Dance S L, Maxey M R
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 1):031403. doi: 10.1103/PhysRevE.68.031403. Epub 2003 Sep 10.
Theoretical predictions for the scaling of particle velocity fluctuations with container size in homogeneous Stokes suspensions are not consistent with experimental observations. Several explanations have been advanced, including the formation of stratification in bounded systems, such as those used in experiments. Numerical simulations of transient Stokes sedimentation in bounded cells are presented here for several cell sizes. The simulated cells have top and bottom wall boundaries and periodic boundaries in the horizontal. Throughout the course of the simulations the number and distribution of particles in the cell evolve, with impacts on the bulk mean particle velocity, velocity fluctuations, and particle density gradient. Initially the sedimentation follows the classical description, with a sharp front and uniform particle concentration below, but this is not sustained. A layer of higher particle concentration develops below the front. This is unstable and there is a large-scale overturning of the fluid. As a consequence, there is a redistribution of the particles, leaving behind a mass loading of the particles, which is stably stratified (subject to small density fluctuations between horizontal levels). The mean velocity and fluctuations of the particles initially grow and then decay once stable stratification has developed.
对于均匀斯托克斯悬浮液中颗粒速度涨落随容器尺寸的标度关系，理论预测与实验观测结果并不一致。已经提出了几种解释，包括在有界系统（如实验中使用的系统）中形成分层现象。本文针对几种细胞大小给出了有界细胞中瞬态斯托克斯沉降的数值模拟。模拟的细胞具有顶壁和底壁边界以及水平方向的周期性边界。在整个模拟过程中，细胞内颗粒的数量和分布不断演变，这对整体平均颗粒速度、速度涨落以及颗粒密度梯度产生影响。最初，沉降遵循经典描述，有一个陡峭的前沿，下方颗粒浓度均匀，但这种情况无法持续。在前沿下方会形成一层颗粒浓度较高的区域。这是不稳定的，会导致流体发生大规模翻转。结果，颗粒重新分布，留下颗粒的质量负载，其呈稳定分层状态（水平层面之间存在小的密度涨落）。一旦形成稳定分层，颗粒的平均速度和涨落最初会增大，然后衰减。
