Pith. sign in

REVIEW 2 major objections 5 minor 63 references

Stability of co-annular active and passive confined fluids

T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A circular droplet inside a confined active nematic can be destabilized by activity in both extensile and contractile systems, with each Fourier mode's growth rate fixed by a compact dispersion relation.

desk verdict A careful and transparent analytic linear stability theory for a confined active–passive interface, internally consistent but resting on an untested Pe→0 limit and a silently dropped flow-alignment parameter. read the letter →

arxiv 2501.04918 v2 pith:7D7APY55 submitted 2025-01-09 cond-mat.soft physics.bio-phphysics.flu-dyn

Tanumoy Dhar , Michael J. Shelley , David Saintillan This is my paper · ORCID
classification cond-mat.softphysics.bio-phphysics.flu-dyn MSC 76A1576D0735B35
keywords activenematicpassivedropletlinearstabilityLorentzreciprocaltheoremStokesflowextensilevscontractileinterfacialinstabilityconfinement
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 asks what happens to a circular passive liquid droplet sitting inside a confined active nematic, a fluid made of self-propelled elongated units, when the outer fluid is active and the whole system is squeezed into a circular domain. Using a linear stability analysis in the sharply aligned, strong-relaxation limit, it derives a dispersion relation for the growth of each interfacial Fourier mode. The central result is that activity destabilizes the droplet in both extensile and contractile systems, but in opposite ways: the translational mode ($m=1$) is stabilized by extensile activity and destabilized by contractile activity, while shape-deforming modes ($m\ge2$) are destabilized by extensile activity for small to intermediate droplets. Capillary and elastic stresses typically resist deformation, and the theory also covers the inverse geometry of an active nematic droplet surrounded by a passive viscous layer, where extensile activity is always destabilizing. These predictions matter because the same stress balance is thought to govern passive compartments in cells, from droplets in bacterial suspensions to nucleoli and heterochromatin inside the nucleus.

What carries the argument

The load-bearing object is the auxiliary Stokes flow used with the Lorentz reciprocal theorem. Instead of solving the actual perturbed velocity field, the paper defines a passive Newtonian problem in the same annulus with a prescribed normal traction jump $\Sigma_0\cos m\theta$ at the interface, whose streamfunction is $G_m(r)$ and solves the biharmonic equation with no-slip at $r=1$ and matching at $r=\eta$. The reciprocal theorem re-expresses the unknown real flow in terms of contour integrals around the circular interface, which involve the already-known linearized active and elastic stresses and $G_m(r)$; the arbitrary $\Sigma_0$ cancels, leaving the ordinary differential equation and dispersion relation for $\tilde\zeta_1$. The same auxiliary problem serves both geometries, with the active stresses moved from the outer annulus to the droplet interior in the inverse case. Also load-bearing is the limit $\mathrm{Pe}\to0$, which makes the director angle $\beta$ satisfy Laplace's equation and turns the nematic orientation into a pure boundary-value problem driven by the instantaneous droplet shape.

What would settle it

Run the same two-annulus system in a finite-$\mathrm{Pe}$ simulation or a microtubule/motor experiment with an extensile nematic, $\eta\approx0.2$, small $\xi^2$, and large $\mathrm{Ca}$: the paper predicts the $m=2$ deformation mode should grow with positive $\Lambda_2$. If the droplet remains circular or the fastest-growing mode differs, the dispersion relation is wrong.

Watch

Extended reading notes

Core claim

Under the strong relaxation limit $\mathrm{Pe}\to0$, the nematic director is determined purely by the geometry: it is the solution of Laplace's equation with strong tangential anchoring at the droplet surface and at the outer boundary. The paper linearizes about the circular concentric base state and represents the interface as $\zeta(\theta,t)=\epsilon\tilde\zeta_1(t)\cos m\theta$. Its central result is the first-order evolution equation $d\tilde\zeta_1/dt=\Lambda_m\tilde\zeta_1$ with $\Lambda_m=\frac{1}{\mathrm{Ca}}\Xi_m^c+S\Xi_m^a+\xi^2\Xi_m^e$, where $\mathrm{Ca}$ is the active capillary number, $S=+1$ for extensile and $S=-1$ for contractile activity, and $\xi$ is the ratio of the active length scale to the confinement radius. The functions $\Xi_m^c$, $\Xi_m^a$, and $\Xi_m^e$ are explicit integrals of the streamfunction of an auxiliary Newtonian flow and depend on the radius ratio $\eta$ and viscosity ratio $\lambda$. The paper computes their signs across the parameter space and concludes that the translational mode is stable under extensile activity but unstable under contractile activity, whereas deformation modes are destabilized by extensile activity in small to intermediate drops; in the inverse geometry an extensile active droplet is always destabilized, and elasticity is predominantly stabilizing. The instability picture is therefore set by a competition of capillary, elastic, and active tractions with bulk active forces.

Load-bearing premise

The load-bearing premise is that the nematic director relaxes infinitely fast ($\mathrm{Pe}\to0$), so the flow never advects or bends the director; the director field at every instant is just the shape-determined solution of Laplace's equation.

Editorial extensions

If this is right

  • A passive droplet in an extensile nematic annulus should not drift on its own at linear order, but should begin to deform through $m\ge2$ modes once the radius ratio falls in the predicted unstable window.
  • In a contractile environment the same droplet should instead be set into translation first, since the active contribution to the translational mode changes sign with $S=-1$.
  • The stability thresholds shift with the viscosity ratio and the relative elastic stress $\xi^2$, so confinement size and drop rheology could be used to tune whether a droplet moves or changes shape.
  • Because all modes grow independently in the linear theory, the mode with the largest $\Lambda_m$ is expected to dominate the observed dynamics in an experiment.
  • The inverse configuration suggests that an extensile active droplet inside a passive layer will generically deform or translate, which is relevant to nucleoli and other active inclusions in the cell nucleus.

Reading between the lines

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

  • Extending beyond the paper: at finite $\mathrm{Pe}$ the director is no longer enslaved to the geometry, so the same dispersion relation would acquire corrections from flow alignment and director advection; recomputing $\Lambda_m$ at small finite $\mathrm{Pe}$ would show whether the $m=1$ stability reversal survives.
  • Extending beyond the paper: the strong-anchoring assumption fixes the director orientation at the interfaces; allowing weak anchoring would introduce a surface energy term that could soften the elastic traction and modify the small-drop limit where the elastic growth rate diverges.
  • Extending beyond the paper: the linear analysis treats all modes independently, but in the inverted problem a $+1$ topological defect sits at the droplet center; defect motion at nonlinear order could break circular symmetry before the predicted linear instability takes over.
  • Extending beyond the paper: the result that the active contribution to translation depends only weakly on viscosity ratio suggests an experimentally robust test: the sign of $\Lambda_1$ should be nearly independent of drop viscosity, which could be checked directly in a microfluidic device.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper presents a two-dimensional linear stability analysis of a passive viscous Newtonian droplet surrounded by an active nematic liquid crystal in circular confinement, and of the inverted configuration in which an active nematic droplet is surrounded by a passive viscous layer. In the sharply aligned limit with strong anchoring and Pe→0, the director field is slaved to the instantaneous geometry through Laplace's equation. Using the Lorentz reciprocal theorem for Stokes flow, the authors reduce the linearized interfacial problem to a first-order amplitude equation for azimuthal Fourier modes and obtain closed-form growth rates Λ_m = (1/Ca)Ξc_m + SΞa_m + ξ²Ξe_m as functions of the radius ratio η, viscosity ratio λ, mode number m, and elastic parameter ξ. They identify stable and unstable regions for the translational mode (m=1) and deformation modes (m≥2) for both extensile (S=+1) and contractile (S=-1) systems, and they visualize the bulk force densities and surface tractions to interpret the mechanisms.

Significance. If correct, this is a useful analytical reference calculation for active-passive interfaces in confinement. Its strengths are the self-contained derivation of the auxiliary Stokes problem, the absence of any fitted parameters, and the explicit closed-form growth rates covering both geometries and both signs of activity. The reciprocal-theorem formulation is elegant and could be reused in related problems. The significance is partly conditional: because the entire calculation is performed in the Pe→0 (strong elastic relaxation) limit and with an isotropic viscous response, the stability phase diagrams apply only in that regime, and the paper does not demonstrate how robust the predictions are at finite Pe.

major comments (2)
  1. [Sec. II.D (Eqs. 14-15) and Sec. V] The central dispersion relation (53)-(57) is derived in the strict limit Pe→0, in which the director is slaved to the instantaneous shape. The authors acknowledge in Sec. V that finite-Pe effects can introduce spontaneous-flow instabilities, but they do not provide any estimate of Pe for the biological systems cited in the abstract and introduction, nor any small-Pe correction. Because the active and elastic stresses generate flows that can advect the director when Pe is not small, the stability phase diagrams (Figs. 2, 5, 7) are conditional on this limit. I request that the authors quantify the regime of validity (parameter estimates for bacterial suspensions and chromatin systems) and either provide a finite-Pe analysis or explicitly restrict the biological claims to Pe≪1.
  2. [Sec. III.F (Eqs. 53-57) and Sec. IV.C] The closed-form growth rates are long and are not validated against any known limit or direct numerical simulation. In particular, setting S=0 and ξ=0 should recover the capillary stability of a confined passive droplet, and the m=1 mode should be neutrally stable for a passive system; the paper does not verify these limits. A few numerical spot checks of the dispersion relation against a direct solution of the linearized Stokes problem would substantially increase confidence in the algebra and in the phase diagrams.
minor comments (5)
  1. [Fig. 4 caption] The caption refers to 'translational modes' for m≥2 and labels the capillary contribution as Ξa_m; both should be corrected to 'deformation modes' and Ξc_m, respectively.
  2. [Sec. II.D] The text states 'we assume that ξ is of order unity', but several figures (e.g., Figs. 5 and 7) use ξ²=0.005 and 0.1; please reconcile this statement with the parameter range shown.
  3. [Eq. (23)] The pressure inside the drop is denoted p0 without the overbar convention established for inner variables; use \bar{p}_0 for consistency.
  4. [Sec. V] There are two typos: 'in unclear' should be 'is unclear' and 'an useful tool' should be 'a useful tool'.
  5. [Sec. III.F.2 and Fig. 4] In the text preceding Eq. (63), the notation Ξa_m is used for both the active contribution and, in the figure caption, for the capillary contribution; please clarify the notation consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dispersion relation is derived analytically from stated governing equations with no fitted parameters or data.

full rationale

The paper's central result, the dispersion relation (Eqs. (53)-(54)), is obtained by a closed-form linear stability analysis: the base state, perturbed director field (Eq. (28)), linearized stresses (Eqs. (30) and (32)), boundary conditions (Eq. (37)), and Lorentz reciprocal theorem reduction (Eqs. (47)-(52)) all follow from the stated model equations and anchoring conditions. The growth-rate coefficients Ξc_m, Ξa_m, and Ξe_m are explicit integrals and algebraic expressions involving the analytically known auxiliary Stokes flow Gm(r); no parameter is fitted to data, and no 'prediction' is equivalent to an input by construction. The main approximation, Pe→0 (Eq. (15), strong nematic relaxation), is a stated physical limit whose consequences the authors explicitly acknowledge in Sec. V ('If the assumption of strong elasticity is relaxed, additional instabilities can arise that involve spontaneous swirling flows...'); it is a scope limitation, not a circular step. Self-citations such as [10] and [48] appear only as biological motivation or prior modeling context, and the cited constitutive results [30,40,41] are independent standard results, not self-citations that carry the derivation. No self-definitional, fitted-input, uniqueness-importation, or ansatz-smuggling pattern is present.

Assumptions & free parameters 0 free parameters · 8 assumptions · 0 invented entities

The paper introduces no new entities and fits no parameters. Its predictions rest on standard active nematic theory plus strong simplifications; the most fragile is the Pe→0 limit, which the authors acknowledge.

assumptions (8)
  • standard math Stokes equations govern the fluid momentum in both phases
    Used throughout Sec. II and III; valid for low Reynolds number active suspensions.
  • standard math Lorentz reciprocal theorem for Stokes flow
    Central tool in Sec. III.E; relies on linearity of Stokes equations.
  • domain assumption Ericksen-Leslie model for nematic liquid crystal
    Eq. (1), Sec. II.A; standard continuum model for active nematics.
  • domain assumption One-constant approximation for Frank elasticity
    Eq. (2) with Fd = K/2 ||∇q||²; used to simplify the molecular field to K∇²q.
  • domain assumption Strong parallel (tangential) anchoring at both the drop interface and outer boundary
    Sec. II.C; fixes the base state and makes the director field a purely geometric solution.
  • ad hoc to paper Pe→0 (strong nematic relaxation)
    Eq. (15); reduces director equation to Laplace's equation ∇²β=0, decoupling the director from flow and making the problem tractable. The authors note relaxing this could introduce new instabilities.
  • ad hoc to paper Isotropic viscous response (flow-alignment parameter ϖ set to zero)
    Eqs. (7) and (16); simplifies the elastic stress to -ξ²∇q·∇qᵀ. This assumption is not explicitly stated in the text.
  • domain assumption Sharply aligned limit |q|=1
    Stated at the start of Sec. II; excludes disclinations except the +1 defect at the origin in the inverted problem.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Stability of co-annular active and passive confined fluids." pith.science (2026). https://pith.science/paper/7D7APY55

@misc{pith2026250104918,
  author       = {Pith},
  title        = {Pith review of: Stability of co-annular active and passive confined fluids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7D7APY55}},
  note         = {Machine review of arXiv:2501.04918}
}
read the original abstract

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and cell nucleus.

Figures

Figures reproduced from arXiv: 2501.04918 by the authors.

Figure 1
Figure 1. FIG. 1. Problem definition: a viscous drop is placed in an apolar active nematic suspension under circular confinement, with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Active contribution Ξ [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Active and (b) elastic bulk force densities and surface tractions at linear order in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Capillary contribution Ξ [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Color map of the total growth rate Λ [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Active and (b) elastic bulk force densities and surface tractions at linear order in [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Active contribution Ξ [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Active contribution Ξ [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 62 canonical work pages

  1. [1]

    (33) are known from Eqs

    = 0, for r > η+ ζ, (33) ∇ ·u1 = 0, ∇ ·σh 1 = 0, for r < η+ ζ, (34) where the active and elastic stresses in Eq. (33) are known from Eqs. (30) and (32). The flows in the two regions are coupled via the dynamic boundary condition (18), which applies at r = η + ζ. Our method of solution, described in Sec. III E, will rely on the Lorentz reciprocal theorem fo...

    work page

  2. [2]

    (22) The pressure inside the passive drop is uniform and is dictated by the stress balance (18): p0 = S ln η − ξ2 2η2 + 1 ηCa

    = S r + ξ2 r3 ˆr = ∇ S ln r − ξ2 2r2 , (21) from which p0(r) = S ln r − ξ2 2r2 . (22) The pressure inside the passive drop is uniform and is dictated by the stress balance (18): p0 = S ln η − ξ2 2η2 + 1 ηCa . (23) B. Domain perturbation and linearized nematic field Leveraging periodicity in the θ direction, we perturb the shape of the interface with an az...

    work page

  3. [3]

    III E and uses the same auxiliary Newtonian flow problem

    Lorentz reciprocal theorem Application of the Lorentz reciprocal theorem follows the same steps as discussed in Sec. III E and uses the same auxiliary Newtonian flow problem. Once again, the main difference with Sec. III E is that active and elastic stresses now appear inside the drop. As a result, the analog of Eq. (45) has no bulk contribution and reads...

    work page

  4. [4]

    · U = (σh 1 + σa 1 + σe

    work page

  5. [5]

    (44) Subtracting Eq

    : E, (43) ∇ · Σh · u1 = Σh : e1. (44) Subtracting Eq. (44) from Eq. (43), integrating over the outer region Ω + 0 , and applying the divergence theorem then yields Z C0 ˆr · Σh · u1 − (σh 1 + σa 1 + σe

    work page

  6. [6]

    · U dℓ = Z Ω+ 0 (σa 1 + σe

    work page

  7. [7]

    Note that the boundary term at r = 1 vanished due to the no-slip condition, and that we used that σh 1 : E = Σh : e1 to simplify the right-hand side

    : E dS, (45) where C0 denotes the circular interface at r = η. Note that the boundary term at r = 1 vanished due to the no-slip condition, and that we used that σh 1 : E = Σh : e1 to simplify the right-hand side. Following an identical process in the inner region Ω − 0 = {(r, θ) | r < η}, we obtain, Z C0 ˆr · h Σ h · u1 − σh 1 · U i dℓ = 0, (46) which doe...

    work page

  8. [8]

    At linear order, it does not affect the curvature of the drop, and therefore the growth is unaffected by surface tension: Ξ c 1(η, λ) = 0

    Translation mode (m = 1) The first normal mode m = 1 captures translation of the drop and is the only mode with a non-zero displacement of the drop center of mass. At linear order, it does not affect the curvature of the drop, and therefore the growth is unaffected by surface tension: Ξ c 1(η, λ) = 0. The function Gm(r) for m = 1 is given in Eq. (A-6). In...

    work page

Show all 63 references
  1. [9]

    The function Gm(r) for m ≥ 2 is given in Eq

    Deformation modes (m ≥ 2) Modes with m ≥ 2 describe deformations of the drop interface and do not involve translation of the center of mass. The function Gm(r) for m ≥ 2 is given in Eq. (A-10). The corresponding capillary, active, and elastic contributions 11 FIG. 4. (a) Capil...

  2. [10]

    Base state In the base state, the nematic field lines inside the drop are also circles centered at the origin, with β0 given by Eq. (19). A topological defect of charge +1 is present at the origin. The base state active and elastic stresses are still given by Eq. (20). They in...

  3. [11]

    (24), which results in the boundary condition of Eq

    Domain perturbation and linearized problem The shape of the drop is once again deformed according to Eq. (24), which results in the boundary condition of Eq. (27) for the perturbation angle β1 at the drop surface. A solution of ∇2β1 = 0 inside the drop that satisfies this cond...

  4. [12]

    Spontaneous motion in hierarchically assembled active matter,

    T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491, 431–434 (2012)

    2012

  5. [13]

    · U i dℓ = Z Ω− 0 (σa 1 + σe

  6. [14]

    Combining Eqs

    : E dS, (74) where Ω − 0 = {(r, θ) | r < η} denotes the interior of the drop in two dimensions. Combining Eqs. (73) and (74) yields the main result Z C0 ˆr · h Σh − Σ h · u1 − σh 1 − σe 1 − σa 1 − σh 1 · U i dℓ = − Z Ω− 0 σe 1 + σa 1 : E dS. (75) The first term in the contour ...

  7. [15]

    The propagation of active-passive interfaces in bacterial swarms,

    A. E. Patteson, A. Gopinath, and P. E. Arratia, “The propagation of active-passive interfaces in bacterial swarms,” Nat. Commun. 9, 5373 (2018)

    2018

  8. [16]

    Mor- phological instability and roughening of growing 3D bacterial colonies,

    A. Mart ´ ınez-Calvo, T. Bhattacharjee, R. K. Bay, H. N. Luu, A. M. Hancock, N. S. Wingreen, and S. S. Datta, “Mor- phological instability and roughening of growing 3D bacterial colonies,” Proc. Natl. Acad. Sci. USA 119, e2208019119 (2022)

    2022

  9. [17]

    Nucleating actin for invasion,

    A. N¨ urnberg, T. Kitzing, and R. Grosse, “Nucleating actin for invasion,” Nat. Rev. Cancer. 11, 177 (2011)

    2011

  10. [18]

    Signaling inputs to invadopodia and podosomes,

    D. Hoshino, K. M Branch, and A. M Weaver, “Signaling inputs to invadopodia and podosomes,” J. Cell Sci.126, 2979–2989 (2013)

    2013

  11. [19]

    Parallels between tissue repair and embryo morphogenesis,

    P. Martin and S. M. Parkhurst, “Parallels between tissue repair and embryo morphogenesis,” Development 131, 3021–3034 (2004)

    2004

  12. [20]

    Epithelia are multiscale active liquid crystals,

    J.-M. Armengol-Collado, L. N. Carenza, J. Eckert, D. Krommydas, and L. Giomi, “Epithelia are multiscale active liquid crystals,” Nat. Phys. 19, 1773–1779 (2023)

    2023

  13. [21]

    On the origin of shape fluctuations of the cell nucleus,

    F.-Y. Chu, S. C. Haley, and A. Zidovska, “On the origin of shape fluctuations of the cell nucleus,” Proc. Natl. Acad. Sci. USA 114, 10338 (2017)

    2017

  14. [22]

    Intracellular fluid mechanics: Coupling cytoplasmic flow with active cytoskeletal gel,

    A. Mogilner and A. Manhart, “Intracellular fluid mechanics: Coupling cytoplasmic flow with active cytoskeletal gel,” Annu. Rev. Fluid Mech. 50, 347 (2018)

    2018

  15. [23]

    Surface fluctuations and coalescence of nucleolar droplets in the human cell nucleus,

    C. M. Caragine, S. C. Haley, and A. Zidovska, “Surface fluctuations and coalescence of nucleolar droplets in the human cell nucleus,” Phys. Rev. Lett. 121, 148101 (2018)

    2018

  16. [24]

    Euchromatin activity enhances segregation and compaction of heterochromatin in the cell nucleus,

    A. Mahajan, W. Yan, A. Zidovska, D. Saintillan, and M. J Shelley, “Euchromatin activity enhances segregation and compaction of heterochromatin in the cell nucleus,” Phys. Rev. X 12, 041033 (2022)

    2022

  17. [25]

    Active hydrodynamic theory of euchromatin and heterochro- matin,

    S. A. Rautu, A. Zidovska, D. Saintillan, and M. J. Shelley, “Active hydrodynamic theory of euchromatin and heterochro- matin,” arXiv:2503.20964 (2025)

    2025 arXiv

  18. [26]

    Object transport by a confined active suspension,

    J. B. Freund, “Object transport by a confined active suspension,” J. Fluid Mech. 960, A16 (2023)

    2023

  19. [27]

    The dynamics of microtubule/motor-protein assemblies in biology and physics,

    M. J. Shelley, “The dynamics of microtubule/motor-protein assemblies in biology and physics,” Annu. Rev. Fluid Mech. 48, 487–506 (2016)

    2016

  20. [28]

    Dynamics of active liquid interfaces,

    R. Adkins, I. Kolvin, Z. You, S. Witthaus, M. C. Marchetti, and Z. Dogic, “Dynamics of active liquid interfaces,” Science 377, 768–772 (2022)

    2022

  21. [29]

    Spontaneous symmetry breaking in active droplets provides a generic route to motility,

    E. Tjhung, D. Marenduzzo, and M. E. Cates, “Spontaneous symmetry breaking in active droplets provides a generic route to motility,” Proc. Natl. Acad. Sci. USA 109, 12381–12386 (2012)

    2012

  22. [30]

    A drop of active matter,

    J. F. Joanny and S. Ramaswamy, “A drop of active matter,” J. Fluid Mech. 705, 46–57 (2012)

    2012

  23. [31]

    Spontaneous division and motility in active nematic droplets,

    L. Giomi and A. DeSimone, “Spontaneous division and motility in active nematic droplets,” Phys. Rev. Lett. 112, 147802 (2014)

    2014

  24. [32]

    Active polar fluid flow in finite droplets,

    C. A. Whitfield, D. Marenduzzo, R. Voituriez, and R. J. Hawkins, “Active polar fluid flow in finite droplets,” Eur. Phys. J. E 37, 1–15 (2014). 19

    2014

  25. [33]

    Motility of active fluid drops on surfaces,

    D. Khoromskaia and G. P. Alexander, “Motility of active fluid drops on surfaces,” Phys. Rev. E 92, 062311 (2015)

    2015

  26. [34]

    The many behaviors of deformable active droplets,

    Y.-N. Young, M. Shelley, and D. Stein, “The many behaviors of deformable active droplets,” MBE 18 (2021)

    2021

  27. [35]

    Fingering instability of active nematic droplets,

    R. Alert, “Fingering instability of active nematic droplets,” J. Phys. A: Math. Theor. 55, 234009 (2022)

    2022

  28. [36]

    Generic phase diagram of active polar films,

    R. Voituriez, J. F. Joanny, and J. Prost, “Generic phase diagram of active polar films,” Phys. Rev. Lett. 96, 028102 (2006)

    2006

  29. [37]

    Instabilities and waves in thin films of living fluids,

    S. Sankararaman and S. Ramaswamy, “Instabilities and waves in thin films of living fluids,” Phys. Rev. Lett. 102, 118107 (2009)

    2009

  30. [38]

    Motility of active nematic films driven by “active anchoring

    M. L. Blow, M. Aqil, B. Liebchen, and D. Marenduzzo, “Motility of active nematic films driven by “active anchoring”,” Soft Matter 13, 6137–6144 (2017)

    2017

  31. [39]

    Interfacial instabilities in active viscous films,

    R. Alonso-Matilla and D. Saintillan, “Interfacial instabilities in active viscous films,” J. Nonnewton. Fluid Mech. 269, 57–64 (2019)

    2019

  32. [40]

    for a derivation. In Eq. (4), we adopt the convention ( ∇ ·σ)i = ∂kσki for the tensorial divergence; accordingly, the traction on a surface with outward unit normal n is defined as t = n · σ. In the passive viscous drop, the only stress is hydrodynamic, and the governing equat...

  33. [41]

    Free object in a confined active contractile nematic fluid: Fixed-point and limit-cycle behaviors,

    J. B. Freund, “Free object in a confined active contractile nematic fluid: Fixed-point and limit-cycle behaviors,” Phys. Rev. Fluids 9, 053302 (2024)

    2024

  34. [42]

    The Taylor–Couette motor: spontaneous flows of active polar fluids between two coaxial cylinders,

    S. F¨ urthauer, M. Neef, S. W. Grill, K. Kruse, and F. J¨ ulicher, “The Taylor–Couette motor: spontaneous flows of active polar fluids between two coaxial cylinders,” New J. Phys. 14, 023001 (2012)

    2012

  35. [43]

    Active nematic response to a deformable body or boundary: elastic deformations and anchoring-induced flow,

    T. G. J. Chandler and S. E. Spagnolie, “Active nematic response to a deformable body or boundary: elastic deformations and anchoring-induced flow,” arXiv:2409.15617v1 (2024)

    2024 arXiv

  36. [44]

    The reciprocal theorem in fluid dynamics and transport phenomena,

    H. Masoud and H. A. Stone, “The reciprocal theorem in fluid dynamics and transport phenomena,” J. Fluid Mech. 879, P1 (2019)

    2019

  37. [45]

    Conservation laws for liquid crystals,

    J. L. Ericksen, “Conservation laws for liquid crystals,” Trans. Soc. Rheol. 5, 23–34 (1961)

    1961

  38. [46]

    Hydrostatic theory of liquid crystals,

    J. L. Ericksen, “Hydrostatic theory of liquid crystals,” Arch. Ration. Mech. Anal. 9, 371–378 (1962)

    1962

  39. [47]

    Some constitutive equations for liquid crystals,

    F. M. Leslie, “Some constitutive equations for liquid crystals,” Arch. Ration. Mech. Anal. 28, 265–283 (1968)

    1968

  40. [48]

    L. D. Laudau, E. M. Lifschitz, A. M. Kosevich, and L. P. Pitaevskii, Theory of Elasticity(Elsevier, 1986)

    1986

  41. [49]

    P. G. De Gennes and J. Prost, The Physics of Liquid Crystals(Clarendon Press, 1995)

    1995

  42. [50]

    I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction(CRC Press, 2004)

    2004

  43. [51]

    Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid,

    T. Gao, M. D. Betterton, A. S. Jhang, and M. J. Shelley, “Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid,” Phys. Rev. Fluids 2, 093302 (2017)

    2017

  44. [52]

    Active suspensions and their nonlinear models,

    D. Saintillan and M. J. Shelley, “Active suspensions and their nonlinear models,” C. R. Physique 14, 497–517 (2013)

    2013

  45. [53]

    Rheology of active fluids,

    D. Saintillan, “Rheology of active fluids,” Annu. Rev. Fluid Mech. 50, 563–592 (2018)

    2018

  46. [54]

    Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions,

    M. E. Cates and E. Tjhung, “Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions,” J. Fluid Mech. 836, P1 (2018)

    2018

  47. [55]

    Rigid and deformable bodies in nematic liquid crystals,

    T. G. J. Chandler and S. E. Spagnolie, “Rigid and deformable bodies in nematic liquid crystals,” Phys. Rev. Fluids 9, 110511 (2024)

    2024

  48. [56]

    Liquid crystal flow: dynamics and static configurations,

    M. C. Calderer and C. Liu, “Liquid crystal flow: dynamics and static configurations,” SIAM J. Appl. Math. 60, 1925–1949 (2000)

    2000

  49. [57]

    Spontaneous circulation of confined active suspensions,

    F. G. Woodhouse and R. E. Goldstein, “Spontaneous circulation of confined active suspensions,” Phys. Rev. Lett. 109, 168105 (2012)

    2012

  50. [58]

    Rectified rotational dynamics of mobile inclusions in two-dimensional active nematics,

    S. Ray, J. Zhang, and Z. Dogic, “Rectified rotational dynamics of mobile inclusions in two-dimensional active nematics,” Phys. Rev. Lett. 130, 238301 (2023)

    2023

  51. [59]

    Geometric control of active collective motion,

    M. Theillard, R. Alonso-Matilla, and D. Saintillan, “Geometric control of active collective motion,” Soft Matter 13, 363–375 (2017)

    2017

  52. [60]

    Controlling wall–particle interactions with activity,

    L. Neville, J. Eggers, and T. B. Liverpool, “Controlling wall–particle interactions with activity,” Soft Matter 20, 8395–8406 (2024)

    2024

  53. [61]

    Chromatin hydrodynamics,

    R. Bruinsma, A. Y. Grosberg, Y. Rabin, and A. Zidovska, “Chromatin hydrodynamics,” Biophys. J. 106, 1871–1881 (2014)

    2014

  54. [62]

    Extensile motor activity drives coherent motions in a model of interphase chromatin,

    D. Saintillan, M. J. Shelley, and A. Zidovska, “Extensile motor activity drives coherent motions in a model of interphase chromatin,” Proc. Natl. Acad. Sci. USA 115, 11442–11447 (2018)

    2018

  55. [63]

    Interphase chromatin undergoes a local sol-gel transition upon cell differentia- tion,

    I. Eshghi, J. A. Eaton, and A. Zidovska, “Interphase chromatin undergoes a local sol-gel transition upon cell differentia- tion,” Phys. Rev. Lett. 126, 228101 (2021)

    2021

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.