Settling velocities of fractal aggregates
Settling velocities of fractal aggregates
复制标题
DOI：
10.1021/es950604g
复制
发表时间：
1996-06-01
影响因子：
11.4
通讯作者：
Logan, BE
中科院分区：
文献类型：
--
作者：
Johnson, CP;Li, XY;Logan, BE
在水和废水处理系统中产生的聚集体和在自然系统中发现的聚集体是分形的，因此具有与使用斯托克斯定律的沉降速度计算中假设的不同的标度特性。为了证明不渗透的球体的基础上的沉降速度模型不准确地关联骨料的大小，孔隙率和沉降速度高度多孔的分形聚集体，我们生成的分形聚集体的胶乳微球在桨式搅拌机的凝聚和分析每个聚集体单独的大小，孔隙率和沉降速度。这些聚集体的沉降速度平均比使用不可渗透球模型（斯托克斯定律）或可渗透球模型预测的高4-8.3倍，所述可渗透球模型指定聚集体内颗粒均匀分布的聚集体渗透性。从三批聚集体的尺寸-孔隙度关系得到的分形维数（D）为1.78 +/- 0.10、2.19 +/- 0.12和2.25 +/- 0.10。基于Stokes定律，利用分形维数预测了骨料粒径与沉降速度之间的幂律关系。当假定阻力系数Co为常数并固定在蠕动流区的C-D = 24/Re（Re远小于1）时，尺寸和沉降速度的预测斜率仅与D > 2的数据集一致。结果表明，当D < 2时，集料孔隙率将被高估，由沉降速度数据和斯托克斯定律计算的分形维数将不正确。
Aggregates generated in water and wastewater treatment systems and those found in natural systems are fractal and therefore have different scaling properties than assumed in settling velocity calculations using Stokes' law. In order to demonstrate that settling velocity models based on impermeable spheres do not accurately relate aggregate size, porosity and settling velocity for highly porous fractal aggregates, we generated fractal aggregates by coagulation of latex microspheres in paddle mixers and analyzed each aggregate individually for its size, porosity, and settling velocity. Settling velocities of these aggregates were on average 4-8.3 times higher than those predicted using either an impermeable sphere model (Stokes' law) or a permeable sphere model that specified aggregate permeability for a homogeneous distribution of particles within an aggregate. Fractal dimensions (D) derived from size-porosity relationships for the three batches of aggregates were 1.78 +/- 0.10, 2.19 +/- 0.12 and 2.25 +/- 0.10. These fractal dimensions were used to predict power law relationships between aggregate size and settling velocity based on Stokes' law. When it was assumed that the the drag coefficient, Co, was constant and fixed at its value of C-D = 24/Re for the creeping flow region (Re much less than 1), predicted slopes of size and settling velocity were in agreement with only the data sets where D > 2. As a result, when D < 2, aggregate porosities will be overestimated and fractal dimensions will be calculated incorrectly from settling velocity data and Stokes' law.