Stress-gradient-induced polymer migration in Taylor–Couette flow,Soft Matter

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Stress-gradient-induced polymer migration in Taylor–Couette flow
Soft Matter ( IF 2.9 ) Pub Date : 2017-07-28 00:00:00 , DOI: 10.1039/c7sm00821j
Elnaz Hajizadeh _{1,

2,

3,

4} , Ronald G. Larson _{1,

2,

3,

4}

Affiliation

We apply our recent continuum theory for stress-gradient-induced migration of polymers in solution (G. Zhu et al., J. Rheol., 2016, 60, 327–343) to rotational shearing flow in the gap between concentric cylinders (the so-called Taylor–Couette flow), where we have also accounted for the effect of polymer depletion from the solid boundaries on migration patterns. The steady-state distribution of dilute solutions of polymer dumbbells, obtained both using a systematic perturbation analysis in terms of the Weissenberg number (Wi) and by solving numerically the transport problem coupled to the upper-convected Maxwell equation, shows accumulation of polymers near the inner cylinder. This accumulation becomes so strong that most polymers are driven near the inner cylinder once Wi > 4. We also show that there is no first-order contribution to the polymer migration in Taylor–Couette flow due to the absence of a velocity component in the r-direction. Brownian dynamics (BD) simulations for a Hookean dumbbell give a concentration distribution in good agreement with the theoretical predictions of our theory, confirming the accuracy of the theory when the dumbbell radius of gyration is around an order of magnitude or much smaller than the gap. The demonstration of the accuracy of our continuum theory by direct molecular simulation opens the door to application of the theory to journal bearing and other lubrication flows containing polymers that may migrate due to stress gradients.

中文翻译：

应力梯度诱导的泰勒-库埃特流中的聚合物迁移

我们运用我们最近的连续体理论的聚合物溶液（G.朱应力梯度诱导的迁移等，J. Rheol。，2016年，60（327-343）到同心圆柱体之间的间隙中的旋转剪切流（所谓的泰勒-库埃特流），在这里我们还考虑了固体边界处的聚合物耗竭对迁移模式的影响。使用Weissenberg数（Wi）进行系统扰动分析并通过数值求解与上对流Maxwell方程耦合的输运问题获得的聚合物哑铃稀溶液的稳态分布表明，聚合物的堆积在内筒。当Wi> 4时，这种积聚变得非常强烈，以至于大多数聚合物被驱动到内圆柱附近。我们还表明，由于r中不存在速度分量，因此在泰勒-库埃特流中对聚合物迁移没有一阶贡献。-方向。Hookean哑铃的布朗动力学（BD）模拟给出了与我们理论的理论预测非常一致的浓度分布，从而当哑铃回转半径约为一个数量级或比间隙小得多时，证实了该理论的准确性。通过直接分子模拟证明我们的连续体理论的准确性，为将该理论应用于轴颈轴承和其他含有可能由于应力梯度而迁移的聚合物的润滑流打开了大门。

更新日期：2017-09-13

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