Effect of flow kinematics on extensional viscosity of dilute polymer solutions

Abstract

We investigate the effect of flow kinematics on the extensional viscosity of dilute polymer solutions by conducting dissipative particle dynamics simulations under uniaxial, planar, and biaxial extensional flows. At high extension rates, dilute polymer solutions exhibit strain hardening under these flows, while the quantitative behavior depends on the flow type. To elucidate the physical origin of this flow-kinematics dependence, we relate the extensional viscosity to polymer conformation using an analytical expression derived from a single-chain model. The resulting relation allows us to separate the contribution of flow-induced polymer conformational changes and the purely kinematic contribution determined by the structure of the velocity gradient tensor. When polymers remain almost unperturbed by extensional flows, differences in the extensional viscosity are governed primarily by the purely kinematic effects. In contrast, as polymers are stretched, the gyration radius in the extensional direction becomes the dominant factor, and differences in the stretching degree in this direction lead to corresponding variations in the extensional viscosity.

Figures (8)

• Figure 1: Snapshots of the polymer solution (a) at $t=0$ (i.e., just before the onset of the imposed flow) and (b-d) at $\dot{\epsilon}_\alpha t = 15$ in (b) uniaxial, (c) planar, and (d) biaxial extensional flows, with $\dot{\epsilon}_\alpha=0.0376$ for all cases. Polymer and solvent particles are shown in red and blue, respectively. For clarity, all particles are rendered semi-transparent, except for selected polymers.
• Figure 2: Relative temperature error $|k_BT(\dot{\epsilon}_\alpha)-1|$ as a function of the extension rate $\dot{\epsilon}_\alpha$ for uniaxial, planar, and biaxial extensional flows. The error bars denote the standard deviations from ten independent simulations.
• Figure 3: Polymer contribution $\eta_{\alpha,\mathrm{p}}^+(t;\dot{\epsilon}_\alpha)$ (thick solid curves) to the extensional viscosity growth function as a function of time $t$ normalized by the longest relaxation time $\tau$ of the polymers for (a) uniaxial, (b) planar, and (c) biaxial extensional flows at different Weissenberg numbers $\mathrm{Wi}_\alpha$. The thin gray curves represent the LVE envelopes. The black dashed curves represent the predictions based on the Rouse-type model [Eq. \ref{['eq:eta_Rouse_relation']}].
• Figure 4: Time series for (a-d) $\mathrm{Wi}_\alpha=1$ and (e-h) $\mathrm{Wi}_\alpha=6$: (a,e) $\eta_{\alpha,\mathrm{p}}^{+}(t;\dot{\epsilon}_\alpha)$; (b,f) $\Phi_{\alpha,+}(t;\dot{\epsilon}_\alpha)$, $\Phi_{\alpha,-}(t;\dot{\epsilon}_\alpha)$, and $\Phi_{\alpha,\Delta}(t;\dot{\epsilon}_\alpha)$; (c,g) $R_{g,+}^2(t;\dot{\epsilon}_\alpha)$ and $R_{g,-}^2(t;\dot{\epsilon}_\alpha)$; (d,h) ${d R_{g,+}^2(t;\dot{\epsilon}_\alpha)}/{dt}$ and $-dR_{g,-}^2(t;\dot{\epsilon}_\alpha)/dt$.
• Figure 5: Mean-square end-to-end distance $R^2(t;\dot{\epsilon}_\alpha)$ as a function of $t/\tau$ at $\mathrm{Wi}_\alpha=1$ (thin curves) and $6$ (thick curves).