Elastic Rayleigh–Plateau instability: dynamical selection of nonlinear states

Pandey, Anupam; Kansal, Minkush; Herrada, Miguel A.; Eggers, Jens; Snoeijer, Jacco H.

doi:10.1039/d0sm02195d

Cited by 11 publications

(11 citation statements)

References 41 publications

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“…The Plateau–Rayleigh capillary instability was also observed in thin filaments formed by solid gels . As follows from a comparison of elastic and surface energies, the instability arises when the radius of the filament decreases below the length scale , where G is the elastic shear modulus of the solid. − As a result, two types of morphology have been identified: cylinders on a string and beads on a string …”

Section: Introductionmentioning

confidence: 97%

“…51−53 As a result, two types of morphology have been identified: cylinders on a string and beads on a string. 53 Another type of instability arising in polymer solution strings is associated with the formation of blistering patterns or pearling patterns at the end of the exponential thinning regime, when the polymer chains are highly stretched, 36,54−60 or with phase separation accompanied by the emergence of small solvent droplets onto the jet surface during a flow-induced extension. 61−63 These types of instabilities differ from the classical Plateau−Rayleigh pinching.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of Dilute Polymer Solutions at the Final Stages of Capillary Thinning

Субботин

Semenov

2022

Macromolecules

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The dynamics of capillary breakup of a fluid thread of a dilute polymer solution near the Θ-point is studied using a molecular approach. Several regimes arising during the development of capillary instability have been identified and investigated. We show that in the course of thread thinning, the macromolecules can undergo a coil−stretch transition and analyze its kinetics. In the process of chain stretching, the inertial regime turns into a viscoelastic stage and then a highly viscous quasi-Newtonian regime with almost completely stretched macromolecules. In the viscoelastic regime, the hydrodynamic friction force is proportional to the chain extension, and the radius of the thread decreases according to a power law. This differs from the experimentally observed exponential law arising from the linear dependence of the friction force on the contour length of the chain. A possible physical mechanism giving rise to an exponential thinning of the thread formed by dilute polymer solution is discussed. We further established that once the thread radius becomes smaller than the chain contour length after the end of the viscoelastic regime, such ultrafine thread becomes unstable with respect to the development of annular solvent droplets. It is predicted that the formation of the droplets occurs with no energy barrier, so a "beads-on-string" structure emerges readily as a result.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Dynamics of Dilute Polymer Solutions at the Final Stages of Capillary Thinning

Субботин

Semenov

2022

Macromolecules

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“…In contrast to the experimental findings, the existing methods employing quasi-static stability analysis predict infinite-wavelength for the pattern, suggesting global deformations rather than periodic waves [66,67]. Recently, Pandey, et al (2020) performed a dynamic analysis using hyperelastic solids, indicating that the pattern selection, i.e., the critical wavelength of cylinder-like formations, is due to a dynamical process, similar to the selection of bead size in fluid P-R instabilities [68].…”

Section: State Of the Art Review Of Solid Plateau-rayleigh Instabilitymentioning

confidence: 93%

“…The increase in surface tension deforms the cylinder, resulting in experimentally observed cylinder-like beadings. This geometry is also referred to as cylinders-on-a-string (COAS) formations [68]. At vanishing shear modulus, e.g., the case of liquids, we expect the bulge to resemble a spherical bead due to dominating surface tension.…”

Section: Post-instability Behavior Of Compressible P-r Instabilitymentioning

confidence: 99%

Plateau Rayleigh instability of soft elastic solids. Effect of compressibility on pre and post bifurcation behavior

Dortdivanlioglu

Javili

2022

Extreme Mechanics Letters

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“…The connection between the initial localized bifurcation solution and the final "two-phase" state was explained both theoretically and through numerical simulations by Fu et al (2021). The beading instability in solid cylinders has since been studied dynamically (Pandey et al, 2021) and through the active strain approach (Riccobelli, 2021). The observations of Fu et al (2021) for a solid cylinder have also been fully extended to the case of an incompressible hollow tube by Emery and Fu (2021b,c).…”

Section: Introductionmentioning

confidence: 99%

Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

Emery¹

2022

Preprint

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Localized pattern formations and "two-phase" deformations are studied theoretically in soft compressible cylinders subject to surface tension and axial loading through several forcecontrolled loading scenarios. By drawing upon known results for separate yet mathematically similar elastic localization problems, a concise family of analytical bifurcation conditions for localized bulging or necking are derived in terms of a general compressible strain energy function. The effect of material compressibility and strain-stiffening behaviour on the bifurcation point is analysed, and comparisons between our theoretical bifurcation conditions and the corresponding numerical simulation results of Dortdivanlioglu and Javili (Extreme Mech. Lett. 55, 2022) are made. It is then explained how the fully developed "two-phase" (Maxwell) state which evolves from the initial localized bifurcation solution can be comprehensively understood using the simple analytical expressions for the force parameters corresponding to the primary axial tension deformation. The power of this simple analytical approach in validating numerical simulation results for elastic localization and phase-separation-like problems of this nature is highlighted.

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Elastic Rayleigh–Plateau instability: dynamical selection of nonlinear states

Abstract: A slender thread of elastic hydrogel is susceptible to a surface instability that is reminiscent of the classical Rayleigh-Plateau instability of liquid jets. The final, highly nonlinear states that are...

Cited by 11 publications

References 41 publications

Dynamics of Dilute Polymer Solutions at the Final Stages of Capillary Thinning

Dynamics of Dilute Polymer Solutions at the Final Stages of Capillary Thinning

Plateau Rayleigh instability of soft elastic solids. Effect of compressibility on pre and post bifurcation behavior

Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

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