Collision Frequencies of Fractal Aggregates with Small Particles by Differential Sedimentation
Collision Frequencies of Fractal Aggregates with Small Particles by Differential Sedimentation
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1997
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在罐式搅拌装置中，乳胶微球（2.84 μm）凝聚生成两组分形维数分别为1.81（0.09）和2.33（0.07）的聚集体。这些分形聚集体（200-1000 μm）和小（1.48 μm）颗粒之间的碰撞率进行了测量，为单个聚集体，已通过悬浮液的小颗粒沉降。从测得的沉降速度计算的总渗透率为3个数量级大于预测的渗透率模型的基础上的一次颗粒内的聚集体的均匀分布。碰撞频率比曲线模型预测的高1个数量级，比直线碰撞模型预测的低约2个数量级。基于由聚集体扫出的水的总体积，通过沉降聚集体对小颗粒的捕获效率<0.2%。分形聚集体的流体收集效率、碰撞频率和颗粒捕获效率随分形维数的增大而降低。分形渗透率模型是通过修改Brinkman相关性来描述作为骨料尺寸的函数的渗透率。该模型与过滤模型结合使用，通过沉降分形聚集体来预测小颗粒的捕获速率和捕获效率。基于这些实验和模型，有人认为，高骨料的渗透性和低的整体颗粒捕获效率的分形聚集体可以解释通过大集群之间形成的大孔内的聚集体的流动。
Two groups of aggregates with fractal dimensions of 1.81 ( 0.09 and 2.33 ( 0.07 were generated by coagulation of latex microspheres (2.84 μm) in a Jar-test (paddle-mixing) device. The collision rates between these fractal aggregates (200-1000 μm) and small (1.48 μm) particles were measured for individual aggregates that had settled through a suspension of the small particles. Aggregate permeabilities calculated from measured settling velocities were 3 orders of magnitude greater than predicted by a permeability model based on a homogeneous distribution of primary particles within the aggregates. Collision frequencies were 1 order of magnitude higher than predicted by a curvilinear model and about 2 orders of magnitude lower than predicted by a rectilinear collision model. The capture efficiencies of small particles by settling aggregates were <0.2% based on the total volume of water swept out by an aggregate. Fluid collection efficiencies, collision frequencies, and particle capture efficiencies of the fractal aggregates decreased with the magnitude of fractal dimensions. A fractal permeability model was developed by modifying the Brinkman correlation to describe the permeability as a function of aggregate size. This model was used in conjunction with a filtration model to predict capture rates and capture efficiencies of small particles by settling fractal aggregates. Based on these experiments and models, it is argued that the high aggregate permeabilities and the low overall particle capture efficiencies of fractal aggregates can be explained by flow through macropores formed between large clusters within the aggregates.