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arXiv · 2512.21059

Rayleigh-Plateau instability of an elasto-viscoplastic filament

James D. Shemilt·Neil J. Balmforth
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Abstract

A slender-thread model is used to explore the Rayleigh-Plateau instability of a filament of elasto-viscoplastic fluid. Without elasticity, a finite yield stress suppresses any linear instability for a filament of constant radius. Including sub-yield elastic deformation permits an elastic Rayleigh-Plateau instability above a critical Deborah number. If stresses over the thinner sections of the thread breach the yield threshold, viscoplastic deformations then drive the filament towards pinch-off. The thread consequently evolves to a beads-on-a-string structure. The elasto-plastic anatomy of the beads is explored and categorized.

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James D. Shemilt, Neil J. Balmforth. 2025-12-24. Rayleigh-Plateau instability of an elasto-viscoplastic filament. https://arxiv.org/abs/2512.21059

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