聚合氯化铁-腐殖酸(PFC-HA)絮体的不同拓扑空间下分形维数的研究

通过对PFC混凝去除水中HA过程中所形成的PFC-HA絮体的研究结果表明,原水pH分另4为9.0、7.0和5.0时,最佳投药量下形成的絮体的平均沉降速度之间的比值为1.17:1.00:0.49,而且所有絮体的水平投影方向的平均直径与垂直投影方向的平均直径的比值均接近0.85.结合Logan公式和有效密度-长轴的双对数关系计算出的絮体三维空间的分形维数Df较为可靠,在本试验中3种pH的原水下形成的PFC-HA絮体的Df均小于2.0.絮体沉降速度的变化是质量分形维数Df、有效密度和粒径等因素的变化综合影响结果,因此,絮体的Df、有效密度各自的变化趋势有可能与沉降速度的不一致.原水pH=7.0时絮体的Df稍大于原水pH=9.0时絮体的Df,但比原水pH=5.0时絮体的Df大11.73%.可见,与原水pH=9.0时形成的絮体相比,原水pH=7.0时形成了稍微密实的小絮体,但原水pH=5.0时却形成了较为疏松的、很小的絮体.在本试验的图像分辨率下,PFC-HA絮体在一维拓扑空间下的分形维数D1比较低,一般都低于1.10.基于投影面积-长轴关系计算的二维拓扑空间的分形维数D2变化趋势为样品3稍大于样品2,样品1最小;然而基于投影面积一周长计算的二维拓扑空间的分形维数D2却呈现不同的变化趋势.另外,尽管PFC-HA絮体的Df小于2,但其与基于投影面积-长轴关系计算的二维拓扑空间的分形维数D2不相等,不符合Meakin的结论,这与本试验中CCD相机的分辨率和絮体样本数量有关.

Fractal dimensions of polyferric chloride-humic acid(PFC-HA) flocs in different topological spaces

The fractal dimensions of PFC-HAflocs in different topological spaces were calculated from their effective density-maximum diameter and image analysis. The ratio between the average diameters for PFC-HAflocs from the horizontal projected view and the vertical projected view were close to 0.85. And the ratio among the average sedimentation rates for flocs produced from HAwater at initial pHs of 9.0, 7.0 and 5.0 was 1.17:1:0.49. The mass fractal dimensions D_f of PFC-HAflocs at initial pHof 7.0, all less than 2.0, calculated from the bi-logarithmic relationship of effective density to maximum diameter and the Logan equation, was little greater than that at initial pHof 9.0, but 11.73% greater than that at an initial pHof 5.0. Therefore, compared with the PFC-HAflocs in HAwater with an initial pHof 9.0, smaller and slightly more compact flocs were formed in HAwater at an initial pHof 7.0, and much smaller and looser ones were formed in HAwater at an initial pHof 5.0. The mass fractal dimensions D_f ,effective density and diameters of PFC-HAflocs affected their sedimentation rates, and neither the highest value of D_f nor the effective density of PFC-HAflocs could fully determine the highest sedimentation rate. At the image resolutions in the experiments, the fractal dimensions D₁ in₁Dtopological space were less than 1.10 The D₂ (lgA-lgd_L) of PFC-HAflocs formed in HAwater at initial pHof 5.0 was a little greater than that at initial pHof 7.0, and the smallest one was found in HAwater at initial pHof 9.0. But D₂ (lgA-lgP) of PFC-HA flocs in HAwater at different initial pHvalues showed a different trend. In addition, not unlike the conclusion from Meakin, the mass fractal dimensions D_f of PFC-HA flocs were not equal to their D₂(lgA-lgd_L) values, which may be caused by image resolution and number of flocs sampled.