Shear banding in entangled polymer solutions is an elusive phenomenon in polymer rheology. One recently proposed mechanism for the existence of banded velocity profiles in entangled polymer solutions stems from a coupling of the flow to banded concentration profiles. Recent work [Burroughs et al., Phys. Rev. Lett. 126, 207801 (2021)] provided experimental evidence for the development of large gradients in concentration across the fluid. Here, a more systematic investigation is reported of the transient and steady-state banded velocity and concentration profiles of entangled polybutadiene in dioctyl phthalate solutions as a function of temperature $(T)$, number of entanglements ($Z$), and applied shear rate ($W{i}_{app}$), which control the susceptibility of the fluid to unstable flow-concentration coupling. The results are compared to a two-fluid model that accounts for coupling between elastic and osmotic polymer stresses, and a strong agreement is found between model predictions and measured concentration profiles. The interface locations and widths of the time-averaged, steady-state velocity profiles are quantified from high-order numerical derivatives of the data. At high levels of entanglement and large $W{i}_{app}$, a significant wall slip is observed at both inner and outer surfaces of the flow geometry but is not a necessary criterion for a nonhomogeneous flow. Furthermore, the transient evolution of flow profiles for large Z indicate transitions from curved to “stair-stepped” and, ultimately, a banded steady state. These observed transitions provide detailed evidence for shear-induced demixing as a mechanism of shear banding in polymer solutions.

中文翻译：

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流量-浓度耦合决定了缠结聚合物溶液中非均匀流动和剪切带的特征

缠结聚合物溶液中的剪切带是聚合物流变学中难以捉摸的现象。最近提出的一种在纠缠聚合物溶液中存在带状速度分布的机制源于流动与带状浓度分布的耦合。最近的工作 [Burroughs et al ., Phys. 莱特 牧师 126 , 207801 (2021)] 为流体中大浓度梯度的发展提供了实验证据。在这里，报告了更系统的研究，即作为温度函数的邻苯二甲酸二辛酯溶液中缠结聚丁二烯的瞬态和稳态带状速度和浓度分布$(吨)$, 纠缠数 ($Z$), 和施加的剪切率 ($W{\mathrm{一世}}_{\mathrm{一种}pp}$), 它控制流体对不稳定的流量-浓度耦合的敏感性。将结果与解释弹性和渗透聚合物应力之间耦合的双流体模型进行比较，并且在模型预测和测量的浓度分布之间发现了很强的一致性。时间平均的稳态速度剖面的界面位置和宽度是从数据的高阶数值导数中量化的。在高水平的纠缠和大$W{\mathrm{一世}}_{\mathrm{一种}pp}$，在流动几何的内表面和外表面都观察到明显的壁滑移，但这不是非均匀流动的必要标准。此外，大Z的流动剖面的瞬态演变表明从弯曲到“阶梯状”的过渡，最终是带状稳态。这些观察到的转变为剪切诱导分层作为聚合物溶液中剪切带的机制提供了详细证据。