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arxiv: 2604.10211 · v1 · submitted 2026-04-11 · ❄️ cond-mat.soft · physics.flu-dyn

Concentration regimes in salt-free aqueous xanthan solutions under shear

Ammar El Menayyir , Markus Neuner , Polina Fuks , Vahid A. Z. Alashloo , Halim Altuntas , Zehau Luo , Melike \"Ozg\"ul , Claudia Seeberger
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Sharadwata Pan Andreas Wierschem
This is my paper

Pith reviewed 2026-05-10 15:40 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.flu-dyn
keywords xanthanconcentration regimesspecific viscosityshear ratepolyelectrolytespower-law scalingsalt-free solutionsrheological regimes
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The pith

Salt-free xanthan solutions exhibit power-law specific viscosity scaling with concentration at all shear rates, identifying six regimes.

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

The paper establishes that salt-free aqueous xanthan solutions follow power-law relationships between specific viscosity and concentration not only at zero shear but across the entire shear-rate range examined. This scaling identifies six concentration regimes, extending the four standard polyelectrolyte regimes (dilute, semidilute unentangled, semidilute entangled, and neutral semidilute entangled) by adding a linear regime at high concentration and low shear where gelation occurs and a further regime at high concentration and high shear. Exponents within each regime vary smoothly with shear rate, especially near the onset of shear thinning, and some regimes merge when their exponents converge. The continuity of these scalings away from equilibrium shows that critical concentrations retain meaning under flow and can track how interaction mechanisms shift with shear. A reader would care because the result suggests equilibrium-derived scaling laws remain usable for interpreting flowing polyelectrolyte solutions.

Core claim

For salt-free aqueous xanthan solutions the specific viscosity depends on concentration through power laws at every shear rate. Six concentration regimes are distinguished: the four familiar from zero-shear polyelectrolyte solutions plus a linear regime at low shear and high concentration associated with gelation and an additional regime at higher concentrations and shear rates. The power-law exponents change smoothly with shear rate within regimes, particularly around the start of shear thinning, and some regimes merge as exponents approach one another. This continuity indicates that the scaling laws remain applicable away from thermodynamic equilibrium and can be used to follow the shift,

What carries the argument

Shear-rate-dependent power-law scaling of specific viscosity versus concentration, which maps concentration regimes and reveals continuous changes in dominant molecular interactions such as entanglement, electrostatic repulsion, and disaggregation.

If this is right

  • Critical concentrations separating the regimes remain valid at finite shear rates.
  • Changes in power-law exponents with shear rate directly indicate shifts in the balance among entanglement, electrostatics, and disaggregation.
  • Scaling analysis under shear can locate thresholds for shear-induced disentanglement or disaggregation.
  • The approach extends the known scalings of the zero-shear and infinite-shear plateaus continuously into the shear-thinning region.

Where Pith is reading between the lines

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

  • The same scaling analysis could be applied to other polyelectrolytes to test whether regime persistence under shear is general.
  • Smooth exponent variation implies that shear modulates existing molecular mechanisms rather than introducing entirely new structures at the regime boundaries.
  • Rheological predictions for xanthan in applications could use shear-dependent regime maps to identify concentration windows where specific interactions dominate.

Load-bearing premise

The observed power-law exponents and their smooth variation with shear rate directly reflect shifts in the same molecular interaction mechanisms that govern zero-shear behavior, without shear-induced structures or measurement artifacts altering the scaling.

What would settle it

Measure specific viscosity versus concentration curves at fixed intermediate shear rates in the transition zones between proposed regimes and test whether the fitted power-law exponents change continuously or exhibit abrupt discontinuities.

read the original abstract

Concentration regimes in polymer and polyelectrolyte solutions can be identified by scaling laws for the relation between specific zero-shear viscosity and concentration. Recently, we have shown that the same is true for the infinite-shear viscosity plateau. The shear-thinning range is usually accessed by focusing on the viscosity functions for the respective concentration regime. For salt-free aqueous xanthan solutions, we find power-law dependencies of the specific viscosity on concentration throughout the entire shear-rate range. We distinguish six different concentration regimes. Apart from those already known for the zero-shear viscosity of polyelectrolyte solutions, i.e. dilute, semidilute unentangled, semidilute entangled and neutral semidilute entangled, we identify a linear regime for low shear rates at high concentrations, where the solution gels and a regime at both, higher concentrations and higher shear rates. Within some regimes, the power-law exponents change smoothly with shear rate, particularly, when deviating from the zero-shear viscosity plateau before the power-law of the viscosity function. Some regimes merge as their power-law exponents approach each other. The fact that the regimes extend smoothly from the zero-shear regime into finite shear rates, i.e. away from thermodynamic equilibrium, shows that indicators such as critical concentrations remain valid at finite shear rates. This motivates us to interpret the data in the light of existing scaling laws and current knowledge about shear-rate dependent interaction mechanisms in polyelectrolyte solutions, particularly in xanthan solutions. It allows to follow the shift of relevant interaction mechanisms with shear rate. We think that the consideration of scaling laws under shear can be particularly helpful for identifying, for instance, thresholds for shear-induced disentanglement or disaggregation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript examines salt-free aqueous xanthan solutions and reports that the specific viscosity follows power-law dependencies on concentration across the full range of accessible shear rates. Six concentration regimes are identified: the four standard polyelectrolyte regimes (dilute, semidilute unentangled, semidilute entangled, neutral semidilute entangled) plus a linear regime at high concentration and low shear (where the solution gels) and an additional regime at both higher concentration and higher shear rate. Power-law exponents vary smoothly with shear rate, particularly away from the zero-shear plateau, and some regimes merge as exponents converge. The authors interpret these observations as evidence that critical concentrations and scaling indicators remain valid under shear, allowing tracking of shifts in interaction mechanisms (entanglement, electrostatics, disaggregation).

Significance. If the regime boundaries and exponents prove robust, the work extends the established zero-shear scaling framework for polyelectrolytes to finite shear rates in a concrete, experimentally accessible system. The demonstration that power-law behavior persists and evolves continuously away from equilibrium provides a practical route to monitor shear-dependent changes in molecular interactions, which is directly relevant to processing and flow of xanthan-based materials. The approach of mapping viscosity-concentration power laws at fixed shear rates is simple and could be applied to other systems.

major comments (2)
  1. [Abstract and Results (high-concentration regime)] Abstract and high-concentration regime description: the linear regime at low shear/high concentration is presented as a distinct gelling regime whose power-law persists under shear. Xanthan is known to be thixotropic; the manuscript must demonstrate that steady-state viscosity was reached (e.g., via time sweeps, preshear protocols, or hysteresis checks) in this regime, otherwise apparent power-laws could arise from incomplete relaxation or shear-induced aggregate breakdown rather than equilibrium scaling.
  2. [Discussion] Discussion section on exponent evolution: the claim that smooth changes in power-law exponents with shear rate directly reflect continuous shifts in the same mechanisms (entanglement, electrostatics, disaggregation) that govern zero-shear regimes requires explicit exclusion of new shear-induced structures. Without supporting data (e.g., structural probes under shear or concentration-dependent relaxation times), this interpretation remains an assumption rather than a demonstrated result.
minor comments (3)
  1. [Methods] Methods: specify the exact concentration and shear-rate windows used to delineate each of the six regimes and the criterion (intersection of fits, statistical test, or visual) employed to locate boundaries.
  2. [Figures] Figures: all log-log viscosity-concentration plots should include error bars, the number of replicates, and the fitted lines with reported exponents and uncertainties for each regime at each shear rate.
  3. [Notation] Notation: ensure consistent use of “specific viscosity” versus “relative viscosity” and clarify whether the reported power laws are for specific viscosity or for the viscosity function itself.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments highlight important aspects of data interpretation and experimental rigor that we address below. We have revised the manuscript to incorporate clarifications and more cautious language where appropriate.

read point-by-point responses

  1. Referee: [Abstract and Results (high-concentration regime)] Abstract and high-concentration regime description: the linear regime at low shear/high concentration is presented as a distinct gelling regime whose power-law persists under shear. Xanthan is known to be thixotropic; the manuscript must demonstrate that steady-state viscosity was reached (e.g., via time sweeps, preshear protocols, or hysteresis checks) in this regime, otherwise apparent power-laws could arise from incomplete relaxation or shear-induced aggregate breakdown rather than equilibrium scaling.

    Authors: We agree that confirming steady-state conditions is essential for thixotropic materials such as xanthan solutions. We will revise the Methods and Results sections to include a more detailed description of the rheological protocol, specifically addressing how steady-state viscosity was ensured in the high-concentration regime (including any preshear, equilibration times, and verification steps). This addition will clarify that the reported linear regime corresponds to steady-state measurements rather than transient effects. revision: yes

  2. Referee: [Discussion] Discussion section on exponent evolution: the claim that smooth changes in power-law exponents with shear rate directly reflect continuous shifts in the same mechanisms (entanglement, electrostatics, disaggregation) that govern zero-shear regimes requires explicit exclusion of new shear-induced structures. Without supporting data (e.g., structural probes under shear or concentration-dependent relaxation times), this interpretation remains an assumption rather than a demonstrated result.

    Authors: We accept that the interpretation of continuous mechanism shifts is based on the observed smooth evolution of exponents and the persistence of distinct power-law regimes. We will revise the Discussion to present this more explicitly as an interpretation motivated by the scaling continuity, rather than a definitively proven result. We will also note the potential value of future structural studies (e.g., rheo-SAXS) to further test for shear-induced structures. No new experimental data are added in this revision. revision: partial

standing simulated objections not resolved
  • We do not possess in-situ structural data under shear or concentration-dependent relaxation times in the current study, limiting our ability to fully exclude new shear-induced structures beyond the scaling arguments presented.

Circularity Check

0 steps flagged

No circularity: central claims are direct experimental observations of power-law scaling

full rationale

The paper reports experimental measurements of specific viscosity versus concentration at fixed shear rates for salt-free xanthan solutions, from which power-law exponents are extracted and six concentration regimes are identified by changes in scaling. No derivation, prediction, or fitted parameter is claimed that reduces by construction to the same dataset; the results are presented as observations and then interpreted against pre-existing scaling laws for polyelectrolytes. The single self-citation to the authors' prior work on the infinite-shear plateau is not load-bearing for the new finite-shear findings. The derivation chain is therefore self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The interpretation rests on established polyelectrolyte scaling theories rather than new postulates. No free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Power-law scaling of specific viscosity with concentration remains a valid indicator of molecular interaction regimes even at finite shear rates.
    Invoked to justify extending zero-shear regime boundaries into the shear-thinning region.

pith-pipeline@v0.9.0 · 5663 in / 1227 out tokens · 35044 ms · 2026-05-10T15:40:39.887122+00:00 · methodology

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Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages

  1. [1]

    Rubinstein, M., and R. H. Colby, Polymer Physics (Oxford University Press, New York, 2003)

    work page 2003

  2. [2]

    W., Polymer Liquids and Networks: Dynamics and Rheology (Garland science, New York, 2008)

    Graessley, W. W., Polymer Liquids and Networks: Dynamics and Rheology (Garland science, New York, 2008)

    work page 2008

  3. [3]

    H., ‘‘Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions,’’ Rheol

    Colby, R. H., ‘‘Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions,’’ Rheol. Acta 49(5), 425-442 (2010)

    work page 2010

  4. [4]

    A. V. Dobrynin, Polyelectrolyte solutions and gels, in The Oxford Handbook of Soft Condensed Matter (ed. E. M. Terentjev, D. A. Weitz) (Oxford University Press, Oxford, UK, 2015)

    work page 2015

  5. [5]

    Universal solvent quality crossover of the zero shear rate viscosity of semidilute DNA solutions,

    Pan, S., D. A. Nguyen, P. Sunthar, T. Sridhar, and J. R. Prakash, “Universal solvent quality crossover of the zero shear rate viscosity of semidilute DNA solutions,” J. Rheol. 58(2), 339–368 (2014)

    work page 2014

  6. [6]

    Viscosity radius in dilute polymer solutions: Universal behaviour from DNA rheology and Brownian dynamics simulations,

    Pan, S., D. Ahirwal, D. A. Nguyen, P. Sunthar , T. Sridhar, and J. R. Prakash, “Viscosity radius in dilute polymer solutions: Universal behaviour from DNA rheology and Brownian dynamics simulations,” Macromolecules 47(21), 7548 – 7560 (2014)

    work page 2014

  7. [7]

    Muthukumar, M., ‘‘50 th anniversary perspective: A perspective on polyelectrolyte solutions,’’ Macromolecules 50(24), 9528−9560 (2017). 14

    work page 2017

  8. [8]

    The scaling of zero -shear viscosities of semidilute polymer solutions with concentration,

    Heo, Y. , and R. G. Larson, “The scaling of zero -shear viscosities of semidilute polymer solutions with concentration,” J. Rheol. 49(5), 1117-1128 (2005)

    work page 2005

  9. [9]

    Semidilute polymer solutions at equilibrium and under shear flow,

    Huang, C.-C., R. G. Winkler, G. Sutmann, and G. Gompper, “Semidilute polymer solutions at equilibrium and under shear flow,” Macromolecules 43(23), 10107 – 10116 (2010)

    work page 2010

  10. [10]

    Shear thinning in dilute and semidilute solutions of polystyrene and DNA,

    Pan, S., D. A. Nguyen, B. Dünweg, P. Sunthar, T. Sridhar, and J. R. Prakash, “Shear thinning in dilute and semidilute solutions of polystyrene and DNA,” J. Rheol. 62(4), 845-867 (2018)

    work page 2018

  11. [11]

    Rheology of entangled polyelectrolyte solutions ,

    Han, A. , and R. H. Colby, “Rheology of entangled polyelectrolyte solutions ,” Macromolecules 54(3), 1375-1387 (2021)

    work page 2021

  12. [12]

    Rheology of polyelectrolyte solutions: current understanding and perspectives,

    Matsumoto, A., “Rheology of polyelectrolyte solutions: current understanding and perspectives,” Nihon Reoroji Gakkaishi 50(1), 43-50 (2022)

    work page 2022

  13. [14]

    Dilute polyelectrolyte solutions: recent progress and open questions,

    Lopez, C. G., A. Matsumoto, and A. Q. Shen, “Dilute polyelectrolyte solutions: recent progress and open questions,” Soft Matter 20(12), 2635-2687 (2024)

    work page 2024

  14. [15]

    Auhl, and A

    Dakhil, H., D. Auhl, and A. Wierschem, ‘‘Infinite-shear viscosity plateau of salt-free aqueous xanthan solutions,’’ J. Rheol. 63(1), 63-69 (2019)

    work page 2019

  15. [16]

    Dakhil, H., S. K. Basu, S. Steiner, Y. Gerlach, A. Soller, S. Pan, N. Germann, M. Leidenberger, B. Kappes, and A. Wierschem, ‘‘Buffered λ-DNA solutions at high shear rates,’’ Journal of Rheology 65(2), 159-169 (2021)

    work page 2021

  16. [17]

    M., ‘‘Rheology of non -Newtonian fluids: A new flow equation for pseudoplastic systems,’’ J

    Cross, M. M., ‘‘Rheology of non -Newtonian fluids: A new flow equation for pseudoplastic systems,’’ J. Colloid Sci. 20(5), 417-437 (1965)

    work page 1965

  17. [18]

    Yasuda, K., R. C. Armstrong, and R. E. Cohen, ‘‘Shear flow properties of concentrated solutions of linear and star branched polystyrenes,’’ Rheol. Acta 20(2), 163-178 (1981)

    work page 1981

  18. [19]

    B., and M

    Wyatt, N. B., and M. W. Liberatore, ‘‘Rheology and viscosity scaling of the polyelectrolyte xanthan gum,’’ J. Appl. Polym. Sci. 114(6), 4076-4084 (2009)

    work page 2009

  19. [20]

    You, F., Y. Wu, Y. Guo, and Y. Zheng, ‘‘Rheological aspects of xanthan gum: Governing factors and applications in water-based drilling fluids and enhanced oil recovery,’’ Carbohydr. Polym. 359, 123579 (2025)

    work page 2025

  20. [21]

    Garcı́a-Ochoa, F., V. E. Santos, J. A. Casas, and E. Gómez, ‘‘Xanthan gum: Production, recovery, and properties,’’ Biotechnol. Adv. 18(7), 549-579 (2000)

    work page 2000

  21. [22]

    Kim, and G.-S

    Song, K.-W., Y.-S. Kim, and G.-S. Chang, ‘‘Rheology of concentrated xanthan gum solutions: Steady shear flow behavior,’’ Fibers and Polymers 7(2), 129-138 (2006)

    work page 2006

  22. [23]

    Dynamics of dilute and semidilute DNA solutions in the start-up of shear flow,

    Hur, J. S., E. S. G. Shaqfeh, H. P. Babcock, D. E. Smith, and S. Chu, “Dynamics of dilute and semidilute DNA solutions in the start-up of shear flow,” J. Rheol. 45(2), 421–450 (2001)

    work page 2001

  23. [24]

    Concentration dependence of the longest relaxation times of dilute and semi-dilute polymer solutions,

    Liu, Y., Y. Jun, and V. Steinberg, “Concentration dependence of the longest relaxation times of dilute and semi-dilute polymer solutions,” J. Rheol. 53(5), 1069- 1085 (2009). 15

    work page 2009

  24. [25]

    R. G. Larson, The Structure and Rheology of Complex Fluids ( Oxford University Press, New York, 1999)

    work page 1999

  25. [26]

    M., and R

    Dealy, J. M., and R. G. Larson, Structure and Rheology of Molten Polymers: From Structure to Flow Behavior and Back Again (Carl Hanser-Verlag, Munich, 2006)

    work page 2006

  26. [27]

    Wierschem, N

    Pan, S., A. Wierschem, N. Germann, and T. Becker, ‘‘Functional trends and rheological evaluation of polyurethane microcapsules in dermato -cosmetic applications,’’ Transp. Phenom. 1, 20260006 (2026)

    work page 2026

  27. [28]

    Nardone, S., S. J. Haward, A. Q. Shen, and V. Calabrese, ‘‘Capillary -driven thinning of DNA solutions,’’ Rheol. Acta 64(9-10), 531-540 (2025)

    work page 2025

  28. [29]

    15(3), 368–379 (2026)

    Calabrese, V., ‘‘Emergent interpolymer interactions in flowing polymer solutions ,’’ ACS Macro Lett. 15(3), 368–379 (2026)

    work page 2026

  29. [30]

    Clasen, C., and W. M. Kulicke, ‘‘Determination of viscoelastic and rheo -optical material functions of water-soluble cellulose derivatives,’’ Prog. Polym. Sci. 26(9), 1839-1919 (2001)

    work page 1919

  30. [31]

    Kuk, and G.-S

    Song, K.-W., H.-Y. Kuk, and G.-S. Chang, ‘‘Rheology of concentrated xanthan gum solutions: Oscillatory shear flow behavior,’’ Korea-Australia Rheol. J. 18(2), 67-81 (2006)

    work page 2006

  31. [32]

    Essadik, J

    N’gouamba, E., M. Essadik, J. Goyon, T. Oerther, and P. Coussot, ‘‘Yielding and rheopexy of aqueous xanthan gum solutions,’’ Rheol. Acta 60(11), 653-660 (2021)

    work page 2021

  32. [33]

    Katzbauer, B., ‘‘Properties and applications of xanthan gum,’’ Polym. Degrad. Stab. 59(1), 81-84 (1998)

    work page 1998

  33. [34]

    Philippova, O. E., A. V. Shibaev, D. A. Muravlev, and D. Y. Mityuk, ‘‘Structure and rheology of solutions and gels of stiff polyelectrolyte at high salt concentration,’’ Macromolecules 49(16), 6031-6040 (2016)

    work page 2016

  34. [35]

    Application and function of synthetic polymeric flocculents in wastewater treatment

    Rey, P. A., and R. G. Varsanik, “Application and function of synthetic polymeric flocculents in wastewater treatment.” Water-Soluble Polymers (American Chemical Society, 1986)

    work page 1986

  35. [36]

    P., Encyclopedia of Fluid Mechanics Vol

    Singh, R. P., Encyclopedia of Fluid Mechanics Vol. 9 (Gulf Publishing, Houston, 1990)

    work page 1990

  36. [37]

    Avadanei, M

    Brunchi, C.-E., M. Avadanei, M. Bercea, and S. Morariu, ‘‘Chain conformation of xanthan in solution as influenced by temperature and salt addition, ’’ J. Mol. Liq. 287, 111008 (2019)

    work page 2019

  37. [38]

    Priel, and Y

    Cohen, J., Z. Priel, and Y. Rabin, ‘‘Viscosity of dilute polyelectrolyte solutions,’’ J. Chem. Phys. 88(11), 7111–7116 (1988)

    work page 1988

  38. [39]

    G., The Rheology Handbook, 2nd ed

    Mezger, T. G., The Rheology Handbook, 2nd ed. (Vincentz Network, Hannover, 2006)

    work page 2006

  39. [40]

    Direct determination of the flow curves of non‐ Newtonian fluids. II. Shearing rate in the concentric cylinder viscometer,

    Krieger, I. M., and H. Elrod, “Direct determination of the flow curves of non‐ Newtonian fluids. II. Shearing rate in the concentric cylinder viscometer,” J. Appl. Phys. 24, 134-136 (1953)

    work page 1953

  40. [41]

    Wierschem, ‘‘Measuring low viscosities and high shear rates with a rotational rheometer in a thin-gap parallel-disk configuration,’’ App

    Dakhil, H., and A. Wierschem, ‘‘Measuring low viscosities and high shear rates with a rotational rheometer in a thin-gap parallel-disk configuration,’’ App. Rheol. 24(6), 63795-63801 (2014). 16

    work page 2014

  41. [42]

    Dakhil, A

    Kokkinos, D., H. Dakhil, A. Wierschem, H. Briesen, and A. Braun, ‘‘Deformation and rupture of Dunaliella salina at high shear rates without the use of thickeners,’’ Biorheology 53(1), 1-11 (2016)

    work page 2016

  42. [43]

    Dakhil, H., D. F. Gilbert, D. Malhotra, A. Limmer, H. Engelhardt, A. Amtmann, J. Hansmann, H. Hübner, R. Buchholz, O. Friedrich, and A. Wierschem, ‘‘Measuring average rheological quantities of cell monolayers in the linear viscoelastic regime,’’ Rheol. Acta 55(7), 527-536 (2016)

    work page 2016

  43. [44]

    Dakhil, H., H. Do, H. Hübner, and A. Wierschem, ‘‘Measuring the adhesion limit of fibronectin for fibroblasts with a narrow -gap rotational rheometer,’’ Bioprocess. Biosyst. Eng. 41(3), 353-358 (2018)

    work page 2018

  44. [45]

    Lee, S., K. M. I. Bashir, D. H. Jung, S. K. Basu, G. Seo, M.-G. Cho, and A. Wierschem, ‘‘Measuring the linear viscoelastic regime of MCF -7 cells with a monolayer rheometer in the presence of microtubule -active anticancer drugs at high concentrations,’’ Interface Focus 12(6), 20220036 (2022)

    work page 2022

  45. [46]

    Büyükurgancı, B., S. K. Basu, M. Neuner, J. Guck, A. Wierschem, and F. Reichel, ‘‘Shear rheology of methyl cellulose based solutions for cell mechanical measurements at high shear rates,’’ Soft Matter 19(9), 1739-1748 (2023)

    work page 2023

  46. [47]

    Schmid, ‘‘Guard ring induced distortion of the steady velocity profile in a parallel plate rheometer,’’ App

    Pieper, S., and H.-J. Schmid, ‘‘Guard ring induced distortion of the steady velocity profile in a parallel plate rheometer,’’ App. Rheol. 26(6), 64533 (2016)

    work page 2016

  47. [48]

    Cardinaels, R., N. K. Reddy, and C. Clasen, ‘‘Quantifying the errors due to overfilling for Newtonian fluids in rotational rheometry ,’’ Rheol. Acta 58(8), 525– 538 (2019)

    work page 2019

  48. [49]

    W., Rheology: Principles, Measurements and Applications (Wiley- VCH, New York, 1994)

    Macosko, C. W., Rheology: Principles, Measurements and Applications (Wiley- VCH, New York, 1994)

    work page 1994

  49. [50]

    Montillet, I

    Missi, E., A. Montillet, I. Capron, J. Bellettre, and T. Burghelea, ‘‘Thermo- rheological properties of xanthan solutions: from shear thinning to elastoviscoplastic behavior,’’ Soft Matter 20(33), 6582-6594 (2024)

    work page 2024

  50. [51]

    Sokolov, and W

    Kestin, J., M. Sokolov, and W. A. Wakeham, ‘‘Viscosity of liquid water in the range −8 °C to 150 °C,’’ J. Phys. Chem. Ref. Data 7(3), 941-948 (1978)

    work page 1978

  51. [52]

    Mayoral, E., J. D. Hernández Velázquez, and A. Gama Goicochea, ‘‘The viscosity of polyelectrolyte solutions and its dependence on their persistence length, concentration and solvent quality,’’ RSC Adv. 12(55), 35494 (2022)

    work page 2022

  52. [53]

    Zhang, F

    Matsumoto, A., C. Zhang, F. Scheffold, and A. Q. Shen, ‘‘Microrheological approach for probing the entanglement properties of polyelectrolyte solutions, ’’ ACS Macro Lett. 11(1), 84−90 (2022)

    work page 2022

  53. [54]

    Matsumoto, A., I. Kato, C. Zhang, S. Sugihara, Y. Maeda, F. Scheffold, and A. Q. Shen, ‘‘Microrheological study on the entanglement dynamics of salt -free polyelectrolyte solutions in the semidilute entangled regime,’’ Polym. J. 57(2), 1215-1225 (2025)

    work page 2025

  54. [55]

    Dobrynin, A. V., R. H. Colby, and M. Rubinstein, ‘‘Scaling theory of polyelectrolyte solutions,’’ Macromolecules 28(6), 1859-1871 (1995)

    work page 1995

  55. [56]

    Kumar, A., K. M. Rao, and S. S. Han, ‘‘Application of xanthan gum as polysaccharide in tissue engineering: A review,’’ Carbohydr. Polym. 180, 128–144 (2018). 17

    work page 2018

  56. [57]

    Petri, D. F. S., ‘‘ Xanthan gum: A versatile biopolymer for biomedical and technological applications,’’ J. Appl. Polym. Sci. 132(23), 42035 (2015)

    work page 2015

  57. [58]

    Cohen, and Z

    Rabin, Y., J. Cohen, and Z. Priel, ‘‘Viscosity of polyelectrolyte solutions —the generalized Fuoss law,’’ J. Polym. Sci. C 26(9), 397-399 (1988)

    work page 1988

  58. [59]

    A., and K

    Camesano, T. A., and K. J. Wilkinson, ‘‘Single molecule study of xanthan conformation using atomic force microscopy,’’ Biomacromolecules 2(4), 1184 - 1191 (2001)

    work page 2001

  59. [60]

    Zheng, K. K., K. Chen, W. B. Ren, J. F. Yang, and J. Zhao, ‘‘Shear-induced counterion release of a polyelectrolyte, ’’ Macromolecules 55(5), 1647 −1656 (2022)

    work page 2022

  60. [61]

    Zhou, C., K. Chen, K. Zheng, J. Yang, and J. Zhao, ‘‘Counterions redistribution of a polyelectrolyte induced by shear flow ,’’ Macromolecules 57(12), 5739−5746 (2024)

    work page 2024

  61. [62]

    Carrillo, J. -M. Y., and Y. Yang, ‘‘Shear -induced conformations of salt -free polyelectrolytes in semidilute solutions,’’ ACS Macro Lett. 14(5), 933-939 (2025)

    work page 2025

  62. [63]

    Chain dynamics in a polyelectrolyte solution under shear: A rheological NMR investigation,

    Bartosch, S., B. Kohn, and U. Scheler, “Chain dynamics in a polyelectrolyte solution under shear: A rheological NMR investigation,” Appl. Magn. Reson. 54, 1533–1541 (2023)

    work page 2023

  63. [64]

    O., ‘‘A dispersed anisotropic phase as the origin of the weak -gel properties of aqueous xanthan gum,’’ J

    Carnali, J. O., ‘‘A dispersed anisotropic phase as the origin of the weak -gel properties of aqueous xanthan gum,’’ J. Appl. Polym. Sci. 43(2), 929-941 (1991)

    work page 1991

  64. [65]

    Morariu, M

    Brunchi, C.-E., S. Morariu, M. -M. Iftime, and I. Stoica, ‘‘Xanthan gum in solution and solid-like state: Effect of temperature and polymer concentration,’’ J. Mol. Liq. 387, 122600 (2023)

    work page 2023

  65. [66]

    Lim, T., J. T. Uhl, and R. K. Prud’homme , ‘‘Rheology of self -associating concentrated xanthan solutions,’’ J. Rheol. 28(2), 367-379 (1984)

    work page 1984