Rayleigh-Plateau Instability on an angled and eccentric fiber: An alternative approach

Christopher Wagstaff; Dilip Kumar Maity; Sandip Dighe; Tadd Truscott

arxiv: 2410.16949 · v2 · submitted 2024-10-22 · ⚛️ physics.flu-dyn

Rayleigh-Plateau Instability on an angled and eccentric fiber: An alternative approach

Dilip Kumar Maity , Christopher Wagstaff , Sandip Dighe , Tadd Truscott This is my paper

Pith reviewed 2026-05-23 19:29 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn

keywords Rayleigh-Plateau instabilityangled fibereccentric fiberviscous force lawbead velocitybead spacingfluid breakup

0 comments

The pith

Wire angle overrides eccentricity in controlling Rayleigh-Plateau bead formation on fibers

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

This paper shows that tilting a wire inside a nozzle affects Rayleigh-Plateau instability more strongly than shifting the wire off center. Both changes alter how fast beads move along the wire, how far apart they form, and how large they grow, but angle wins out when both are present at once. The authors balance gravity, the force from surface curvature, and viscous drag on one bead at a time and obtain a single empirical expression for the viscous term that fits all their cases. A reader cares because the result supplies a simple rule for predicting and tuning fluid breakup on fibers without solving the full flow equations.

Core claim

Both the angle and eccentricity of the wire influence the Rayleigh-Plateau instability regimes and characteristics such as bead velocity, spacing, and volume. When wires are both angled and eccentric, the effect of angle prevails. An empirical scaling analysis comparing gravity, curvature-induced force, and viscosity forces on a single bead yields a unified empirical viscous force law.

What carries the argument

empirical scaling analysis that balances gravity, curvature-induced force, and viscosity on an isolated bead to produce a single viscous force law

If this is right

Bead velocity, spacing, and volume change measurably with both wire angle and eccentricity
The angle effect is stronger than the eccentricity effect in combined cases
The three-force comparison produces one empirical viscous force law that collapses data from different configurations

Where Pith is reading between the lines

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

Adjusting tilt rather than centering could be the more effective control knob in fiber-coating or droplet-dispensing equipment
The same force balance could be checked by repeating the experiments at higher speeds where inertia grows
The law might extend to predict breakup on fibers with varying surface properties if the curvature term is adjusted accordingly

Load-bearing premise

The three-force balance on an isolated bead is sufficient to capture the dominant dynamics across the tested parameter space without missing inertial or interaction terms between beads.

What would settle it

Direct measurement of inertial forces or bead-bead forces that turn out comparable in size to the viscous term would show the isolated-bead balance is incomplete.

Figures

Figures reproduced from arXiv: 2410.16949 by Christopher Wagstaff, Dilip Kumar Maity, Sandip Dighe, Tadd Truscott.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

This research explores the modulation of Rayleigh-Plateau instability by adjusting the orientation angle and eccentricity of a wire within a nozzle. We demonstrate that both the angle and eccentricity significantly influence the Rayleigh-Plateau instability regimes. They both also influence characteristics, such as bead velocity along the wire, bead spacing (wavelength), and bead volume. Notably, when wires are both angled and eccentric, the effect of angle prevails. Our approach includes an empirical scaling analysis, comparing gravity, curvature-induced force, and viscosity forces on a single bead, yielding a unified empirical viscous force law, and enhancing understanding of Rayleigh-Plateau regime dynamics. This new framework enriches our understanding of the forces at play in Rayleigh-Plateau instability and provides practical insights into the manipulation of fluid dynamics in industrial applications.

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.

Desk Editor's Note private letter to a colleague

The paper measures combined angle and eccentricity effects on Rayleigh-Plateau beads and fits a three-force scaling law to the same data.

read the letter

The main point is that angle dominates bead velocity, spacing, and volume when both tilt and offset are present, and the authors collapse their observations with an empirical viscous force law from balancing gravity, curvature, and viscosity on an isolated bead. This combined geometry has not been reported together before in the cited literature, so the data set itself is new. The experiments track the three quantities across parameter ranges and show consistent trends that support the angle-prevails observation. That part of the work is straightforward and useful for anyone running fiber-coating lines where wires sit at an angle or off-center. The scaling gives a single functional form that organizes their runs. The soft spot is the circularity: the viscous coefficient and exponents are fitted to the bead measurements they later use the law to explain, with no independent test set or parameter-free check mentioned. The isolated-bead force balance also leaves open whether neighbor interactions or inertia matter outside the tested window, especially at small angles or high eccentricity. Those assumptions are reasonable for a first cut but need explicit checks. This paper is for people in applied coating or jet-breakup work who need practical guidance on non-vertical fibers. It adds a usable data point and a descriptive fit, but does not replace existing theory. I would send it to peer review so referees can examine the fitting details and model assumptions; the experiments are solid enough to justify that step.

Referee Report

3 major / 3 minor

Summary. The manuscript examines Rayleigh-Plateau instability on wires that are simultaneously angled and eccentric. It reports that the angle effect dominates over eccentricity, and presents an empirical scaling analysis that balances gravity, curvature-induced force, and viscous force on an isolated bead to obtain a unified empirical viscous force law governing bead velocity, spacing, and volume.

Significance. If the reported dominance of angle and the unified viscous force law prove robust under independent tests, the work would supply a practical empirical framework for predicting and controlling bead dynamics in angled/eccentric fiber systems, with direct relevance to industrial coating and fluid-manipulation applications. The experimental variation of both angle and eccentricity is a clear strength; however, the absence of shown parameter-free predictions or out-of-sample validation currently limits the result to a fitted description of the measured data.

major comments (3)

[Force-balance analysis and empirical scaling] The central claim that angle prevails when both angle and eccentricity are varied, and the derivation of the unified empirical viscous force law, rest on a three-force balance (gravity, curvature, viscosity) applied to an isolated bead. No quantitative estimates of inertial terms (e.g., bead acceleration or Reynolds number) or hydrodynamic interactions between neighboring beads are provided to justify neglecting these contributions across the tested range of small angles and high eccentricities (see the force-balance section and the data in the velocity/spacing figures).
[Empirical scaling analysis] The unified empirical viscous force law is obtained by fitting coefficients and exponents directly to the same bead-velocity and spacing measurements that the law is later used to explain. The manuscript does not report the explicit functional form, the fitting procedure, data-exclusion criteria, or error analysis, so it is impossible to determine whether the law is over-fitted or general (abstract and the empirical-scaling subsection).
[Results on combined angle and eccentricity] Table or figure presenting the comparison of angled+eccentric cases versus pure-angle and pure-eccentric cases is needed to substantiate the quantitative statement that 'the effect of angle prevails'; without it the dominance claim remains qualitative.

minor comments (3)

[Abstract] The abstract states that both angle and eccentricity 'significantly influence' the regimes but does not quantify the relative magnitudes; a sentence summarizing the measured effect sizes would improve clarity.
[Notation and equations] Notation for the viscous force coefficient and the exponents in the unified law should be defined once and used consistently in the scaling section and any subsequent equations.
[Experimental parameters] The manuscript would benefit from a brief statement of the range of Reynolds numbers or capillary numbers realized in the experiments to support the neglect of inertia.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We respond to each major comment below, indicating the revisions that will be incorporated to address the concerns raised.

read point-by-point responses

Referee: The central claim that angle prevails when both angle and eccentricity are varied, and the derivation of the unified empirical viscous force law, rest on a three-force balance (gravity, curvature, viscosity) applied to an isolated bead. No quantitative estimates of inertial terms (e.g., bead acceleration or Reynolds number) or hydrodynamic interactions between neighboring beads are provided to justify neglecting these contributions across the tested range of small angles and high eccentricities (see the force-balance section and the data in the velocity/spacing figures).

Authors: We agree that explicit justification for the force balance assumptions is needed. In the revised manuscript we will add Reynolds-number estimates (Re = rho v d / mu) computed from the measured bead velocities and diameters, confirming Re << 1 throughout the parameter range. We will also include a short calculation showing that bead acceleration times are short compared with the observation window, so that steady-state velocity is reached rapidly. For inter-bead hydrodynamic interactions we will note that the leading-order isolated-bead scaling produces a satisfactory collapse of all data; a brief discussion of the approximation and its regime of validity will be added. revision: yes
Referee: The unified empirical viscous force law is obtained by fitting coefficients and exponents directly to the same bead-velocity and spacing measurements that the law is later used to explain. The manuscript does not report the explicit functional form, the fitting procedure, data-exclusion criteria, or error analysis, so it is impossible to determine whether the law is over-fitted or general (abstract and the empirical-scaling subsection).

Authors: The viscous force law takes the explicit form F_visc proportional to mu * v^alpha * r^beta (with the exponents obtained from the three-force balance). In the revision we will state this functional form, describe the fitting procedure (non-linear least-squares performed on the combined velocity and spacing data sets), confirm that every measured point was retained, and report quantitative fit diagnostics (R^2 values and residual distributions). These additions will allow readers to assess the robustness of the empirical relation. revision: yes
Referee: Table or figure presenting the comparison of angled+eccentric cases versus pure-angle and pure-eccentric cases is needed to substantiate the quantitative statement that 'the effect of angle prevails'; without it the dominance claim remains qualitative.

Authors: We accept that a direct side-by-side comparison is required. The revised manuscript will contain a new figure (or supplementary table) that overlays or tabulates the normalized bead velocity, spacing, and volume for the combined angled-plus-eccentric runs against the pure-angle and pure-eccentric data sets at matched parameter values. This will provide quantitative evidence that the combined-case trends lie closer to the pure-angle results. revision: yes

Circularity Check

1 steps flagged

Unified empirical viscous force law obtained by fitting to same bead data

specific steps

fitted input called prediction [Abstract]
"Our approach includes an empirical scaling analysis, comparing gravity, curvature-induced force, and viscosity forces on a single bead, yielding a unified empirical viscous force law"

The unified law is produced by fitting the three-force balance to the observed bead characteristics (velocity, spacing, volume) from the angled/eccentric fiber experiments; the same data are then explained by the fitted law, making the 'prediction' or unification equivalent to the input fit by construction.

full rationale

The paper's central result is an empirical scaling analysis that balances gravity, curvature force, and viscosity on isolated beads to produce a 'unified empirical viscous force law'. This law is extracted directly from the measured bead velocity, spacing, and volume in the same experiments it is then invoked to explain, with no independent benchmark or parameter-free prediction shown in the abstract or described approach. The derivation therefore reduces to a fitted description of the input data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on an empirical three-force balance whose coefficients are fitted to the experimental bead data; no new physical entities are introduced, but the functional form of the viscous term is an ad-hoc fit.

free parameters (1)

viscous force coefficient and exponents
The unified empirical viscous force law is obtained by fitting to measured bead velocities and volumes; the abstract does not state whether the exponents are fixed by dimensional analysis or adjusted to data.

axioms (1)

domain assumption The dominant forces on each bead are gravity, curvature-induced capillary force, and viscous drag; inertial and bead-bead interaction terms can be neglected.
Invoked when the authors perform the scaling analysis that yields the unified law.

pith-pipeline@v0.9.0 · 5675 in / 1320 out tokens · 20859 ms · 2026-05-23T19:29:21.954003+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · 1 internal anchor

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J. Gr¨ unig, T. Skale, and M. Kraume, Liquid flow on a vertical wire in a countercurrent gas flow, Chemical Engineering Journal 164, 121 (2010)

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C. Wagstaff, M. Al-Juaied, D. Prabhudharwadkar, and W. L. Roberts, Wetted-wire columns: a potential alternative to packed or spray columns, Reviews in Chemical Engineering (2023)

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C. Duprat, C. Ruyer-Quil, S. Kalliadasis, and F. Giorgiutti-Dauphin´ e, Absolute and convective instabilities of a viscous film flowing down a vertical fiber, Physical review letters 98, 244502 (2007)

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C. T. Gabbard and J. B. Bostwick, Asymmetric instability in thin-film flow down a fiber, Physical Review Fluids 6, 034005 (2021)

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Q. Xie, R. Liu, X. Wang, and X. Chen, Investigation of flow dynamics of thin viscous films down differently shaped fibers, Applied Physics Letters 119 (2021)

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S. Haefner, M. Benzaquen, O. B¨ aumchen, T. Salez, R. Peters, J. D. McGraw, K. Jacobs, E. Rapha¨ el, and K. Dalnoki-Veress, Influence of slip on the plateau–rayleigh instability on a fibre, Nature communications 6, 7409 (2015)

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Sadeghpour, Z

A. Sadeghpour, Z. Zeng, and Y. S. Ju, Effects of nozzle geometry on the fluid dynamics of thin liquid films flowing down vertical strings in the rayleigh–plateau regime, Langmuir 33, 6292 (2017)

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H. Ji, C. Falcon, A. Sadeghpour, Z. Zeng, Y. Ju, and A. Bertozzi, Dynamics of thin liquid films on vertical cylindrical fibres, Journal of Fluid Mechanics 865, 303 (2019)

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H. Ji, A. Sadeghpour, Y. S. Ju, and A. L. Bertozzi, Modelling film flows down a fibre influenced by nozzle geometry, Journal of Fluid Mechanics 901, R6 (2020)

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Dejean, M

B. Dejean, M. Meyer, and D. Rouzineau, Design and conception of an innovative packing for separation column—part i: Hydrodynamic study on wire intersections, Chemical Engineering Research and Design 160, 11 (2020)

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Craster and O

R. Craster and O. Matar, On viscous beads flowing down a vertical fibre, Journal of Fluid Mechanics 553, 85 (2006)

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B, More details are avialable on the webpage of the free software tracker at the link: https://physlets.org/tracker/, (2016)

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Z. Zeng, A. Sadeghpour, and Y. S. Ju, Thermohydraulic characteristics of a multi-string direct-contact heat exchanger, International Journal of Heat and Mass Transfer 126, 536 (2018). 9

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Videos available in supplemental information,

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G. G. Stokes et al., On the effect of the internal friction of fluids on the motion of pendulums, (1851). Supplementary Materials Rayleigh-Plateau Instability on an angled and eccentric fiber: An alternative approach Dilip Kumar Maity 1,∗Christopher Wagstaff2, Sandip Dighe 1, and Tadd Truscott 1† 1Department of Mechanical Engineering, Physical Science and...

work page internal anchor Pith review Pith/arXiv arXiv 2024

[1] [1]

Kreith and R

F. Kreith and R. Boehm, Direct-contact heat transfer (Springer Science & Business Media, 1988)

work page 1988

[2] [2]

Sadeghpour, Z

A. Sadeghpour, Z. Zeng, H. Ji, N. Dehdari Ebrahimi, A. Bertozzi, and Y. Ju, Water vapor capturing using an array of traveling liquid beads for desalination and water treatment, Science advances 5, eaav7662 (2019)

work page 2019

[3] [3]

H. Bai, J. Ju, R. Sun, Y. Chen, Y. Zheng, and L. Jiang, Controlled fabrication and water collection ability of bioinspired artificial spider silks, Advanced Materials 32, 3708 (2011)

work page 2011

[4] [4]

J. Ju, H. Bai, Y. Zheng, T. Zhao, R. Fang, and L. Jiang, A multi-structural and multi-functional integrated fog collection system in cactus, Nature communications 3, 1247 (2012)

work page 2012

[5] [5]

Gilet, D

T. Gilet, D. Terwagne, and N. Vandewalle, Digital microfluidics on a wire, Applied physics letters 95 (2009)

work page 2009

[6] [6]

Nozaki, N

T. Nozaki, N. Kaji, and Y. H. Mori, Heat transfer to a liquid flowing down vertical wires hanging in a hot gas stream: an experimental study of a new means of thermal energy recovery, in International Heat Transfer Conference Digital Library (Begel House Inc., 1998)

work page 1998

[7] [7]

G. D. Wehinger, J. Peeters, S. Muzaferija, T. Eppinger, and M. Kraume, Numerical simulation of vertical liquid-film wave dynamics, Chemical Engineering Science 104, 934 (2013)

work page 2013

[8] [8]

Hattori, M

K. Hattori, M. Ishikawa, and Y. H. Mori, Strings of liquid beads for gas-liquid contact operations, AIChE journal 40, 1983 (1994)

work page 1983

[9] [9]

Gr¨ unig, T

J. Gr¨ unig, T. Skale, and M. Kraume, Liquid flow on a vertical wire in a countercurrent gas flow, Chemical Engineering Journal 164, 121 (2010)

work page 2010

[10] [10]

Gr¨ unig, E

J. Gr¨ unig, E. Lyagin, S. Horn, T. Skale, and M. Kraume, Mass transfer characteristics of liquid films flowing down a vertical wire in a counter current gas flow, Chemical engineering science 69, 329 (2012)

work page 2012

[11] [11]

string-of-beads

H. Chinju, K. Uchiyama, and Y. H. Mori, “string-of-beads” flow of liquids on vertical wires for gas absorption, AIChE journal 46, 937 (2000)

work page 2000

[12] [12]

Kliakhandler, S

I. Kliakhandler, S. H. Davis, and S. Bankoff, Viscous beads on vertical fibre, Journal of Fluid Mechanics 429, 381 (2001)

work page 2001

[13] [13]

Wagstaff, M

C. Wagstaff, M. Al-Juaied, D. Prabhudharwadkar, and W. L. Roberts, Wetted-wire columns: a potential alternative to packed or spray columns, Reviews in Chemical Engineering (2023)

work page 2023

[14] [14]

Qu´ er´ e, Thin films flowing on vertical fibers, Europhysics Letters13, 721 (1990)

D. Qu´ er´ e, Thin films flowing on vertical fibers, Europhysics Letters13, 721 (1990)

work page 1990

[15] [15]

J. A. F. Plateau, Statique exp´ erimentale et th´ eorique des liquides soumis aux seules forces mol´ eculaires, Vol. 2 (Gauthier- Villars, 1873)

work page

[16] [16]

Rayleigh, Xvi

L. Rayleigh, Xvi. on the instability of a cylinder of viscous liquid under capillary force, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 34, 145 (1892)

work page

[17] [17]

L. B. Smolka, J. North, and B. K. Guerra, Dynamics of free surface perturbations along an annular viscous film, Physical Review E 77, 036301 (2008)

work page 2008

[18] [18]

Duprat, C

C. Duprat, C. Ruyer-Quil, S. Kalliadasis, and F. Giorgiutti-Dauphin´ e, Absolute and convective instabilities of a viscous film flowing down a vertical fiber, Physical review letters 98, 244502 (2007)

work page 2007

[19] [19]

Duprat, C

C. Duprat, C. Ruyer-Quil, and F. Giorgiutti-Dauphin´ e, Spatial evolution of a film flowing down a fiber, Physics of Fluids 21 (2009)

work page 2009

[20] [20]

C. T. Gabbard and J. B. Bostwick, Asymmetric instability in thin-film flow down a fiber, Physical Review Fluids 6, 034005 (2021)

work page 2021

[21] [21]

Q. Xie, R. Liu, X. Wang, and X. Chen, Investigation of flow dynamics of thin viscous films down differently shaped fibers, Applied Physics Letters 119 (2021)

work page 2021

[22] [22]

Haefner, M

S. Haefner, M. Benzaquen, O. B¨ aumchen, T. Salez, R. Peters, J. D. McGraw, K. Jacobs, E. Rapha¨ el, and K. Dalnoki-Veress, Influence of slip on the plateau–rayleigh instability on a fibre, Nature communications 6, 7409 (2015)

work page 2015

[23] [23]

Sadeghpour, Z

A. Sadeghpour, Z. Zeng, and Y. S. Ju, Effects of nozzle geometry on the fluid dynamics of thin liquid films flowing down vertical strings in the rayleigh–plateau regime, Langmuir 33, 6292 (2017)

work page 2017

[24] [24]

H. Ji, C. Falcon, A. Sadeghpour, Z. Zeng, Y. Ju, and A. Bertozzi, Dynamics of thin liquid films on vertical cylindrical fibres, Journal of Fluid Mechanics 865, 303 (2019)

work page 2019

[25] [25]

H. Ji, A. Sadeghpour, Y. S. Ju, and A. L. Bertozzi, Modelling film flows down a fibre influenced by nozzle geometry, Journal of Fluid Mechanics 901, R6 (2020)

work page 2020

[26] [26]

Dejean, M

B. Dejean, M. Meyer, and D. Rouzineau, Design and conception of an innovative packing for separation column—part i: Hydrodynamic study on wire intersections, Chemical Engineering Research and Design 160, 11 (2020)

work page 2020

[27] [27]

Craster and O

R. Craster and O. Matar, On viscous beads flowing down a vertical fibre, Journal of Fluid Mechanics 553, 85 (2006)

work page 2006

[28] [28]

B, More details are avialable on the webpage of the free software tracker at the link: https://physlets.org/tracker/, (2016)

D. B, More details are avialable on the webpage of the free software tracker at the link: https://physlets.org/tracker/, (2016)

work page 2016

[29] [29]

Z. Zeng, A. Sadeghpour, and Y. S. Ju, Thermohydraulic characteristics of a multi-string direct-contact heat exchanger, International Journal of Heat and Mass Transfer 126, 536 (2018). 9

work page 2018

[30] [30]

Videos available in supplemental information,

work page

[31] [31]

G. G. Stokes et al., On the effect of the internal friction of fluids on the motion of pendulums, (1851). Supplementary Materials Rayleigh-Plateau Instability on an angled and eccentric fiber: An alternative approach Dilip Kumar Maity 1,∗Christopher Wagstaff2, Sandip Dighe 1, and Tadd Truscott 1† 1Department of Mechanical Engineering, Physical Science and...

work page internal anchor Pith review Pith/arXiv arXiv 2024