The effect of wall depletion and hydrodynamic interactions on stress-gradient-induced polymer migration.
The effect of wall depletion and hydrodynamic interactions on stress-gradient-induced polymer migration.
复制标题
壁损耗和流体动力相互作用对应力梯度诱导的聚合物迁移的影响。
DOI：
10.1039/c6sm00885b
复制
发表时间：
2016
期刊：
影响因子：
3.4
通讯作者：
R. Larson
中科院分区：
文献类型：
--
作者：
Hossein Rezvantalab;Guorui Zhu;R. Larson
我们将我们最近的连续统理论推广到聚合物的应力梯度诱导迁移[Zhu等人，J. Rheol.，2016，60，327-343]通过结合固体边界对浓度变化的影响。对于一个模型流在一个通道中的周期性滑动壁速度，这可以在原则上产生的电场中存在的正弦壁电荷，我们得到的理论结果的稳态分布的稀溶液的聚合物哑铃使用系统的微扰分析Weissenberg数Wi。我们发现，薄壁耗尽区的存在下，改变了最低阶的解决方案，从第二到第一在Wi和急剧影响的浓度场远离耗尽层，由于耦合的二阶导数的速度场的浓度梯度，和对流的聚合物耗尽流体在这一层的大部分流体。壁流体动力相互作用（HI）引起的其他影响进行评估，将聚合物通量从壁HI迁移理论的马和格雷厄姆到我们的连续理论。我们建立了我们的理论的有效性范围通过比较的理论结果与布朗动力学（BD）模拟：实现了良好的协议相对较小的分子，而理论崩溃时，梯度数Gd大于0.5，其中Gd是聚合物线圈的大小的比率的长度尺度的速度梯度变化。BD模拟也扩展到长的Hookean链的情况下，每个链的弹簧数量从1到32，其中发现，对于固定的Gd和Wi，结果几乎是相同的，表明所有重要的现象被捕获的一个简单的哑铃模型，从而支持连续介质理论推导的哑铃的情况下。此外，随机旋转动力学（SRD）的方法来评估HI的迁移模式的作用，产生的效果与连续理论结合壁迁移通量一致。一般来说，我们证明聚合物集中在通道的截然不同的区域，具体取决于Gd和Wi。
We generalize our recent continuum theory for the stress-gradient-induced migration of polymers [Zhu et al., J. Rheol., 2016, 60, 327-343] by incorporating the effect of solid boundaries on concentration variations. For a model flow in a channel with periodic slip wall velocity, which can in principle be produced by an electric field in the presence of a sinusoidal wall charge, we obtain theoretical results for the steady-state distribution of dilute solutions of polymer dumbbells using a systematic perturbation analysis in Weissenberg number Wi. We find that the presence of a thin wall depletion zone changes the lowest order solution from second to first in Wi and drastically affects the concentration field far from the depletion layer, due both to a coupling of the second derivative of the velocity field to the concentration gradient, and to convection of the polymer-depleted fluid in this layer into the bulk of the fluid. Additional effects induced by wall hydrodynamic interaction (HI) are assessed by incorporating polymer flux from the wall-HI migration theory of Ma and Graham into our continuum theory. We establish the range of validity of our theory by comparing the theoretical results with Brownian dynamics (BD) simulations: excellent agreement is achieved for relatively small molecules, while the theory breaks down when the Gradient number Gd is greater than 0.5, where Gd is the ratio of polymer coil size to the length scale over which the velocity gradient changes. The BD simulations are also extended to the case of long Hookean chains with numbers of springs per chain ranging from 1 to 32, where it is found that for fixed Gd and Wi, the results are nearly identical, showing that all important phenomena are captured by a simple dumbbell model, thus supporting the continuum theory which was derived for the case of dumbbells. In addition, the Stochastic Rotation Dynamics (SRD) method is employed to evaluate the role of HI on the migration pattern, producing effects consistent with the continuum theory incorporating the wall-migration flux. In general, we demonstrate that the polymer concentrates in drastically different regions of the channel depending on Gd and Wi.