Polymer stretch in dilute fixed beds of fibres or spheres
Polymer stretch in dilute fixed beds of fibres or spheres
复制标题
纤维或球体稀固定床中的聚合物拉伸
作者：
E. Shaqfeh;D. Koch
发展了一种理论来描述聚合物在流过稀释的、随机的球体或纤维固定床时的构象变化。平均方程的方法用于分析随机速度波动对聚合物构象的影响，通过类似于我们以前分析流经这些床的颗粒取向的方法（Shaqfeh & Koch 1988 a，B）。将聚合物视为被动示踪剂，即在计算随机流场时忽略流体中的聚合物应力。简单的哑铃模型（线性或FENE）用于模拟聚合物构象变化。在所有情况下，我们发现，长程相互作用提供了最大的贡献（在极限的消失小床体积分数）的构象的概率密度的演化方程。这些相互作用在这样的方程中产生构象依赖的扩散率。二阶矩的分布的解决方案表明，有一个临界的孔径德博拉数超过该线性哑铃的回转半径将无限增长和FENE哑铃将增长到其最大可扩展性的一个大部分。这种行为被证明是有关的发展“代数尾巴”的分布函数。这种临界条件的物理原因进行了检查，并分析了其对床层结构的依赖。这些结果被证明是等价的，我们得到的聚合物在一类各向异性高斯流场的考虑。因此，我们的研究结果是明确相关的最近的工作模型湍流中的聚合物拉伸。最后讨论了密切相互作用的影响及其对我们以前结果的修正。
A theory is developed to describe the conformation change of polymers in flow through dilute, random fixed beds of spheres or fibres. The method of averaged equations is used to analyse the effect of the stochastic velocity fluctuations on polymer conformation via an approach similar to that used in our previous analysis of particle orientation in flow through these beds (Shaqfeh & Koch 1988a, b). The polymers are treated as passive tracers, i.e. the polymeric stress in the fluid is neglected in calculating the stochastic flow field. Simple dumbbell models (either linear or FENE) are used to model the polymer conformation change. In all cases we find that the long-range interactions provide the largest contribution (in the limit of vanishingly small bed volume fraction) to an evolution equation for the probability density of conformation. These interactions create a conformation-dependent diffusivity in such an equation. Solutions for the second moment of the distribution demonstrate that there is a critical pore-size Deborah number beyond which the radius of gyration of a linear dumbbell will grow indefinitely and that of the FENE dumbbell will grow to a large fraction of its maximum extensibility. This behaviour is shown to be related to the development of ‘algebraic tails’ in the distribution function. The physical reasons for this critical condition are examined and its dependence on bed structure is analysed. These results are shown to be equivalent to those which we derive by the consideration of a polymer in a class of anisotropic Gaussian flow fields. Thus, our results are explicitly related to recent work regarding polymer stretch in model turbulent flows. Finally, the effect of close interactions and their modification of our previous results is discussed.