AI 中文总结
研究多分散聚合物溶液毛细驱动细流变学，用多模式FENE - PM模型表明$\tau_{EC}$仅反映被流动拉伸的分子量分布子集，其取决于分子量分布、聚合物浓度及实验参数，非内在流体属性。
AI 中文摘要
由于毛细作用而自稀释的聚合物溶液液桥，当聚合物链被拉伸流动拉伸且由此产生的弹性应力贡献超过粘性应力时，会从类似牛顿的线性稀释转变为指数弹性毛细（EC）稀释。Oldroyd - B模型预测EC稀释率由聚合物的松弛时间（$\tau$）设定，从指数衰减中提取的特征稀释时间尺度（$\tau_{EC}$）通常被解释为$\tau$的直接度量。本文表明，对于实际的多分散聚合物溶液，$\tau_{EC}$仅反映分子量（MW）分布的一个子集——那些被流动积极拉伸的链。我们使用多模式FENE - PM模型进行了验证，该模型明确纳入了分子量分布，并与Calabrese等人[《物理评论X》15, 021025 (2025)]关于窄分布低MW和高MW聚苯乙烯溶液双分散共混物的细丝细化实验进行了对比。模型预测只有有效魏森贝格数$Wi = \dot{\varepsilon} \tau > 1/2 $的链会被流动拉伸并贡献弹性应力；这个阈值自然有利于高分子量物种，其较长的松弛时间使它们在弹性毛细区域内保持拉伸状态。因此，测得的$\tau_{EC}$由这个产生应力的子集合而非整个分布决定。此外，我们的模型预测$\tau_{EC}$取决于分子量分布、总聚合物浓度以及包括预拉伸和初始细丝直径在内的实验参数，这证实了它最好被理解为一个特定于实验的量而非一种内在的流体属性。
英文摘要
Liquid bridges of polymer solutions that are self-thinning due to the action of capillarity undergo a transition from Newtonian-like linear thinning to exponential elastocapillary (EC) thinning when the polymer chains are stretched by the elongational flow and the resulting elastic contribution to the stress exceeds the viscous stress. As the Oldroyd-B model predicts that the EC thinning rate is set by the relaxation time ($τ$) of the polymer, the characteristic thinning timescale extracted from the exponential decay ($τ_{EC}$) is commonly interpreted as a direct measure of $τ$. Here we show that for real polydisperse polymer solutions, $τ_{EC}$ reflects only a subset of the molecular weight (MW) distribution -- those chains actively stretched by the flow. We demonstrate this using a multi-mode FENE-PM model that explicitly incorporates the molecular weight distribution, validated against the filament thinning experiments of Calabrese et al. [Phys. Rev. X 15, 021025 (2025)] on bidisperse blends of narrowly-distributed low-MW and high-MW polystyrene solutions. The model predicts that only chains with effective Weissenberg number $Wi = \dot{\varepsilon} τ> 1/2 $ are extended by the flow and contribute elastic stress; this threshold naturally favors high molecular weight species, whose longer relaxation times allow them to remain stretched throughout the elastocapillary regime. The measured $τ_{EC}$ is therefore set by this stress-contributing sub-ensemble rather than the full distribution. Further, our model predicts that $τ_{EC}$ depends on both the molecular weight distribution and total polymer concentration, as well as experimental parameters including pre-stretch and initial filament diameter, confirming that it is best understood as an experiment-specific quantity rather than an intrinsic fluid property.
Comments16 pages, 10 figures
