quantitative. read the letter →

arxiv 2506.02851 v1 pith:XOZ3CBQA submitted 2025-06-03 cond-mat.soft physics.flu-dyn

Zaiyi Shen , Dongfang Fu , Juho Lintuvuori This is my paper
classification cond-mat.softphysics.flu-dyn MSC 76D0576M28
keywords rotationalpropulsioninertialsecondaryflowcolloidalself-propulsionsnowmandimerReynoldsnumberlatticeBoltzmannsimulationcargotransport
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

This paper sets out to show that at moderate Reynolds numbers a purely rotating pair of spheres can propel itself along the rotation axis, without reciprocal shape changes or external translational forcing. Using lattice Boltzmann simulations, it studies three setups: two co-rotating spheres driven by an external field, two counter-rotating spheres driven by equal and opposite internal torques, and a single spinner with a passive cargo sphere. In each case, inertial secondary flows hydrodynamically bind the spheres, and size asymmetry breaks head-to-tail symmetry to create net propulsion. The paper's main new result is that the co-rotating dimer can reverse its direction of motion as the aspect ratio and Reynolds number are varied, with the reversal boundary near aspect ratio α≈0.82 at Re≈53. If correct, these results establish a simple design principle: rotational degrees of freedom alone can generate, tune, and even reverse translational motion in colloidal assemblies.

What carries the argument

The carrier of the argument is the inertial secondary flow generated by a single rotating sphere: beyond the purely azimuthal Stokes flow, inertia creates a meridional circulation that draws fluid in at the poles and ejects it near the equator, approximated at small Re by $v_r(r)=-(\omega R^4/8r^2)(3\cos^2\psi-1)(1-R/r)^2\,\mathrm{Re}$ plus the corresponding polar component. When two spheres of different radii share an axis, the unequal secondary flows at the two ends break head-to-tail symmetry, yielding a net hydrodynamic force along the axis. The scaling for the counter-rotating swimmer is built by subtracting the radial flows at the front and rear, giving $\mathrm{Re}_T\cdot\alpha^3/(1-\alpha^3)\sim\mathrm{Re}^2$, and the mechanism analysis identifies two regimes: polar pull at low Re and equatorial jet push at high Re.

What would settle it

Run the co-rotating dimer simulation at Re≈53 in boxes of side 30R and 40R with the same lattice spacing and compare the steady velocity for α=0.7 and α=0.94; if the direction switch disappears or the crossing moves far from α≈0.82, the claimed reversal boundary fails. Alternatively, a tabletop experiment with magnetically driven colloids at Re of order 50 could look for the same reversal as the size ratio is tuned.

Watch

Extended reading notes

Core claim

The central claim is that a snowman dimer of two spheres rotating about their common axis translates along that axis whenever inertial secondary flows are significant and the spheres differ in size. For two externally driven co-rotating spheres, the dimer moves toward the larger sphere at low Re, reaches a peak speed near Re≈7, then decelerates; above Re≈20 the direction becomes aspect-ratio dependent, reversing at α≈0.82 for Re=53.33. For a force-free swimmer of two counter-rotating spheres, the dimer always moves toward the smaller sphere, and its translational Reynolds number follows the scaling ReT·α³/(1−α³)∼Re² for Re<5. For a single spinner and a passive cargo, the two spheres first attract, then translate together, with an optimal cargo size ratio between roughly 1.2 and 1.5 that grows with Re. Throughout, the propulsion mechanism shifts from fluid pulled in at the poles at low Re to equatorial jets at high Re, with head-to-tail asymmetry as the common driver.

Load-bearing premise

The results assume that the periodic box of side L=20R and the repulsive contact gap between spheres do not significantly distort the high-Reynolds-number jet flows that set the direction-reversal boundary; if they do, the critical aspect ratio α≈0.82 at Re=53 is not quantitatively robust.

Editorial extensions

If this is right

  • A purely rotating asymmetric dimer is a swimmer only when inertia matters; in the Stokes limit it remains stationary.
  • The propulsion direction of the externally driven co-rotating dimer can be selected by geometry and rotation rate, with a reversal boundary near α≈0.82 at Re≈53.
  • The force-free counter-rotating swimmer always swims toward the smaller sphere, with speed set by the volume asymmetry and controlled by the Re² scaling at low Re.
  • A single spinner can pick up and carry a passive particle, with an optimal cargo size near α≈1.2–1.5 that increases with Reynolds number.
  • Both propulsion regimes (low-Re polar pulling and high-Re equatorial jet pushing) still obey the same principle, so the design rules carry over across Reynolds numbers.

Reading between the lines

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

  • The reversal boundary at α≈0.82 is likely to shift near confining walls, since the paper notes wall-induced secondary flows may tilt the equatorial jet; a wall could either suppress or enhance the reversal depending on separation.
  • The clean α³/(1−α³) collapse for the counter-rotating swimmer suggests the net force is proportional to the difference in sphere volumes; this can be tested experimentally by measuring swim speed as a function of size ratio at fixed torque.
  • The cargo-carrying result opens a direct extension to multi-particle transport: a spinner might bind a chain of passive particles, with the optimal payload size growing with Re; the paper does not explore collective cargo loading.
  • At even higher Re, the single-spinner jet may become unstable or break axisymmetry, which would modify the dimer propulsion; the paper stops at Re≈100, so the onset of wake asymmetry is a natural next check.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper uses lattice Boltzmann simulations (the open-source Ludwig code) to study three rotating-sphere dimer configurations at moderate rotational Reynolds numbers (Re up to roughly 65–80): (i) a co-rotating snowman dimer driven by an external field, (ii) a counter-rotating, torque- and force-free swimmer, and (iii) a single spinner with a passive cargo sphere. The single-sphere flow is validated against Bickley's asymptotic secondary-flow solution and against prior numerical data of Liu & Prosperetti; the low-Re co-rotating dimer is validated against Nadal et al. The main new results are: the co-rotating dimer can reverse its propulsion direction for Re>20, with a critical aspect ratio alpha≈0.82 at Re=53.33; the counter-rotating swimmer translates toward the smaller sphere and obeys a scaling Re_T alpha^3/(1-alpha^3) ~ Re^2 for Re<5; and the spinner-passive cargo dimer translates with a non-monotonic speed as a function of cargo size, with an optimal alpha* that increases with Re.

Significance. If the numerical results are robust, the paper makes a useful contribution to inertial propulsion at moderate Reynolds numbers: it demonstrates a purely geometric and inertia-based direction switch in a simple dimer, gives a clean scaling collapse for the counter-rotating swimmer, and identifies a mechanism for cargo transport by a single spinner. The manuscript has real strengths: the method is validated against an exact asymptotic solution for a single sphere, the low-Re co-rotating results agree with an independent finite-element study, the scaling law is derived from the Bickley secondary flow and then checked against the simulation collapse rather than imposed, and the code is open source. The principal weakness is that the headline quantitative claim—the reversal boundary at alpha≈0.82—is not backed by dimer-specific convergence or uncertainty tests, so the significance is contingent on those tests being supplied.

major comments (3)
  1. [Results, 'Two co-rotating spheres', Figs. 2 and 4] The reversal boundary alpha≈0.82 at Re=53.33 is a central quantitative result, but no dimer-specific finite-size, resolution, or contact-gap sensitivity study is presented. The only convergence test, Fig. 2a, is for a single sphere and measures the polar radial velocity profile, not the equatorial jet tilt that controls the reversal in Fig. 4a,b. For alpha=0.5–0.5625 the smaller sphere has a radius of only 4–4.5Δx (with R=8Δx), and the repulsive cutoff of 0.5Δx leaves a bound-state gap of order one lattice spacing. These factors could plausibly shift the jet tilt and hence the zero crossing in Fig. 4d. Since the tunable direction is the paper's headline claim, the authors should provide at least one L=30R or L=40R dimer run near Re≈53 and alpha≈0.82, and a resolution test with a larger R in lattice units.
  2. [Results, 'Two co-rotating spheres', Fig. 3c] The text explicitly attributes the high-Re deviations from Nadal et al. to 'periodic boundary effects, numerical resolution, or the surface distance between the spheres' without quantifying any of these three effects. Because these same effects are exactly those that could shift the reversal threshold in Fig. 4d, the manuscript should either quantify them for the dimer configuration or soften the quantitative reading of the reversal boundary. As written, the admitted discrepancy leaves the high-Re extension of the validated low-Re regime unsupported.
  3. [Numerical Methods; all results] No error bars, multiple realizations, or time-averaging windows are reported for any of the measured translational velocities. The zero crossing in Fig. 4d is read from a single set of curves, so the precision of the stated alpha≈0.82 is not established. At minimum, the authors should describe how u was time-averaged in the steady state and, for the reversal cases, repeat the runs with independent initial conditions or different grid phasing to assess the sensitivity of the critical alpha.
minor comments (4)
  1. [Numerical Methods and Validation, Eqs. (1)–(3)] The spherical velocity components are labelled vθ, vr and vψ without defining ψ; since sinψ and cosψ appear, ψ is evidently the polar angle, but the notation should be made explicit and consistent across the equations and the accompanying text.
  2. [All figures] The symbol for the translational Reynolds number is typeset inconsistently (ReT in some caption text, Re_T on some axes); a single notation should be used throughout.
  3. [Data Availability] The data availability statement lists only the Ludwig code, not the input scripts, parameter files, or raw output data for the specific runs shown. Providing these would make the quantitative figures reproducible and would strengthen the paper.
  4. [Conclusions] The concluding statement places the explored range at 'Re≈0...100', but the largest rotational Reynolds number actually reported in the figures appears to be about 65–80; the statement should be checked against the parameter ranges used in Figs. 3–5.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all quantitative claims are simulation results or are derived from independent analytic benchmarks; self-citations are methodological and not load-bearing.

full rationale

The paper's central quantitative results are read from lattice-Boltzmann simulations and benchmarked against external work: the single-sphere secondary flow is validated against Bickley's asymptotic solution and Liu & Prosperetti's results; the low-Re co-rotating dimer propulsion is compared with Nadal et al.'s finite-element data; the high-Re direction reversal and the threshold α≈0.82 are read directly from the simulated Re_T-versus-α curve (Fig. 4d), not imposed or fitted. The counter-rotating scaling law Re_T·α^3/(1−α^3) ∼ Re^2 is derived from the independently established Bickley secondary-flow scaling and then checked against the simulated data collapse (Fig. 5e), so the check is not circular. Self-citations (refs 19, 24, 25, 27) are used only for simulation methodology (short-range repulsion) and for the general fact that secondary flows arise in rotating-sphere systems; they do not supply the reversal threshold, the optimal aspect ratios, or the scaling collapse. The absence of a dimer-specific finite-size/resolution study for the high-Re jet flows concerns numerical robustness of the reversal boundary, not circularity. No step in the paper reduces a claimed prediction to its own inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claims rest on standard LBM hydrodynamics plus several numerical choices. No physical constant is fitted: Re and alpha are scan parameters. The scaling law uses the Bickley asymptotic flow as a starting point and is then tested by data collapse, so it is not an input-output identity. The main unvalidated choice is the periodic domain size and contact gap for dimers at high Re.

free parameters (2)
  • Particle contact separation set by repulsion cutoff = 0.5 delta-x
    The short-range repulsive force cutoff is chosen by hand and sets the surface-to-surface gap at contact; hydrodynamic coupling and jet formation depend on this gap, yet no systematic variation is reported.
  • Lattice resolution for the larger sphere = R = 8 delta-x
    The larger spinner is resolved by 8 lattice spacings; resolution may affect the high-Re jet details, and no resolution study is shown for the dimer configurations.
assumptions (4)
  • domain assumption No-slip boundary condition on particle surfaces via bounce-back on links
    Standard lattice Boltzmann approach used for all particle-fluid coupling; validated for a single sphere against the Bickley asymptotic solution.
  • domain assumption Incompressible Navier-Stokes dynamics captured by the lattice Boltzmann method accurately describe moderate-Re inertial flows
    The simulations solve LBM at Re up to about 65; no thermal fluctuations or compressibility effects are included.
  • standard math Bickley asymptotic secondary-flow solution (Eqs. 1-3) is a valid low-Re description
    Used to explain the low-Re pulling mechanism and to derive the scaling Re_T alpha^3/(1-alpha^3) proportional to Re^2.
  • ad hoc to paper Periodic boundary conditions at L=20R do not qualitatively alter dimer propulsion at high Re
    Only tested for a single sphere in Fig. 2a; the high-Re dimer results may be affected by periodicity, as the authors acknowledge for deviations from Nadal et al.

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Pith. "Pith review of Inertia-driven propulsion of asymmetric spinner-dimers at moderate Reynolds numbers." pith.science (2026). https://pith.science/paper/XOZ3CBQA

@misc{pith2026250602851,
  author       = {Pith},
  title        = {Pith review of: Inertia-driven propulsion of asymmetric spinner-dimers at moderate Reynolds numbers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XOZ3CBQA}},
  note         = {Machine review of arXiv:2506.02851}
}
read the original abstract

We investigate the translational motion of rotating colloidal systems at moderate Reynolds numbers (Re), focusing on particle dimers in snowman-like configurations under three scenarios: (i) two co-rotating spheres driven by an external field, (ii) two counter-rotating spheres driven by an internal torque as a swimmer, and (iii) a single rotating spinner with a passive sphere for cargo delivery, using hydrodynamic simulations. In all the three cases, the particles are bound together hydrodynamically, and the purely rotational motion of the spinners produces a net propulsion of the dimers along the axis of rotation due to a symmetry breaking. We demonstrate tunable dynamics, where the propulsion direction of the co-rotating dimer can be reversed by tuning the aspect ratio and Reynolds number, as well as cargo transport where a dimer consisting of a single spinner and a passive cargo particle can have a sustained locomotion due to broken head-to-tail symmetry of the overall flow fields. These findings highlight the critical role of inertia in creating locomotion from rotational motion and offer new avenues for controlling and optimizing translational motion in colloidal assemblies through rotational degrees of freedom.

Figures

Figures reproduced from arXiv: 2506.02851 by the authors.

Figure 1
Figure 1. FIG. 1. The flow field in the meridional plane for a spherical particle rotating at Reynolds numbers (Re) ranging from 0.01 to [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The normalized radial component of the fluid velocity along the spinning pole for Re = 0 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Two coaxial spherical particles rotating at the same angular velocity [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The dimer moves downward (from the larger sphere to the smaller one) when [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) A schematic of a swimmer composed of two coaxial spinners driven by equal and opposite internal torques. When [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) A time series illustrating the positions of two particles when particle 2 is rotating. The passive particle (particle [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Flow fields at relatively small Reynolds number (Re [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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Works this paper leans on

34 extracted references · 28 canonical work pages

  1. [1]

    Once they come into contact, the two particles move forward together

    is drawn toward the rotating particle by hydrodynamic interactions. Once they come into contact, the two particles move forward together. (b) The velocity of the resulting two-particle assembly is shown for different size ratiosα= 0.75,α= 1.25, andα= 1.75. In each case, a constant velocity is eventually reached in the final state. Re=32 Re=16 Re=3.2 Re=1....

    work page

  2. [2]

    Lauga, Bacterial hydrodynamics, Annual Review of Fluid Mechanics48, 105 (2016)

    E. Lauga, Bacterial hydrodynamics, Annual Review of Fluid Mechanics48, 105 (2016)

    work page 2016

  3. [3]

    Lauga and T

    E. Lauga and T. R. Powers, The hydrodynamics of swim- ming microorganisms, Reports on Progress in Physics72, 096601 (2009)

    2009

  4. [4]

    Klotsa, K

    D. Klotsa, K. A. Baldwin, R. J. Hill, and M. R. Swift, Propulsion of a two-sphere swimmer, Physical Review Letters115, 248102 (2015)

    work page 2015

  5. [5]

    Dreyfus, J

    R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone, and J. Bibette, Microscopic artificial swimmers, Nature437, 862 (2005)

    2005

  6. [6]

    Klotsa, As above, so below, and also in between: mesoscale active matter in fluids, Soft Matter15, 8946 (2019)

    D. Klotsa, As above, so below, and also in between: mesoscale active matter in fluids, Soft Matter15, 8946 (2019). 9

    work page 2019

  7. [7]

    N. J. Derr, T. Dombrowski, C. H. Rycroft, and D. Klotsa, Reciprocal swimming at intermediate reynolds number, Journal of Fluid Mechanics952, A8 (2022)

    work page 2022

  8. [8]

    P. Chen, S. Weady, S. Atis, T. Matsuzawa, M. J. Shel- ley, and W. T. Irvine, Self-propulsion, flocking and chi- ral active phases from particles spinning at intermediate reynolds numbers, Nature Physics , 1 (2024)

    work page 2024

Show all 34 references
  1. [9]

    L¨ owen, Inertial effects of self-propelled particles: From active brownian to active langevin motion, The Journal of Chemical Physics152, 040901 (2020)

    H. L¨ owen, Inertial effects of self-propelled particles: From active brownian to active langevin motion, The Journal of Chemical Physics152, 040901 (2020)

    2020

  2. [10]

    E. M. Purcell, The efficiency of propulsion by a rotat- ing flagellum, Proceedings of the National Academy of Sciences94, 11307 (1997)

    1997

  3. [11]

    Klumpp, C

    S. Klumpp, C. T. Lef` evre, M. Bennet, and D. Faivre, Swimming with magnets: from biological organisms to synthetic devices, Physics Reports789, 1 (2019)

    2019

  4. [12]

    Bricard, J.-B

    A. Bricard, J.-B. Caussin, N. Desreumaux, O. Dauchot, and D. Bartolo, Emergence of macroscopic directed mo- tion in populations of motile colloids, Nature503, 95 (2013)

    2013

  5. [13]

    Rodenborn, C.-H

    B. Rodenborn, C.-H. Chen, H. L. Swinney, B. Liu, and H. Zhang, Propulsion of microorganisms by a helical flag- ellum, Proceedings of the National Academy of Sciences 110, E338 (2013)

    2013

  6. [14]

    Driscoll, B

    M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev, and P. Chaikin, Unstable fronts and motile structures formed by microrollers, Nature Physics13, 375 (2017)

    2017

  7. [15]

    Kaiser, A

    A. Kaiser, A. Snezhko, and I. S. Aranson, Flocking ferro- magnetic colloids, Science Advances3, e1601469 (2017)

    2017

  8. [16]

    B. A. Grzybowski, H. A. Stone, and G. M. Whitesides, Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface, Nature405, 1033 (2000)

    2000

  9. [17]

    Alapan, U

    Y. Alapan, U. Bozuyuk, P. Erkoc, A. C. Karacakol, and M. Sitti, Multifunctional surface microrollers for tar- geted cargo delivery in physiological blood flow, Science Robotics5, eaba5726 (2020)

    2020

  10. [18]

    W.-Z. Fang, S. Ham, R. Qiao, and W.-Q. Tao, Magnetic actuation of surface walkers: The effects of confinement and inertia, Langmuir36, 7046 (2020)

    2020

  11. [19]

    Goto and H

    Y. Goto and H. Tanaka, Purely hydrodynamic ordering of rotating disks at a finite reynolds number, Nature Com- munications6, 5994 (2015)

    2015

  12. [20]

    Nadal, O

    F. Nadal, O. S. Pak, L. Zhu, L. Brandt, and E. Lauga, Rotational propulsion enabled by inertia, The European Physical Journal E37, 1 (2014)

    2014

  13. [21]

    Shen and J

    Z. Shen and J. S. Lintuvuori, Collective flows drive cav- itation in spinner monolayers, Physical Review Letters 130, 188202 (2023)

    2023

  14. [22]

    Liu and A

    Q. Liu and A. Prosperetti, Wall effects on a rotating sphere, Journal of Fluid Mechanics657, 1 (2010)

    2010

  15. [23]

    Bickley, Lxv

    W. Bickley, Lxv. the secondary flow due to a sphere ro- tating in a viscous fluid, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 25, 746 (1938)

    1938

  16. [24]

    Z. Shen, A. W¨ urger, and J. S. Lintuvuori, Hydrodynamic interaction of a self-propelling particle with a wall: Com- parison between an active janus particle and a squirmer model, The European Physical Journal E41, 1 (2018)

    2018

  17. [25]

    Henrich, jlintuvuori, dmarendu, qikaifzj, austin1997, shanCHEN123, ludwig cf, jurijsab, S

    kevinstratford, O. Henrich, jlintuvuori, dmarendu, qikaifzj, austin1997, shanCHEN123, ludwig cf, jurijsab, S. G. Leyva, and sumeshpt, ludwig-cf/ludwig: Ludwig 0.22.0 (2024)

    2024

  18. [26]

    Climent, K

    E. Climent, K. Yeo, M. R. Maxey, and G. E. Karniadakis, Dynamic self-assembly of spinning particles, Journal of Fluids Engineering129, 379 (2006)

    2006

  19. [27]

    Z. Shen, A. W¨ urger, and J. S. Lintuvuori, Hydrodynamic self-assembly of active colloids: chiral spinners and dy- namic crystals, Soft Matter15, 1508 (2019)

    2019

  20. [28]

    L. Kroo, J. P. Binagia, N. Eckman, M. Prakash, and E. S. Shaqfeh, A freely suspended robotic swimmer propelled by viscoelastic normal stresses, Journal of Fluid Mechan- ics944, A20 (2022)

    2022

  21. [29]

    Shen and J

    Z. Shen and J. S. Lintuvuori, Hydrodynamic cluster- ing and emergent phase separation of spherical spinners, Physical Review Research2, 013358 (2020)

    2020

  22. [30]

    Goychuk, V

    I. Goychuk, V. O. Kharchenko, and R. Metzler, Molec- ular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion, Physical Chemistry Chemical Physics16, 16524 (2014)

    2014

  23. [31]

    J. P. Binagia and E. S. Shaqfeh, Self-propulsion of a freely suspended swimmer by a swirling tail in a viscoelastic fluid, Physical Review Fluids6, 053301 (2021)

    2021

  24. [32]

    The color map represents the magnitude of the secondary flow normalized by the maximum radial velocity obtained from the asymptotic solution. -1 -0.5 0 0 5 10 15 20 vr/vm r L=20R L=30R L=40R BickleyRe=0.0128 Re=0.8 Re=32 0.0001 0.001 0.01 0.1 1 0.01 0.1 1 10 100 max|vr/ωR| Re ...

  25. [33]

    G. Li, E. Lauga, and A. M. Ardekani, Microswimming in viscoelastic fluids, Journal of Non-Newtonian Fluid Me- chanics297, 104655 (2021)

    2021

  26. [34]

    Theeyancheri, R

    L. Theeyancheri, R. Sahoo, P. Kumar, and R. Chakrabarti, In silico studies of active probe dynamics in crowded media, ACS omega7, 33637 (2022)

    2022

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Reviewed August 7, 2026 · model on record in the stance chip above.