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Pressure-driven elasto-viscoplastic channel flows are linearly unstable at zero Reynolds number.

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2026-06-28 16:50 UTC pith:ORVX77TF

load-bearing objection The paper reports zero-Re linear instability in elasto-viscoplastic channel flow, with high-k modes localizing near yield surfaces, using finite-time IVP followed by jump-conditioned normal modes. the 2 major comments →

arxiv 2606.01010 v1 pith:ORVX77TF submitted 2026-05-31 physics.flu-dyn

Start-up and inertialess instability of elasto-viscoplastic channel flow

James D. Shemilt , Neil J. Balmforth , Duncan R. Hewitt This is my paper
classification physics.flu-dyn
keywords elasto-viscoplastic flowchannel flowlinear stabilityyield stresszero Reynolds numberstart-up flowplug flow
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper examines the start-up and linear stability of pressure-driven channel flow of an elasto-viscoplastic fluid governed by Saramito's constitutive law. Streamwise-uniform base states evolve depending on initial stress, forming true plugs or pseudo-plugs with eventual stress discontinuities at yield surfaces. Linear stability analysis of the initial-value problem at finite times and normal-mode analysis of the final states shows that these base flows are unstable at zero Reynolds number. The most unstable modes have the largest streamwise wavenumbers and localize near regions where stress is close to the yield value. A sympathetic reader cares because the result indicates that steady plug-like states cannot persist in the inertialess limit for this class of materials.

Core claim

Regardless of whether the base flows contain true plugs or pseudo-plugs, the base states are found to be linearly unstable at zero Reynolds number. The most unstable perturbations possess the highest streamwise wavenumbers and become spatially localized to the regions where stresses lie close to the yield stress.

What carries the argument

Normal-mode analysis of the final base states that incorporates jump conditions across yield surfaces.

Load-bearing premise

The linear initial-value problem and normal-mode analysis with jump conditions across yield surfaces fully capture the stability of the discontinuous final states.

What would settle it

A numerical simulation of the full nonlinear equations at zero Reynolds number in which the base state remains unperturbed after arbitrarily long times would falsify the instability claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The instability exists for both true plugs and pseudo-plugs produced by different initial stress configurations.
  • Perturbations with the highest streamwise wavenumbers grow fastest.
  • Unstable modes localize spatially where the stress is near the yield stress.
  • Finite-time initial-value analysis avoids the need to resolve infinite-time discontinuities.

Where Pith is reading between the lines

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

  • The result implies that start-up transients in elasto-viscoplastic channel flows cannot settle into steady states at long times even without inertia.
  • Nonlinear saturation of the localized high-wavenumber modes may produce sustained unsteadiness or secondary flows near the yield surfaces.
  • Analogous instabilities could appear in pipe flows or other pressure-driven geometries once the same constitutive law is used.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the start-up and linear stability of pressure-driven channel flow of an elasto-viscoplastic fluid obeying Saramito's constitutive law. Streamwise-uniform base states are non-unique and develop discontinuities in normal stresses and shear rate at yield surfaces over infinite time; these can be avoided via extensional pre-stress, yielding pseudo-plugs instead of true plugs. Stability is examined first via the linear initial-value problem (IVP) evolved alongside the base states at finite times (keeping states continuous) and then via normal-mode analysis of the final discontinuous states that incorporates jump conditions at yield surfaces. The central result is that all such base states are linearly unstable at Re=0, with the most unstable perturbations occurring at the largest streamwise wavenumbers and localizing where stresses approach the yield stress.

Significance. If the result holds, the work establishes the existence of inertialess linear instabilities in elasto-viscoplastic channel flows driven by the coupling of elasticity and yield-surface dynamics. This has potential implications for the initiation and control of flows in applications involving yield-stress materials. The dual IVP-plus-normal-mode strategy is a methodological strength that directly addresses the continuous-to-discontinuous transition.

major comments (2)
  1. [Abstract; stability-analysis section] Abstract and stability-analysis section: the reported unbounded growth toward highest streamwise wavenumbers (with localization precisely at future discontinuity sites) is obtained from normal-mode analysis that inserts jump conditions. The manuscript states that the IVP already detects instability while states remain continuous, yet no quantitative comparison is given between late-time IVP growth rates and the normal-mode dispersion relation at large k. This leaves open whether the short-wave behavior is altered by the jump conditions.
  2. [Normal-mode analysis] Normal-mode formulation: because the base states become discontinuous only at t=∞, the jump conditions are applied to states that are formally the infinite-time limit. It is not shown that the resulting eigenvalue problem remains well-posed or that the growth rate remains finite when the same continuous base state is used in the IVP at successively later (but finite) times.
minor comments (2)
  1. [Base-flow section] The distinction between true plugs and pseudo-plugs is introduced in the abstract and base-flow section but would benefit from an explicit equation or diagram showing the stress and velocity profiles in each case.
  2. Notation for the yield surfaces and jump conditions should be defined once in a dedicated subsection rather than introduced piecemeal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript concerning the start-up and inertialess instability of elasto-viscoplastic channel flow. We address the major comments point by point below, providing clarifications and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract; stability-analysis section] Abstract and stability-analysis section: the reported unbounded growth toward highest streamwise wavenumbers (with localization precisely at future discontinuity sites) is obtained from normal-mode analysis that inserts jump conditions. The manuscript states that the IVP already detects instability while states remain continuous, yet no quantitative comparison is given between late-time IVP growth rates and the normal-mode dispersion relation at large k. This leaves open whether the short-wave behavior is altered by the jump conditions.

    Authors: We agree that providing a quantitative comparison between the growth rates obtained from the late-time IVP and those from the normal-mode analysis at large wavenumbers would better demonstrate that the short-wave instability is intrinsic to the continuous base states and not introduced by the jump conditions. In the revised version, we will include such a comparison, for example by plotting the maximum growth rate as a function of wavenumber from both methods at selected late times, showing convergence of the IVP results toward the normal-mode dispersion relation as the base state approaches its asymptotic form. revision: yes

  2. Referee: [Normal-mode analysis] Normal-mode formulation: because the base states become discontinuous only at t=∞, the jump conditions are applied to states that are formally the infinite-time limit. It is not shown that the resulting eigenvalue problem remains well-posed or that the growth rate remains finite when the same continuous base state is used in the IVP at successively later (but finite) times.

    Authors: The normal-mode analysis is applied to the limiting discontinuous states, with jump conditions obtained by integrating the linearized equations across the yield surfaces. While a rigorous mathematical proof of well-posedness is not provided, the numerical eigenvalue problem is well-behaved and produces finite growth rates. To address the concern, we will add in the revision a demonstration that the growth rates extracted from the IVP remain finite and approach the normal-mode values as time increases and the base state develops sharper gradients near the yield surfaces. This numerical evidence supports that the instability persists without the growth rate becoming unbounded in the continuous regime. revision: partial

Circularity Check

0 steps flagged

No circularity: instability derived from linearized IVP and normal-mode analysis of continuous-to-discontinuous states

full rationale

The derivation solves the linear initial-value problem on finite-time continuous base states (no discontinuities yet) and then performs normal-mode analysis on the final states with explicit jump conditions. The instability result (Re=0, high-k most unstable, localized near yield stress) is reported as the output of these calculations rather than being presupposed by parameter fitting, self-definition, or load-bearing self-citation. No equations reduce the claimed growth rates or localization to the input assumptions by construction. The analysis is self-contained against the stated constitutive law and boundary conditions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on Saramito's constitutive law (domain assumption), the validity of linearization around evolving base states, and the use of jump conditions at yield surfaces. No free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Saramito's constitutive law accurately describes the elasto-viscoplastic response.
    Invoked as the model for the fluid throughout the abstract.
  • domain assumption Linear stability analysis with jump conditions across yield surfaces is sufficient to determine instability of the final discontinuous states.
    Central to both the finite-time and normal-mode analyses described.

pith-pipeline@v0.9.1-grok · 5757 in / 1402 out tokens · 17243 ms · 2026-06-28T16:50:05.163286+00:00 · methodology

0 comments
read the original abstract

An exploration is presented of the start-up and linear stability of pressure-driven channel flow of an elasto-viscoplastic fluid described by Saramito's constitutive law. Streamwise uniform base states are non-unique, depending on the initial stress configuration, and develop discontinuities in the normal stresses and shear rate at the yield surfaces over infinite times. Such stress discontinuities can be eliminated by introducing a sufficient extensional pre-stress; true plugs bordered by stress jumps then become replaced by marginally yielded, plug-like flow, or pseudo-plugs. To examine the stability of all of these state, the linear initial-value problem is solved along with the evolving base states. Because this analysis is performed for finite times, the base states remain continuous and there is no need to perturb any stress discontinuities. Armed with the insights provided, stability is then analyzed as a normal-mode problem for the final states, building in perturbations to the stress discontinuities via certain jump conditions across any yield surfaces. Regardless of whether the base flows contain true plugs or pseudo-plugs, the base states are found to be linearly unstable at zero Reynolds number. The most unstable perturbations possess the highest streamwise wavenumbers and become spatially localized to the regions where stresses lie close to the yield stress.

Figures

Figures reproduced from arXiv: 2606.01010 by Duncan R. Hewitt, James D. Shemilt, Neil J. Balmforth.

Figure 1
Figure 1. Figure 1: Base state solutions with no initial polymer stress, for (a,b) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Base state solutions for Bi = 1 2 with initial extensional pre-stress (a,b) 𝑎0 = 0.44, (c,d) 𝑎0 = 2 3 and (e,f) 𝑎0 = −1, and with { 𝛿, 𝛽} = { 1 20 , 1 2 }, 𝑇xx (𝑦, 0) = 𝑎0 and 𝑇xy (𝑦, 0) = 0. Plotted are (a,c,e) times series of 𝑇xx (𝑦, 𝑡) for fifteen stations in 𝑦 across the upper half of the channel (colour-coded by position 𝑦) and 𝑈(0, 𝑡), and (b,d,f) the final profiles of 𝑇xx and 𝑇xy (thick pink lines).… view at source ↗
Figure 3
Figure 3. Figure 3: Final profiles of (a) 𝑇xx, (b) 𝑇xy and (c) 𝑈, with {Bi, 𝛿, 𝛽} = { 1 2 , 1 20 , 1 2 }, 𝑇xx (𝑦, 0) = 𝑎0 and 𝑇xy (𝑦, 0) = 0, for 𝑎0 = {−20, −2, −0.8, −0.3, 0, 0.25, 0.5, 0.7, 1}. The cases shown by thicker (blue) lines indicate the examples shown in figures 1 and 2. elastically, first near the walls, but only over long times near the centre of the channel. For the solution in figure 2(e,f), the stress near th… view at source ↗
Figure 4
Figure 4. Figure 4: Solutions of the linear initial-value computation for even and odd [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Solutions of the linear initial-value computation for even and odd [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Growth rates and (b) phase speeds over a range of wavenumbers [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The five most unstable normal modes at 𝑘 = 10 for base states with two values of 𝑎0 (as indicated) and (Bi, 𝛿, 𝛽) = ( 1 2 , 0, 1 2 ), continued to both higher and lower wavenumbers, plotting growth rate 𝜎𝑟 and phase speed 𝑐 = −𝜎𝑖/𝑘. The dot-dashed lines in the bottom row indicate the plug speed 𝑈𝑝. 0 1 -0.5 0 0.5 y (a) k = 10 A 0 1 -0.5 0 0.5 y (b) k = 200 A [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Streamfunctions of the normal modes from figure [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Growth rates 𝜎𝑟 of the most unstable mode against 𝛿 for 𝑘 = {5, 10, 20, 40, 100} (colour-coded, from red to blue, and as indicated by the arrow in (b)), for (a) 𝑎0 = 0.44 and (b) 𝑎0 = 0.5. the curves arise from switches in which mode is the most un￾stable). Instability largely disappears once 𝛿 reaches values of order unity, although detecting where the growth rate vanishes is numerically challenging (in … view at source ↗
Figure 13
Figure 13. Figure 13: plots the resulting growth rates as functions of Bi. As expected, the modes become stable for sufficiently small Bi, al￾though instability looks to persist almost to the Oldroyd-B limit for one of the modes. Unlike the base states with pseudo-plugs, however, the instability in figure 13 also becomes suppressed for Bi → (1−𝛽) −1 . In this second limit, the yielded regions narrow to thin layers against the … view at source ↗
Figure 14
Figure 14. Figure 14: Base states driven by time-dependent pressure gradients for [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

30 extracted references · cited by 1 Pith paper

  1. [1]

    Saramito, A new constitutive equation for elastovis- coplastic fluid flows, J

    P. Saramito, A new constitutive equation for elastovis- coplastic fluid flows, J. Non-Newton. Fluid Mech. 145 (1) (2007) 1–14

    2007

  2. [2]

    Saramito, A new elastoviscoplastic model based on theHerschel–Bulkleyviscoplasticmodel,J.Non-Newton

    P. Saramito, A new elastoviscoplastic model based on theHerschel–Bulkleyviscoplasticmodel,J.Non-Newton. Fluid Mech. 158 (1-3) (2009) 154–161. 18 -2 -1 0 <r -1 0 <i Figure E.18: Example of the linear eigenspectrum for the Saramito model with (𝑘,Bi, 𝛿, 𝛽, 𝑎 0 )=(10, 1 2 ,0, 1 2 , 1 2 ). Thelighter(red)starsshowthecomputed eigenvalues on a grid with 1000 poi...

    2009

  3. [3]

    D.Fraggedakis,Y.Dimakopoulos,J.Tsamopoulos,Yield- ingtheyield-stressanalysis: astudyfocusedontheeffects of elasticity on the settling of a single spherical particle in simple yield-stress fluids, Soft matter 12 (24) (2016) 5378–5401

    2016

  4. [4]

    Moschopoulos, A

    P. Moschopoulos, A. Spyridakis, S. Varchanis, Y. Di- makopoulos,J.Tsamopoulos,Theconceptofelasto-visco- plasticity and its application to a bubble rising in yield stress fluids, J. Non-Newton. Fluid Mech. 297 (2021) 104670

    2021

  5. [5]

    H. L. França, M. Jalaal, C. M. Oishi, Elasto-viscoplastic spreading: From plastocapillarity to elastocapillarity, Phys. Rev. Research 6 (1) (2024) 013226

    2024

  6. [6]

    Zakeri, P

    P. Zakeri, P. Moschopoulos, Y. Dimakopoulos, J. Tsamopoulos, Scaling analysis and self-similarity near breakup of elasto-viscoplastic liquid threads under creep- ing flow, J. Fluid Mech. 1020 (2025) A37

    2025

  7. [7]

    Tsamopoulos, Dynamics of elastoviscoplastic filament stretching, Soft Matter 19 (25) (2023) 4717–4736

    P.Moschopoulos,E.Kouni,K.Psaraki,Y.Dimakopoulos, J. Tsamopoulos, Dynamics of elastoviscoplastic filament stretching, Soft Matter 19 (25) (2023) 4717–4736

    2023

  8. [8]

    Chaparian, O

    E. Chaparian, O. Tammisola, An adaptive finite element method for elastoviscoplastic fluid flows, J. Non-Newton. Fluid Mech. 271 (2019) 104148

    2019

  9. [9]

    Chaparian, M

    E. Chaparian, M. N. Ardekani, L. Brandt, O. Tammisola, Particle migration in channel flow of an elastoviscoplastic fluid, J. Non-Newton. Fluid Mech. 284 (2020) 104376

    2020

  10. [10]

    Cheddadi, P

    I. Cheddadi, P. Saramito, F. Graner, Steady couette flows ofelastoviscoplasticfluidsarenonunique,J.Rheol.56(1) (2012) 213–239

    2012

  11. [11]

    Cheddadi, P

    I. Cheddadi, P. Saramito, C. Raufaste, P. Marmottant, F. Graner, Numerical modelling of foam couette flows, Eur. Phys. J. E 27 (2) (2008) 123–133

    2008

  12. [12]

    Fluid Mech

    I.C.Walton,S.H.Bittleston,TheaxialflowofaBingham plastic in a narrow eccentric annulus, J. Fluid Mech. 222 (1991) 39–60

    1991

  13. [13]

    Chen, Interfacial instability due to elastic stratification inconcentriccoextrusionoftwoviscoelasticfluids,J.Non- Newton

    K. Chen, Interfacial instability due to elastic stratification inconcentriccoextrusionoftwoviscoelasticfluids,J.Non- Newton. Fluid Mech. 40 (2) (1991) 155–175

    1991

  14. [14]

    E. J. Hinch, O. Harris, J. M. Rallison, The instability mechanism for two elastic liquids being co-extruded, J. Non-Newton. Fluid Mech. 43 (2-3) (1992) 311–324

    1992

  15. [15]

    H. A. Castillo, M. R. Jovanović, S. Kumar, A. Morozov, V.Shankar,G.Subramanian,H.J.Wilson,Understanding viscoelastic flow instabilities: Oldroyd-B and beyond, J. Non-Newton. Fluid Mech. 302 (2022) 104742

    2022

  16. [16]

    S.Fielding,Linearinstabilityofplanarshearbandedflow, Phys. Rev. Lett. 95 (13) (2005) 134501

    2005

  17. [17]

    S. S. Datta, A. M. Ardekani, P. E. Arratia, A. N. Beris, I. Bischofberger, G. H. McKinley, J. G. Eggers, J. E. López-Aguilar, S. M. Fielding, A. Frishman, et al., Per- spectives on viscoelastic flow instabilities and elastic tur- bulence, Phys. Rev. Fluids 7 (8) (2022) 080701

    2022

  18. [18]

    H. J. Wilson, J. M. Rallison, Instability of channel flow of a shear-thinning White–Metzner fluid, J. Non-Newton. Fluid Mech. 87 (1) (1999) 75–96

    1999

  19. [19]

    H. J. Wilson, V. Loridan, Linear instability of a highly shear-thinningfluidinchannelflow,J.Non-Newton.Fluid Mech. 223 (2015) 200–208

    2015

  20. [20]

    H. A. Castillo, H. J. Wilson, Elastic instabilities in pressure-driven channel flow of thixotropic-viscoelasto- plastic fluids, J. Non-Newton. Fluid Mech. 261 (2018) 10–24

    2018

  21. [21]

    Bodiguel, J

    H. Bodiguel, J. Beaumont, A. Machado, L. Martinie, H. Kellay, A. Colin, Flow enhancement due to elastic tur- bulence in channel flows of shear thinning fluids, Phys. Rev. Lett. 114 (2) (2015) 028302

    2015

  22. [22]

    Poole, Elastic instabilities in parallel shear flows of a viscoelastic shear-thinning liquid, Phys

    R. Poole, Elastic instabilities in parallel shear flows of a viscoelastic shear-thinning liquid, Phys. Rev. Fluids 1 (4) (2016) 041301

    2016

  23. [23]

    Patne, Yield stress destabilizes viscoelastic fluid flow, Phys

    R. Patne, Yield stress destabilizes viscoelastic fluid flow, Phys. Fluids 37 (4)

  24. [24]

    Non-Newton

    Y.L.Zhang,O.K.Matar,R.V.Craster,Surfactantspread- ing on a thin weakly viscoelastic film, J. Non-Newton. Fluid Mech. 105 (1) (2002) 53–78

    2002

  25. [25]

    Ahmed, L

    H. Ahmed, L. Biancofiore, A new approach for modeling viscoelastic thin film lubrication, J. Non-Newton. Fluid Mech. 292 (2021) 104524

    2021

  26. [26]

    Fluid Mech

    J.Hinch,E.Boyko,H.A.Stone,FastflowofanOldroyd-B model fluid through a narrow slowly varying contraction, J. Fluid Mech. 988 (2024) A11. 19

    2024

  27. [27]

    Boyko, J

    E. Boyko, J. Hinch, H. A. Stone, Flow of an Oldroyd-B fluid in a slowly varying contraction: theoretical results for arbitrary values of deborah number in the ultra-dilute limit, J. Fluid Mech. 988 (2024) A10

    2024

  28. [28]

    Renardy, M

    Y. Renardy, M. Renardy, Stability of shear banded flow foraviscoelasticconstitutivemodelwiththixotropicyield stress behavior, J. Non-Newton. Fluid Mech. 244 (2017) 57–74

    2017

  29. [29]

    M.Khalid,V.Shankar,G.Subramanian,Continuouspath- waybetweentheelasto-inertialandelasticturbulentstates in viscoelastic channel flow, Phys. Rev. Lett. 127 (13) (2021) 134502

    2021

  30. [30]

    Burghelea, M

    T. Burghelea, M. Moyers-González, Elasticity mediated yielding of an elasto-viscoplastic fluid in a plane channel flow, Theor. Comp. Fluid Dyn. 39 (5) (2025) 43. 20

    2025