Relation between extensional viscosity and polymer conformation in dilute polymer solutions

TL;DR

This work addresses how extensional viscosity in dilute polymer solutions relates to polymer conformation under uniaxial extensional flow. Using dissipative particle dynamics (DPD) simulations and a Rouse-type model, the authors connect the extensional viscosity growth function $\eta_E^+(t;\dot{\epsilon})$ to the instantaneous gyration radii in the extensional and transverse directions, $R_{g,\parallel}^2$ and $R_{g,\perp}^2$, together with their time derivatives. They observe strain hardening for $\mathrm{Wi} \gtrsim 1$ and show that both transient and steady-state behavior can be described by the Rouse-based expressions $\Phi_E$ and the steady-state relation $\eta_{E,p}(\dot{\epsilon}) = \rho_p \zeta [R_{g,\parallel}^2(\dot{\epsilon}) + \tfrac{1}{2} R_{g,\perp}^2(\dot{\epsilon})]$, with a single fitted friction coefficient $\zeta$. The results provide a unified framework for predicting extensional rheology across chain lengths and concentrations, while noting limitations from neglected hydrodynamic interactions and possible $\mathrm{Wi}$-dependence of $\zeta$.

Abstract

We investigate extensional viscosity and polymer conformation in dilute polymer solutions under uniaxial extensional flow using dissipative particle dynamics simulations. At high extension rates, polymers are significantly stretched by extensional flows, and the extensional viscosity growth function exhibits strain hardening. To reveal their quantitative relation, we adopt an analysis method based on the Rouse-type model. We demonstrate that the extensional viscosity growth function is determined by the instantaneous gyration radii in the parallel and perpendicular directions to the extensional direction and their time derivatives. Our approach also provides a unified description of the steady-state extensional viscosity of dilute polymer solutions for various chain lengths and concentrations in terms of the polymer gyration radius.

Figures (12)

• Figure 1: Snapshot of the polymer solution for $N_\mathrm{p}=50$ and $\phi=0.025$ under uniaxial extensional flow with $\dot{\epsilon}=0.02$. Polymer particles are shown in red. For clarity, solvent particles are represented by blue dots.
• Figure 2: Relative temperature error $|k_BT(\dot{\epsilon})-1|$ as a function of the extension rate $\dot{\epsilon}$ for various $N_\mathrm{p}$ and $\phi$. The error bars denote the standard deviations from three independent simulations and are smaller than the symbol size.
• Figure 3: Polymer contribution $\eta_{E,\mathrm{p}}^+(t;\dot{\epsilon})$ to the extensional viscosity growth function as a function of the time $t$ normalized by the longest relaxation time $\tau$ of polymers for $N_\mathrm{p}=50$ and $\phi=0.1$. From bottom to top, the curves correspond to $\mathrm{Wi}=0.48$, $0.80$, $1.6$, $3.2$, and $6.4$. The dashed line shows the LVE envelope $3\eta_{0,\mathrm{p}}^+(t)$.
• Figure 4: Mean-square end-to-end distance $R^2(t;\dot{\epsilon})$ as a function of $t/\tau$ for $N_\mathrm{p}=50$ and $\phi=0.1$. From bottom to top, the curves correspond to $\mathrm{Wi}=0.48$, $0.80$, $1.6$, $3.2$, and $6.4$.
• Figure 5: Gyration radius of polymers in (a) the parallel $R_{g,\parallel}(t;\dot{\epsilon})$ and (b) perpendicular $R_{g,\perp}(t;\dot{\epsilon})$ directions to the extensional direction as functions of $t/\tau$ for $N_\mathrm{p}=50$ and $\phi=0.1$. From bottom to top in (a), and from top to bottom in (b), the curves correspond to $\mathrm{Wi}=0.48$, $0.80$, $1.6$, $3.2$, and $6.4$.