Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Pinch-off dynamics for a Newtonian liquid thread draining in a viscoplastic medium

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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

Pith's one-line read A Newtonian liquid thread draining in a viscoplastic medium breaks only when the plastocapillary number J stays below a nearly universal threshold J_c ≈ 8×10^-3, set by the capillary–yield stress balance and largely independent of viscosity

desk verdict The DNS regime maps are a useful new empirical contribution, but the scaling laws and the universal threshold J_c≈8×10^-3 don't survive contact with the paper's own supplement — the equations are dimensionally inconsistent for n≠1, and the regularization claims contradict the shown sensitivity. read the letter →

arxiv 2509.15046 v2 pith:UEWFWPD2 submitted 2025-09-18 physics.flu-dyn

Shu Yang , Konstantinos Zinelis , Sourojeet Chakraborty , C. Ricardo Constante-Amores This is my paper
classification physics.flu-dyn MSC 76D4576A05 PACS 47.55.dr47.57.Qk47.55.nb
keywords pinch-offthreadbreakupviscoplasticmediumHerschel-BulkleyyieldstresscapillarythinningOhnesorgenumberplastocapillary
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 argues that whether a Newtonian liquid thread embedded in a viscoplastic fluid pinches off is controlled by a nearly universal balance between capillary and yield stresses, expressed as a critical value of the plastocapillary number, J_c ≈ 8×10^-3. Using direct two-phase simulations with a regularized Herschel–Bulkley model for the surrounding medium, the authors map breakup and non-breakup in the Ohnesorge–plastocapillary plane and show that the threshold is largely independent of viscosity ratio and of Oh at low Ohnesorge numbers. They extend the classical thin-thread scaling analysis to a viscoplastic outer phase, giving expressions for the minimum thread radius and maximum axial velocity that reduce to the known Newtonian results when the yield stress vanishes. The work matters because it offers a predictive rule for when liquid threads embedded in yield-stress materials, as used in embedded additive manufacturing, will break or persist.

What carries the argument

The load-bearing object is the regularized Herschel–Bulkley constitutive law, whose apparent viscosity contains a yield-stress term τ_y/(2∥D∥+ε) plus a power-law term k_l(2∥D∥+ε)^{n-1}; the small ε smooths the singularity at zero deformation rate. The key dimensionless control is the plastocapillary number J = τ_y R_0/σ, the ratio of yield to capillary stress, together with the Ohnesorge number Oh. The scaling analysis follows the standard slender-thread reduction and balances capillary, viscous, and yield stresses, producing the predicted scalings for h_min and u_max. This machinery turns yield stress into an effective viscosity that arrests thinning once capillary stress falls below the yi

What would settle it

Simulate the same low-Oh thread with a sharp yield-surface method (no ε) at J = 8×10^-3: if the thread does not break, the threshold is a regularization artifact. Or run an experiment with a well-characterized yield-stress fluid at fixed Oh < 0.1, sweeping J through 8×10^-3 by varying yield stress; if the breakup/non-breakup transition shifts by more than a factor of about two when the viscosity ratio changes, the claimed universality is falsified.

Watch

Extended reading notes

Core claim

The central claim is that a Newtonian thread draining in a Herschel–Bulkley medium ruptures when the plastocapillary number falls below J_c ≈ 8×10^-3, the point where capillary pressure can no longer overcome the yield stress of the surroundings. At low Ohnesorge numbers this threshold is nearly universal across viscosity ratios m = 0.1–10 and power-law indices n = 0.5–1.5. Below J_c the thread pinches off; above it, the neck approaches a finite radius and no topological breakup occurs. A scaling analysis built on the slender-thread equations with a viscoplastic external phase yields explicit laws for the minimum radius and maximum axial velocity, matching simulations, and shows that viscous

Load-bearing premise

The universal threshold rests on treating the numerical regularization ε = 10^-4 as the sharp yield-stress limit, yet the Supplement reports that ε = 10^-2 moves the breakup boundary by up to an order of magnitude and is the only value that recovers the experimental result, so the premise that J_c ≈ 8×10^-3 is universal is not validated.

Editorial extensions

If this is right

  • Embedded liquid threads in yield-stress media will reliably break only when J < 8×10^-3 in the low-Oh limit; this gives a design rule for embedded printing and microfluidics.
  • The derived scaling laws let a user predict the minimum neck radius and peak axial velocity from τ_y, k_l, n, σ, and time-to-breakup, without full simulation.
  • Regime maps across Oh and J show how shear-thinning accelerates and shear-thickening retards thinning, shifting the breakup boundary in opposite directions at higher Ohnesorge numbers.
  • At high Ohnesorge numbers and large viscosity ratios, stress localization creates a secondary central neck and can produce satellite droplets, extending the classical pinch-off phenomenology to viscoplastic surroundings.

Reading between the lines

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

  • Editorial inference: the universality of J_c = 8×10^-3 is contingent on the regularization parameter approaching zero; the Supplement shows ε = 10^-2 shifts the boundary by up to an order of magnitude and is the value that reproduces the experimental threshold, so J_c should be read as a sharp-limit prediction until a physically validated yield-surface treatment is used.
  • Editorial inference: the scaling law predicts an approach to singularity, but real systems may arrest at a finite neck radius if yield stress locally exceeds capillary pressure; one could test whether the minimum radius reaches zero or saturates as τ→0 for J just below J_c.
  • Editorial inference: extending these simulations to density ratios far from 1 or to thixotropic/viscoelastic yield-stress fluids would likely break the collapse onto a single curve, since those effects alter the stress-localization picture the paper describes.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper investigates the capillary pinch-off of a Newtonian thread embedded in a Herschel–Bulkley viscoplastic medium using axisymmetric two-phase Basilisk simulations. It reports regime maps in the (Oh, J) plane, claims a nearly universal rupture threshold J_c ≈ 8×10^-3 at low Ohnesorge number, and proposes scaling laws, Eqs. (2)–(4), for the maximum axial velocity, characteristic length, and minimum thread radius as functions of time-to-breakup and the Herschel–Bulkley parameters. The authors state that the n=1 limit reproduces the Lister–Stone scalings and that the theoretical predictions agree with simulations for n=0.5, 1, and 1.5.

Significance. The problem is relevant to embedded additive manufacturing and to the broader understanding of pinch-off in complex fluids. The computational campaign is substantial: converged adaptive-mesh simulations, validation against the Newtonian limit, and regime maps for several viscosity ratios and power-law indices are useful contributions if they are reliable. However, the central theoretical claims are not supported: the proposed scaling laws are not dimensionally consistent for n≠1, their derivation is missing, and the universal threshold J_c is shown by the authors' own Supplement to be sensitive to the regularization parameter. Because these issues bear directly on the paper's main conclusions, the present version cannot be accepted.

major comments (4)
  1. [Scaling laws, Eqs. (2)–(4) and Supplement §3] These equations are dimensionally inconsistent for n≠1. With k_l having units Pa·s^n, the term τ_y τ/k_l has units s^{1-n}, the same as τ^{1-n}; hence Eq. (2) gives velocity units m·s^{-(n+1)/2}, Eq. (3) gives length units m·s^{(1-n)/2} for its second term, and Eq. (4) gives m·s^{2-2n} for h_min. Only n=1 yields the correct dimensions. The scaling laws are therefore not valid for n=0.5 or 1.5, so the comparisons in Fig. 5 are not meaningful as tests of the theory.
  2. [Supplement §3 and Eq. (4)] The derivation of Eqs. (2)–(4) is not shown: the Supplement goes from the constitutive equation (viii) directly to the final expressions (ixa)–(ixc) with no intermediate algebra. Moreover, Eq. (4) contains μ_eff, which is the flow-dependent Herschel–Bulkley viscosity from Eq. (1); unless a specific scaling for ∥D∥ is substituted, Eq. (4) is not a closed prediction and cannot be used to infer the h_min(t) exponents shown in Fig. 5. The main text states the result for n>0, but Supplement §3 says the derivation is for n>1, so the n=0.5 simulation lies outside the claimed theoretical range.
  3. [Results, Fig. 1 and Supplement §2, Supp. Fig. 1(c)] The claim of a universal, regularization-independent threshold J_c≈8×10^-3 is not established. The main text says the simulations 'are robust across regularization choices,' but Supplement §2 and Supp. Fig. 1(c) show that changing ε from 10^-4 to 10^-2 shifts the breakup boundary by up to an order of magnitude. The main text then says that adopting ε=10^-2 recovers the experimental value of Hossain et al., which implies the ε=10^-4 results do not match that experiment. No convergence study of J_c for ε below 10^-4 is presented. The threshold may therefore be a regularization artifact rather than a physical limit.
  4. [Scaling analysis, Eq. (2) and Supplement Table I] The statement that substituting n=1 recovers the Lister–Stone scalings exactly is only true in a special case. With τ_y=0 and n=1, Eq. (2) gives u_max ∼ σ/k_l, whereas the Lister–Stone Stokes-flow scaling in Supplement Table I is u_max ∼ σ/(μ_b m_s^{1/2}) = σ/√(μ_b μ_eff). These agree only if μ_b=μ_eff (i.e., m=1). The main text does not state this restriction, and the comparison in Fig. 5 is performed only at m=1, so the claimed general recovery of Lister–Stone is misleading.
minor comments (4)
  1. [Notation, Eq. (1) and Eq. (4)] The symbol τ is used both for time-to-breakup in Eq. (4) and as part of the stress symbol τ_s in Eq. (1). Please use distinct symbols (e.g., t_b − t or t_br) for time-to-breakup.
  2. [Main text, Fig. 2 caption] The caption says h_min is plotted 'over time up to t=160' but does not define the x-axis. State that time is nondimensionalized by the inertial-capillary time t_i.
  3. [Main text, 'maximum length scale'] L_c is introduced in Eq. (3) as 'maximum length scale' but is never defined physically or plotted. Clarify its meaning and role in the scaling analysis.
  4. [Supplement §3, Eq. (viii)] The definition of ∥D∥ is not repeated in the Supplement, and the notation D for the rate-of-deformation tensor is inconsistent with the main text's D/∥D∥ usage. Please harmonize definitions.

Circularity Check

1 steps flagged · score 5.0 of 10

The h_min scaling law in Eq. (4) is not a closed prediction: it contains the flow-dependent μ_eff, so the agreement with simulations is partly tautological. The claimed ε-convergence of J_c is also contradicted by the Supplement's order-of-magnitude shift.

  1. self definitional [Main text, Eq. (4) and Fig. 5; Supplement Section 3, Eq. (ixc)]
    "hmin ∼ ( στ/µeff ) [ (τyτ/kl) + τ^{1−n} ] ; µeff = τy/(2∥D∥+ε) + kl(2∥D∥+ε)^{n−1}"

    In the thinning neck, the deformation rate ∥D∥ is not an independent input but is set by the same interface: ∥D∥ ∼ (dh_min/dt)/h_min ∼ τ^{-1}. Inserting the constitutive definition of μ_eff into Eq. (4) gives h_min ∼ (σ τ)[τ_y τ/k_l + τ^{1-n}]/[τ_y τ/2 + k_l τ^{1-n}], which for τ→0 reduces to h_min ∼ σ τ/k_l: the yield stress cancels and the exponent becomes n-independent. Thus Eq. (4) is an implicit identity containing h_min on both sides rather than a predictive scaling law. When μ_eff is evaluated from the simulated flow, the 'excellent agreement' in Fig. 5 is by construction; when μ_eff is left as an unspecified constant, the prefactor/slope is free. In either reading, the comparison does not independently validate the yield-stress physics.

full rationale

No load-bearing self-citation chain or imported uniqueness theorem is present. The central threshold J_c≈8×10^-3 is a numerical observation extracted from regime maps, not a derived constant, so it is not circular per se. However, the scaling-law 'prediction' for h_min (Eq. 4) is not closed: it contains μ_eff, which by Eq. (1) depends on the local deformation rate—an output of the same thinning dynamics. Under the natural neck scaling ∥D∥∼τ^{-1}, the yield-stress term cancels, making the purported prediction equivalent to the Newtonian capillary-viscous balance unless μ_eff is treated as an unspecified fitted parameter. That reduces the Fig. 5 'agreement' to a consistency check or a slope fit rather than an independent theoretical test. Separately, the paper's own Supplement (Section 2, Supp. Fig. 1c) reports an order-of-magnitude shift of the breakup boundary when ε is changed from 10^-4 to 10^-2, while the main text calls the results 'robust'; this is a robustness/correctness concern rather than a circularity, but it further undermines the universality claim. Overall, the analysis has one partial reduction-by-construction in the scaling-law comparison, giving a moderate circularity score.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper relies on the standard Herschel-Bulkley model with a regularized effective viscosity, a standard single-fluid VoF solver, and the Eggers/Lister-Stone asymptotic ansatz. No new physical entities are introduced. The main free parameters are the regularization epsilon (which has a first-order effect on the central threshold) and the empirical threshold J_c, plus unconstrained prefactors in the scaling laws.

free parameters (3)
  • Regularization parameter epsilon = 10^-4
    Chosen by hand; the breakup threshold J_c shifts by up to an order of magnitude when epsilon = 10^-2, so the central 'universal' constant depends on this free parameter.
  • Critical plastocapillary number J_c = ~ 8 x 10^-3
    Empirically read from the simulated regime maps, not derived; presented as the universal breakup threshold.
  • Scaling-law prefactors = unspecified O(1)
    Eqs (2)-(4) carry unspecified constants; the 'agreement' in Fig. 5 compares simulation slopes to power laws with unconstrained prefactors.
assumptions (5)
  • domain assumption Herschel-Bulkley constitutive model with regularized effective viscosity (Eq. 1)
    The entire external phase is modeled with this rheology; the yield surface is smeared by epsilon.
  • domain assumption Axisymmetric two-phase Navier-Stokes with volume-of-fluid interface tracking
    The thread and medium are treated as incompressible continua; no slip or thermal effects.
  • domain assumption Gravity neglected; initial thread perturbed sinusoidally with amplitude delta
    Simplifies to capillary-yield-viscous balance; stated in the setup.
  • domain assumption Velocity field predominantly axial u = u(z, t) and interface h = h(z, t) (Eggers/Lister-Stone ansatz)
    Used to derive scaling laws; the paper says it borrows this from refs. 11 and 13.
  • ad hoc to paper Late-stage balance of capillary, viscous, and inertial forces
    Assumed to hold in the thinning regime, but in yield-dominated non-breakup cases this balance is questionable; the paper cites Lister-Stone for this assumption.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Pinch-off dynamics for a Newtonian liquid thread draining in a viscoplastic medium." pith.science (2026). https://pith.science/paper/UEWFWPD2

@misc{pith2026250915046,
  author       = {Pith},
  title        = {Pith review of: Pinch-off dynamics for a Newtonian liquid thread draining in a viscoplastic medium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UEWFWPD2}},
  note         = {Machine review of arXiv:2509.15046}
}
read the original abstract

The pinch-off dynamics of a Newtonian liquid thread embedded in a viscoplastic medium is investigated using direct numerical simulations and theory. Thread breakup occurs below a nearly universal threshold set by the balance of capillary and yield stresses, largely independent of the viscosity ratio at low Ohnesorge numbers. Regime maps in the Ohnesorge-plastocapillary number plane reveal distinct boundaries, and scaling analysis captures the minimum thread radius in excellent agreement with simulations. These results provide a predictive framework for thread dynamics in complex fluids and highlight the role of stress localization in viscoplastic environments. The obtained insights are relevant for embedded additive manufacturing and other technologies involving fluid threads in complex media.

Figures

Figures reproduced from arXiv: 2509.15046 by the authors.

Figure 1
Figure 1. FIG. 1: Regime maps in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Temporal evolution [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Snapshots of the flow field near the capillary [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: shows the evolution of the minimum thread radius hmin as a function of the time to breakup, τ = tb − t, for different flow indices n. Figure 5a corresponds to Oh = 10−2 , J = 5.62 × 10−3 , and figure 5b to Oh = 10−1 , J = 3.16 × 10−3 . The dashed lines indi￾cate refere…

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. End-pinching and inertial-capillary reopening in viscoplastic ligaments at low Ohnesorge number

    physics.flu-dyn 2025-11 unverdicted novelty 7.0 of 10

    Viscoplastic ligaments can escape end-pinching through inertial-capillary reopening as viscosity approaches zero, unlike prior Newtonian predictions of breakup.

Reference graph

Works this paper leans on

28 extracted references · 1 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Eggers and E

    J. Eggers and E. Villermaux, Reports on Progress in Physics71, 036601 (2008)

    2008

  2. [2]

    Derby, Annual Review of Materials Research40, 395 (2010)

    B. Derby, Annual Review of Materials Research40, 395 (2010)

    2010

  3. [3]

    M. Rump, C. Diddens, U. Sen, M. Versluis, D. Lohse, and T. Segers, Role of surfactants on droplet formation in piezoacoustic inkjet printing across microsecond-to- second timescales (2024), arXiv:2406.02389

    arXiv 2024

  4. [4]

    J. M. Lopez-Herrera, A. M. Ga˜ n´ an-Calvo, and M. Perez- Saborid, Journal of Aerosol Science30, 895 (1999)

    1999

  5. [5]

    G. Sun, W. Han, Y. Wang, S. Xin, J. Yang, F. Zou, X. Wang, and C. Xiao, Industrial & Engineering Chem- istry Research61, 1004 (2022)

    2022

  6. [6]

    N. K. Bankapalli, V. Gupta, P. Saxena, A. Bajpai, C. La- hoda, and J. Polte, Composites Part B: Engineering264, 110915 (2023)

    2023

  7. [7]

    Rayleigh, The London, Edinburgh, and Dublin Philo- sophical Magazine and Journal of Science34, 145 (1892)

    L. Rayleigh, The London, Edinburgh, and Dublin Philo- sophical Magazine and Journal of Science34, 145 (1892)

  8. [8]

    O. A. Basaran, H. Gao, and P. P. Bhat, Annual Review of Fluid Mechanics45, 85 (2013)

    2013

Show all 28 references
  1. [9]

    A. A. Castrej´ on-Pita, J. R. Castrej´ on-Pita, and I. M. Hutchings, Physical Review Letters108, 074506 (2012), american Physical Society

    2012

  2. [10]

    H. A. Stone, Annual Review of Fluid Mechanics26, 65 (1994), annual Reviews

    1994

  3. [11]

    Eggers, Physical Review Letters71, 3458 (1993)

    J. Eggers, Physical Review Letters71, 3458 (1993)

    1993

  4. [12]

    D. T. Papageorgiou, Physics of Fluids7, 1529 (1995)

    1995

  5. [13]

    J. R. Lister and H. A. Stone, Physics of Fluids10, 2758 (1998)

    1998

  6. [14]

    R. F. Day, E. J. Hinch, and J. R. Lister, Physical Review Letters80, 704 (1998)

    1998

  7. [15]

    H. Wee, C. R. Anthony, and O. A. Basaran, Physical Review Fluids7, L112001 (2022)

    2022

  8. [16]

    R. V. Craster, O. K. Matar, and D. T. Papageorgiou, Physics of Fluids14, 1364 (2002)

    2002

  9. [17]

    Xu, Y.-C

    Q. Xu, Y.-C. Liao, and O. A. Basaran, Physical Review Letters98, 054503 (2007)

    2007

  10. [18]

    P. M. Kamat, B. W. Wagoner, S. S. Thete, and O. A. Basaran, Physical Review Fluids3, 043602 (2018)

    2018

  11. [19]

    Eggers, Physics of Fluids26, 033106 (2014)

    J. Eggers, Physics of Fluids26, 033106 (2014)

    2014

  12. [20]

    Turkoz, J

    E. Turkoz, J. M. Lopez-Herrera, J. Eggers, C. B. Arnold, and L. Deike, Journal of Fluid Mechanics851, R2 (2018)

    2018

  13. [21]

    Balmforth and D

    N. Balmforth and D. Hewitt, Journal of Fluid Mechanics 1011, P1 (2025)

    2025

  14. [22]

    M. T. Hossain, W. Eom, A. Shah, A. Lowe, D. Fudge, S. H. Tawfick, and R. H. Ewoldt, Journal of Non- Newtonian Fluid Mechanics343, 105440 (2025)

    2025

  15. [23]

    Sanjay, D

    V. Sanjay, D. Lohse, and M. Jalaal, Journal of Fluid Me- chanics922, A2 (2021)

    2021

  16. [24]

    Popinet, Journal of Computational Physics228, 5838 (2009)

    S. Popinet, Journal of Computational Physics228, 5838 (2009)

    2009

  17. [25]

    Popinetet al., Basilisk,http://basilisk.fr(2013– 2025)

    S. Popinetet al., Basilisk,http://basilisk.fr(2013– 2025)

    2013

  18. [26]

    J. R. Castrej´ on-Pita, A. A. Castrej´ on-Pita, S. S. Thete, K. Sambath, I. M. Hutchings, J. Hinch, J. R. Lister, and O. A. Basaran, Proceedings of the National Academy of Sciences112, 4582 (2015)

    2015

  19. [27]

    Basilisk Developers, plateau.c – adaptive mesh re- finement test case,http://basilisk.fr/src/test/ plateau.c(2025), accessed: 2025-09-08

    2025

  20. [28]

    V. Sanjay, two-phaseVP-HB.h – bursting bubble in a viscoplastic medium,https://github.com/ comphy-lab/BurstingBubble_Herschel-Bulkley/ blob/main/src-local/two-phaseVP-HB.h(2025), accessed 8 Sep 2025. 6 Supplemental Information: Pinch-off dynamics for a Newtonian liquid thread ...

    2025

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.