粘弹性流体中颗粒沉降动力学：二维窄缝通道中颗粒链的数值研究
Dynamics of particle sedimentation in viscoelastic fluids: A numerical study on particle chain in two-dimensional narrow channel
摘要：
在这篇文章中，我们提出了一种数值方法来模拟圆形颗粒在填充有FENE-CR型粘弹性流体的二维通道中的沉降，该方法是从[J. Non-Newtonian Fluid Mech.156（2009）95]中开发的Oldrophil-B流体的域/分布拉格朗日乘子法与因子分解方法推广而来的。数值计算结果表明，聚合物的延伸限制L的FENE-CR流体的情况下，两个磁盘和三个磁盘在二维窄通道中的垂直链的最终形成没有影响，至少在本文中考虑的L值，但中间动力学的颗粒相互作用之前，有一个垂直链的L值较小时，增加松弛时间可以是不同的。在FENE-CR型粘弹性流体中，六个颗粒沉降时，4 ~ 6个盘链的形成与聚合物的伸长极限L有关。当L值较小时，FENE-CR型粘弹性流体不能象Oldrophil-B流体那样将它们聚集在一起，而是形成两个分离的三盘链。对于十个圆盘的情况也得到了类似的结果。对多个粒子的数值计算结果表明，L值越小，垂直链的长度越短，团簇的尺寸越小。
英文摘要：
In this article we present a numerical method for simulating the sedimentation of circular particles in two-dimensional channel filled with a viscoelastic fluid of FENE-CR type, which is generalized from a domain/distributed Lagrange multiplier method with a factorization approach for Oldroyd-B fluids developed in [J. Non-Newtonian Fluid Mech. 156 (2009) 95]. Numerical results suggest that the polymer extension limit L for the FENE-CR fluid has no effect on the final formation of vertical chain for the cases of two disks and three disks in two-dimensional narrow channel, at least for the values of L considered in this article; but the intermediate dynamics of particle interaction before having a vertical chain can be different for the smaller values of L when increasing the relaxation time. For the cases of six particles sedimenting in FENE-CR type viscoelastic fluid, the formation of chain of 4 to 6 disks does depend on the polymer extension limit L. For the smaller values of L, FENE-CR type viscoelastic fluid can not bring them together like the case of these particles settling in a vertical chain formation in Oldroyd-B fluid; but two separated chains of three disks are formed. Similar results for the case of ten disks are also obtained. The numerical results of several more particle cases suggest that for smaller values of L, the length of the vertical chain is shorter and the size of cluster is smaller.
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