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arxiv: 2604.06428 · v1 · submitted 2026-04-07 · ❄️ cond-mat.soft · physics.comp-ph

Two-dimensional active polar semiflexible polymer under shear flow

A. Lamura , R. G. Winkler This is my paper

Pith reviewed 2026-05-10 17:58 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.comp-ph
keywords active polymerssemiflexible filamentsshear flownegative viscositytumbling dynamicspolymer rheologymultiparticle collision dynamics
0
0 comments X

The pith

Activity makes semiflexible polymers produce negative viscosity at weak shear rates while imposing a bending-stiffness-determined scaling on their extension.

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

Numerical simulations examine how activity combined with shear flow alters the conformations, alignment, and motion of two-dimensional semiflexible polar polymers immersed in a multiparticle collision dynamics fluid. In an intermediate shear-rate window whose location depends on activity strength, the mean-square end-to-end distance measured along the flow-gradient direction follows a scaling exponent fixed by the polymer's semiflexibility. Activity is also shown to reverse the sign of the effective viscosity at low flow rates and to change the shear dependence of the polymer's tumbling period relative to both flexible active and passive cases. At the highest shear rates the flow overwhelms activity and the polymer recovers passive semiflexible behavior.

Core claim

The simulations reveal that activity in semiflexible polymers leads to conformational changes and alignment under shear, with a characteristic scaling exponent for the mean-square end-to-end distance in the gradient direction in an intermediate activity-dependent shear-rate regime, determined by the polymer's semiflexibility. The tumbling dynamics has a time scale with stronger Weissenberg number dependence than for flexible polymers. Activity impacts rheology strongly, implying negative viscosity for weak flows, while at large shear rates shear dominates and passive behavior emerges.

What carries the argument

Brownian multiparticle collision dynamics simulation of two-dimensional semiflexible active polar polymers under linear shear, with explicit bending energy and polarity.

If this is right

  • Negative viscosity at weak flows implies that the polymer suspension can accelerate rather than resist the imposed shear.
  • The observed scaling exponent for polymer extension is controlled by semiflexibility rather than by activity strength in the intermediate regime.
  • Tumbling period grows more rapidly with Weissenberg number than it does for flexible active or passive polymers.
  • At sufficiently high shear rates the system recovers the conformational statistics and rheology of passive semiflexible polymers.

Where Pith is reading between the lines

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

  • The two-dimensional scaling and negative-viscosity results supply a benchmark for three-dimensional filament simulations or experiments once hydrodynamic screening is accounted for.
  • Negative viscosity suggests possible microfluidic applications in which active filaments could be used to reduce effective drag at low driving rates.
  • Varying the activity implementation or the bending-energy functional would test whether the reported scaling exponent is universal for semiflexible active polymers.

Load-bearing premise

The chosen model of activity, the specific form of semiflexible bending energy, and the multiparticle collision dynamics fluid together produce results that remain valid when the same physics is realized in three dimensions or with other activity implementations.

What would settle it

Measurement of strictly positive viscosity across all weak shear rates, or absence of the semiflexibility-set scaling exponent in the intermediate regime, in either simulation or experiment.

Figures

Figures reproduced from arXiv: 2604.06428 by A. Lamura, R. G. Winkler.

Figure 1
Figure 1. Figure 1: FIG. 1. Normalized probability distribution function of the polymer [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Root mean-square end-to-end distance as a function of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: and the multimedia file movie2.mp4 available online for Lp/L = 0.4, Pe = 103 , Wi = 70). At very high values of the Weissenberg number, the tumbling dynamics is faster and the polymer bends completely, enhanced by activity, while slid￾ing over itself (see the multimedia file movie3.mp4 available online for Lp/L = 0.4, Pe = 103 , Wi = 103 ). The stiffer polymer ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Normalized probability distribution function of the polymer [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Normalized probability distribution function of the polymer [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Mean-square end-to-end distance along the gradient di [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) suggest a weak logarithmic dependence of the aver￾age bond angle on WiPe for large Wi. As expected, the mean bond angles of the stiffer polymer are smaller than those of the more flexible polymer ( [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Normalized probability distribution function of the angle [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Angle [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: displays the simulation results for Lp/L = 2 and various activities. In the passive limit, the viscosity decreases approximately with the exponent −1/2 with increasing shear, as observed and predicted previously26,33,56,58,89,90. Remark￾ably, above a certain Péclet number, the viscosity is nega￾tive over an activity-dependent range of Weissenberg num￾bers, as indicted in [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
read the original abstract

The nonequilibrium structural and dynamical properties of semiflexible active polar polymers subject to linear flow are studied by numerical simulations. Filaments are confined in two dimensions and immersed in a fluid described by the Brownian Multiparticle Collision Dynamics approach. The applied shear flow causes conformational changes of a polymer, aligns it along the flow direction, and induces a tumbling motion at large flow rates. In an intermediate, activity-dependent shear-rate regime, a characteristic scaling exponent for the mean-square end-to-end distance along the gradient direction is observed. This exponent appears to be determined by the semiflexibility of the polymer. The tumbling dynamics exhibits a characteristic time, with a stronger dependence on the Weissenberg number than that of flexible active or passive polymers. Activity strongly impacts the rheological properties of the semiflexible polymers, and even implies a negative viscosity for weak flows. At very large values of the shear rate, shear dominates over activity and passive-polymer behavior is assumed.

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

3 major / 2 minor

Summary. The manuscript numerically studies the nonequilibrium conformational, dynamical, and rheological properties of two-dimensional semiflexible active polar polymers under linear shear flow, modeled with Brownian multiparticle collision dynamics (MPCD) for the fluid. Key observations include shear-induced alignment and tumbling at high rates, an activity-dependent intermediate shear-rate regime exhibiting a characteristic scaling exponent for the mean-square end-to-end distance in the gradient direction that appears controlled by the polymer's semiflexibility, a tumbling time with stronger Weissenberg-number dependence than for flexible polymers, and activity-induced negative viscosity at weak flows, with recovery of passive-polymer behavior at very high shear rates.

Significance. If the reported scaling and negative-viscosity results prove robust, they would add to the literature on active semiflexible filaments under flow, with potential relevance to biological systems such as cytoskeletal networks. The use of MPCD to incorporate hydrodynamic interactions is a methodological strength. However, the strictly two-dimensional setting and the specific polar-activity implementation limit immediate generalization to three-dimensional experimental realizations or alternative activity models.

major comments (3)
  1. [Abstract / conformational results] Abstract and conformational-results section: the statement that the scaling exponent for mean-square end-to-end distance along the gradient direction 'appears to be determined by the semiflexibility of the polymer' is presented as a numerical observation for a single bending-rigidity value; no systematic variation of the bending energy (or direct comparison to the flexible limit) is shown to isolate its effect from the activity-dependent location of the intermediate regime.
  2. [Rheology results] Rheology-results section: the claim of negative viscosity at weak flows rests on the MPCD stress-tensor evaluation under shear; the manuscript provides no explicit formula for the stress, no convergence checks with collision-cell size or particle number, and no discussion of possible 2D artifacts or sensitivity to the chosen collision rules, all of which are load-bearing for the rheological conclusion.
  3. [Methods / all results] Methods and results sections: no error bars, statistical uncertainties, or parameter table (activity strength, bending rigidity, shear rates, Weissenberg numbers) are reported for any of the scaling exponents, tumbling times, or viscosity values, preventing assessment of numerical robustness and reproducibility.
minor comments (2)
  1. [Abstract] The abstract and main text would benefit from a brief statement on how the observed scaling exponent was extracted (fitting range, number of independent runs).
  2. [Discussion / conclusions] A short discussion of the mapping (or lack thereof) from the 2D polar-activity model to three-dimensional force-dipole or non-polar realizations would clarify the scope of the conclusions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the potential significance of our work. We address each major comment below and will revise the manuscript to incorporate the suggested improvements for clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract / conformational results] Abstract and conformational-results section: the statement that the scaling exponent for mean-square end-to-end distance along the gradient direction 'appears to be determined by the semiflexibility of the polymer' is presented as a numerical observation for a single bending-rigidity value; no systematic variation of the bending energy (or direct comparison to the flexible limit) is shown to isolate its effect from the activity-dependent location of the intermediate regime.

    Authors: The reported scaling exponent was obtained for the semiflexible bending rigidity employed in all simulations. While the manuscript does not include a systematic scan of bending energies, the intermediate regime is activity-dependent and the observed exponent is consistent with semiflexible behavior under shear. To isolate the role of semiflexibility, we will add a direct comparison to the flexible (zero bending rigidity) limit in the revised conformational-results section, showing that the scaling changes in the flexible case. revision: yes

  2. Referee: [Rheology results] Rheology-results section: the claim of negative viscosity at weak flows rests on the MPCD stress-tensor evaluation under shear; the manuscript provides no explicit formula for the stress, no convergence checks with collision-cell size or particle number, and no discussion of possible 2D artifacts or sensitivity to the chosen collision rules, all of which are load-bearing for the rheological conclusion.

    Authors: The stress tensor follows the standard MPCD formulation referenced in the methods, but we agree that explicit details are needed to support the negative-viscosity claim. In the revision we will insert the explicit stress-tensor expression, add convergence tests versus collision-cell size and particle number, and include a short discussion of 2D hydrodynamic artifacts and collision-rule sensitivity. revision: yes

  3. Referee: [Methods / all results] Methods and results sections: no error bars, statistical uncertainties, or parameter table (activity strength, bending rigidity, shear rates, Weissenberg numbers) are reported for any of the scaling exponents, tumbling times, or viscosity values, preventing assessment of numerical robustness and reproducibility.

    Authors: We concur that error bars and a parameter summary are essential for reproducibility. The revised manuscript will contain a table listing all key parameters (activity strength, bending rigidity, shear rates, Weissenberg numbers) and will display error bars on all reported quantities, obtained from ensemble averages over multiple independent runs. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of numerical simulations with no derivation chain reducing to inputs or self-citations.

full rationale

The manuscript relies entirely on Brownian MPCD simulations of a 2D semiflexible active polar polymer model under shear. All reported quantities (conformational changes, scaling of mean-square end-to-end distance, tumbling times, and viscosity including negative values) are measured observables from the simulations. No analytical derivation, fitted-parameter prediction, or load-bearing self-citation is invoked to obtain the central claims; the scaling exponent is stated as an observed numerical feature whose origin is attributed to semiflexibility within the chosen model. Self-citations, if present, are not used to justify uniqueness or to close any loop. The work is therefore self-contained against external benchmarks and receives the default non-circularity score.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claims rest on a standard numerical method (Brownian MPCD) plus model choices for activity and bending stiffness; no new entities are postulated.

free parameters (3)
  • activity strength
    Parameter controlling internal driving force, varied to define activity-dependent regimes.
  • bending rigidity
    Controls semiflexibility, directly tied to the reported scaling exponent.
  • shear rate
    External control parameter scanned across regimes.
axioms (1)
  • domain assumption Brownian Multiparticle Collision Dynamics correctly captures the hydrodynamic interactions between polymer and solvent in 2D.
    Invoked as the fluid solver without further justification in the abstract.

pith-pipeline@v0.9.0 · 5459 in / 1334 out tokens · 24414 ms · 2026-05-10T17:58:01.121992+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
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    Relation between the paper passage and the cited Recognition theorem.

    In an intermediate, activity-dependent shear-rate regime, a characteristic scaling exponent for the mean-square end-to-end distance along the gradient direction is observed. This exponent appears to be determined by the semiflexibility of the polymer.

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matches
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unclear
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Reference graph

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