Rayleigh-Plateau instability of an elasto-viscoplastic filament

TL;DR

This paper develops a model to analyze the Rayleigh-Plateau instability in elasto-viscoplastic filaments, revealing how elasticity and yield stress influence filament stability and breakup patterns.

Contribution

It introduces a slender-thread model incorporating elasticity and yield stress effects, advancing understanding of filament stability and breakup in elasto-viscoplastic fluids.

Findings

Finite yield stress suppresses linear instability without elasticity.

Elastic deformation enables instability above a critical Weissenberg number.

Viscoplastic deformations lead to beads-on-a-string structures.

Abstract

A slender-thread model is derived 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 Weissenberg 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.