Dynamics of Viscoelastic Filaments Based on Onsager Principle

TL;DR

This paper develops a thermodynamically consistent theoretical framework based on Onsager principle to analyze the dynamics of viscoelastic filaments, explaining the beads-on-string structure and its evolution.

Contribution

It introduces a novel Onsager principle-based model for viscoelastic filament dynamics, deriving analytical solutions and clarifying the quasi-equilibrium nature of the beads-on-string structure.

Findings

The beads-on-string structure is a thermodynamic quasi-equilibrium state.

The string radius and tensile stress decay exponentially, aligning with classical theory.

The tensile stress prefactor differs from previous theories but matches numerical simulations.

Abstract

When a polymer solution is uniaxially stretched and held fixed at both ends, the solution quickly separates into droplets connected by strings and takes the beads-on-string structure. The string then becomes thinner by capillary forces. Here we develop a theoretical framework on viscoelastic fluids based on Onsager principle, and apply it to the dynamics of viscoelastic filaments. We show that the beads-on-string structure is a thermodynamic quasi-equilibrium state, and derive an equation for the coexistence condition in the pseudo-equilibrium state. Using the condition, we solve the evolution equation analytically and show that the string radius and the tensile stress vary exponentially as predicted by the classical theory of Entov and Hinch [J. Non-Newtonian Fluid Mech. 72, 31 (1997)], but the prefactor for the tensile stress is different from their theory and agrees with the numerical solutions of Clasen et al. [J. Fluid Mech. 556, 283 (2006)].