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Active sorting to boundaries in active nematic -- passive isotropic fluid mixtures

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Pith's one-line read Active nematic sorting at walls is controlled by anchoring, not wetting

desk verdict Solid simulation study showing anchoring-dependent boundary sorting in active-passive mixtures; the mechanism is convincing within the paranematic model, but the S0=0 assumption leaves a real gap for realistic bulk-nematic systems. read the letter →

arxiv 2509.01523 v1 pith:2SLKESRX submitted 2025-09-01 cond-mat.soft physics.bio-ph

Saraswat Bhattacharyya , Julia M. Yeomans This is my paper · ORCID
classification cond-mat.softphysics.bio-ph MSC 76A15
keywords activenematictwo-fluidmodelboundarysortinganchoringordergradientsstresscellconfinement
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 a confined mixture of an active nematic fluid and a passive isotropic fluid sorts spontaneously at a wall, with no thermodynamic wetting needed. The direction of sorting is controlled by two signs: the sign of activity (extensile vs contractile) and the anchoring of the nematic director at the boundary (planar vs homeotropic). Extensile activity accumulates at a planar-anchored wall and is depleted at a homeotropic-anchored wall; contractile activity reverses both. The mechanism is an active force generated by gradients in nematic order between the ordered boundary layer and the disordered bulk. Because the same sorting occurs when anchoring arises spontaneously from active flows, the result suggests a generic route by which active stresses can position cell populations at tissue boundaries.

What carries the argument

The central object is the active stress Π_act = -ζϕQ, where ζ is the activity (positive extensile, negative contractile), ϕ is the active-fluid concentration, and Q is the nematic tensor. Its divergence creates body forces on the combined fluid; retaining spatial variations of concentration and nematic order gives a force ∝ ζ∇(ϕS)·(2nn-I) from order and concentration gradients and a force ∝ ζSϕ∇·(nn) from director curvature. The model is a two-fluid formulation in which a center-of-mass fluid and a relative flow are separated, with strong drag between components, plus Beris-Edwards dynamics for the nematic tensor.

What would settle it

Run the same two-fluid simulations with S0 raised to a finite equilibrium bulk order (e.g. S0 = 0.5) in a square box with planar and homeotropic anchoring: the paper's mechanism predicts the boundary enrichment and depletion for extensile activity should weaken or reverse; if the concentration profile is unchanged, the ∇(ϕS) force is not the controlling factor. Experimentally, in a microtubule-kinesin extensile nematic with a fluorescently labeled active component in a chamber with planar surface anchoring, measure the wall concentration: the paper predicts a stationary enrichment above bulk.

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Extended reading notes

Core claim

In a two-fluid model of an active nematic mixed with a passive isotropic fluid and confined by walls, the paper claims that the active component sorts to the boundary purely through active stresses. With imposed anchoring, an extensile active fluid enriches the boundary layer when anchoring is planar and depletes it when anchoring is homeotropic; a contractile active fluid does the reverse. The same boundary accumulation occurs without imposed anchoring, because active flows spontaneously create planar active anchoring. The driving force is the divergence of the active stress, which produces forces from gradients of the product of concentration and nematic order, with direction set by the an

Load-bearing premise

The model sets the equilibrium nematic order of the bulk to zero, so the sorting relies on a strong contrast between an anchored, ordered boundary and a disordered bulk; if the bulk were already nematic, the order gradient that drives the effect would shrink and the predicted directions could change.

Editorial extensions

If this is right

  • With imposed planar (homeotropic) anchoring, extensile activity enriches (depletes) the boundary layer, and contractile activity does the opposite.
  • The same boundary sorting appears when anchoring is not imposed but generated by active flows, so a bare confining wall is enough for extensile material to accumulate.
  • The active force normal to the wall, ζ∇(ϕS)(2(m·n)^2 - 1), directly ties anchoring angle and activity sign to the direction of sorting.
  • In circular confinement, gradients in the magnitude of nematic order and gradients in director orientation contribute roughly equally to the radial force pushing active material outward.
  • If the active species starts as a thermodynamically phase-separated droplet, activity drives it into a spontaneously rotating boundary ring, showing active forces can override equilibrium placement.

Reading between the lines

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

  • If wall anchoring can be patterned, a single active species should be steerable: regions with planar anchoring attract extensile material, homeotropic patches repel it, so confinement geometry alone could route active components without chemical patterning.
  • The contractile case may map onto actomyosin cell aggregates, where contractile stresses and homeotropic-like alignment at tissue boundaries would drive inward sorting, providing a mechanical complement to differential adhesion in explaining interior placement.
  • Because activity sign is set by motor protein directionality, toggling motor action should reverse the wall concentration in the same chamber, a directly testable prediction of the stress-gradient mechanism.
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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

1 major / 6 minor

Summary. This paper presents lattice-Boltzmann simulations of a two-fluid model in which an active nematic component is mixed with a passive isotropic fluid and confined in square, channel, and circular geometries. The central finding is that an extensile active fluid accumulates at a boundary with planar anchoring and is depleted at a homeotropic boundary, with the opposite behavior for contractile activity. The authors attribute sorting to active forces generated by gradients in nematic order and concentration, and they show that the same mechanism works when boundary anchoring arises spontaneously from active flows. A circular-confinement analysis separates contributions from gradients in the magnitude of nematic order and gradients in director orientation, and a final demonstration shows an active droplet spreading into a rotating boundary ring.

Significance. If the proposed mechanism holds, it provides a minimal nonequilibrium route to boundary sorting that does not rely on differential adhesion, and it yields a clear, falsifiable design rule: the sign of activity and the anchoring angle determine whether the active component accumulates or depletes at the boundary. The paper has notable strengths: the result is measured from simulation rather than obtained by fitting; it uses multiple confinement protocols (free-slip and no-slip boxes, channels, circles); it reports time-averaged concentration profiles with standard deviations; it includes parameter sweeps in activity and radius; and the simulation code is publicly available on GitHub. The analytical decomposition in Sec. V uses standard active-stress expressions, and the supplementary movies and figures support the interpretation. The main caveat, discussed below, is that the model fixes the equilibrium nematic order to zero, making the bulk paranematic; the generality of the sorting mechanism outside this limit is not established.

major comments (1)
  1. [Sec. II, Eq. (16); Sec. IV] The model sets S0=0, so the bulk equilibrium state is isotropic. The sorting mechanism described in Sec. III relies on a gradient of nematic order S between the boundary and the bulk; with S0>0 this gradient is attenuated, and its sign can depend on whether the wall orders more or less strongly than the bulk. The predicted sorting direction, especially for contractile activity, is therefore untested outside the paranematic limit. Indeed, Sec. IV explicitly uses S0=0 to argue that contractile activity produces no active flows when λ>0. Because the abstract and discussion generalize to microtubule-kinesin networks and cell colonies, where bulk nematic order is common, the central claim is not established beyond the paranematic regime. I request either additional simulations with S0>0 or a clear qualification that the results apply to the paranematic limit of the model.
minor comments (6)
  1. [Sec. II, after Eq. (16)] The text says 'If a>0 and b>0' the two fluids are homogeneously mixed, but the simulation parameters list b=0. Clarify that b=0 (a purely quadratic Landau term) is also used and still corresponds to mixing.
  2. [Fig. 1(c) and Fig. 3(c)] The horizontal axis is labeled only 'activity'. Please indicate explicitly that positive values are extensile and negative values are contractile, and state the range of ζ plotted.
  3. [Sec. III, text before Fig. 2] Minor typo: 'as shown in in Fig. 2(a)' contains a duplicated 'in'.
  4. [Eqs. (19)-(20)] The derivation assumes a constant tilting angle Θ0. The text should note that this is an approximation and that near the boundary Θ varies, as acknowledged later when forder changes sign.
  5. [Sec. V, Fig. 4] The method for calculating the concentration enhancement near the wall is described in words, but the annulus width (or the criterion for choosing the peak) is not quantified. Please provide the numerical value used.
  6. [Sec. III, Fig. 2(b)-(c)] The flow arrows in the schematics are illustrative, but the text refers to 'flows due to an extensile active nematic' and 'contractile' without explaining the dipole direction. Adding a sentence defining the dipole force direction would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the boundary-sorting result is measured in simulations and the analytical explanation derives from the active-stress identity.

full rationale

The paper's central claim—that extensile (contractile) active nematics preferentially accumulate at planar (homeotropic) boundaries and deplete for the opposite anchoring—is established by direct numerical simulation of a two-fluid model, not by fitting parameters to the outcome. The analytical explanation in Sec. III is an interpretation of the observed sorting in terms of the divergence of the active stress, Π_act = −ζϕQ (Eq. 14). The normal force formula quoted from Blow et al. [40] follows immediately from this stress: for a gradient ∇(ϕS) along the boundary normal, the force component is ζ|∇(ϕS)|(2(m·n)^2 − 1)m. This is a parameter-free identity, not an independent assumption that contains the sorting result. The same holds for the tangential active-anchoring force in Sec. IV. The model equations are taken from the authors' prior work ([46,48]), but they are the input dynamical framework, not a conclusion masquerading as support; the boundary sorting is an emergent behavior of these equations, verified by simulation. No fitted quantity is renamed as a prediction: the concentrations ϕ_edge are measured, not tuned. No uniqueness theorem is invoked to forbid alternatives, and no ansatz is smuggled in solely via self-citation. The choice S0=0 (Eq. 16) is a stated modeling assumption that creates the order gradient at the wall, but it is a limitation on the scope of the claims, not a circular step. The paper is self-contained against its own simulations and the analytical arguments are direct consequences of the model equations.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

All simulation parameters are standard material and kinetic coefficients chosen to realize the paranematic, well-mixed regime; none are fitted to reproduce the sorting result. The central claim is a qualitative prediction across activity values, not a fit. The paper introduces no new particles, forces, or fields; the active stress and nematic order parameter are standard.

free parameters (5)
  • Landau mixing coefficients a and b = a=0.0001, b=0
    Chosen so the equilibrium state is homogeneously mixed (a>0), isolating active driving. These values affect the strength of sorting but are not fitted to the target.
  • Equilibrium nematic order S0 = 0
    Chosen to be a paranematic so that nematic order only arises from anchoring or activity, creating the S-gradient that drives sorting.
  • Flow-alignment parameter lambda = 0.7
    Controls the response of the director to flow; lambda>0 is required for active anchoring. Not fitted.
  • Drag coefficient gamma = 0.1
    Large-gamma limit is assumed to justify neglecting relative flow; chosen value in simulations.
  • Activity zeta = 0.001 to 0.012 (swept)
    Activity is the control parameter swept to test the sorting; not fitted.
assumptions (6)
  • domain assumption Relative flow between the two fluids is negligible (|delta u| << |u_c|) because the drag gamma is the fastest relaxation mode.
    Invoked in Sec. II to reduce the two-fluid equations to a single COM fluid; underlies the use of the active stress divergence on the COM flow.
  • domain assumption Active stress on the nematic component is Pi_act = -zeta phi Q (Eq. 14).
    Standard active-nematic constitutive relation, taken from prior literature; central to the sorting mechanism.
  • standard math The Beris-Edwards equation (Eq. 10) governs nematic order dynamics.
    Standard model for passive and active nematics; invoked without derivation.
  • domain assumption The boundary anchoring of the director is effectively infinitely strong (perfect anchoring) in Sec. III.
    The simulations impose planar or homeotropic anchoring at the walls; the analysis assumes this creates a fixed S-gradient.
  • domain assumption The free energy Eq. 16 with S0=0 and a>0, b=0 gives a homogeneous mixed paranematic equilibrium.
    This modeling choice ensures sorting is active rather than thermodynamic; it also guarantees the bulk is disordered so boundary anchoring creates the S-gradient.
  • standard math The expression for the normal active force at a boundary, F_norm = zeta |grad(phi S)| (2(m.n)^2 - 1) m, is valid.
    Taken from Blow et al. PRL 2014 (ref. 40) and used to rationalize the simulation results; assumes a slowly varying director relative to S and phi.

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Pith. "Pith review of Active sorting to boundaries in active nematic -- passive isotropic fluid mixtures." pith.science (2026). https://pith.science/paper/2SLKESRX

@misc{pith2026250901523,
  author       = {Pith},
  title        = {Pith review of: Active sorting to boundaries in active nematic -- passive isotropic fluid mixtures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2SLKESRX}},
  note         = {Machine review of arXiv:2509.01523}
}
read the original abstract

We use a two-fluid model to study a confined mixture of an active nematic fluid and a passive isotropic fluid. We find that an extensile active fluid preferentially accumulates at a boundary if the anchoring is planar, whereas its boundary concentration decreases for homeotropic anchoring. These tendencies are reversed if the active fluid is contractile. We argue that the sorting results from gradients in the nematic order, and show that the behaviour can be driven by either imposed boundary anchoring or spontaneous anchoring induced by active flows. Our results can be tested by experiments on microtubule-kinesin motor networks, and may be relevant to sorting to the boundary in cell colonies or cancer spheroids.

Figures

Figures reproduced from arXiv: 2509.01523 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. a (see also Movie 3) shows a slight accumulation of the active component at the boundary. For higher activ￾ities, ζ = 0.01 (Fig. 3b, Movie 4), there is a clear sorting of active fluid to the boundary [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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