Dynamics of Viscoelastic Filaments Based on Onsager Principle

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)].

arXiv comment30 pages, 5 figures, accepted by Phys. Rev. Fluids

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• Derivation of Two-fluid Model Based on Onsager Principle
• Dynamics of a viscoelastic liquid filament connected to two mobile droplets
• Statistical formulation of Onsager-Machlup variational principle
• A theory for the flow of chemically-responsive polymer solutions: equilibrium and shear-induced phase separation
• Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes