摘要
本文通过互相垂直的双镜头同步拍摄技术获取PFC-HA絮体的二维图像,对上述二维图像的表面灰度识别和高度校正技术,确定了聚合氯化铁-腐殖酸混凝体系中不同化学条件时典型絮体的表面高程分布矩阵,然后分别采用空间形貌涨落的一维和二维量测原理与方法,研究不同化学条件下PFC-HA絮体在一维空间不同方向上的变异函数、Hurst指数、分形维数、频谱分布以及二维空间中形貌涨落的分形特征,并分析某些参数的尺度效应和形貌高程变化对PFC-HA絮体各向异性的影响。初步尝试了空间异质性与絮凝过程的关系研究,对于饮用水中腐殖酸的强化混凝去除过程,具有重要的科学意义。
利用CCD高分辨率显微摄像系统拍摄的PFC-HA絮体的形貌照片表明：PFC-HA絮体整体形状很不规则,表面凹凸不平,不同于任何一种简单的欧式几何体,而且絮体存在着许多尺寸不一、形态各异的孔隙。其三维曲面图和三维网格图也直观的体现了絮体空间填充能力及形貌高程的涨落。
不同混凝化学条件下,PFC-HA絮体的粒度分布和平均粒径随PFC投药量和pH的改变均有明显变化,并且它们的变化特征一致。都随着PFC投药量的增加,粒径基本上逐渐减小,并且趋于稳定。随着pH的升高,絮体粒径的变化幅度减小,粒径的大小趋于稳定。
PFC-HA絮体一维空间不同方向上的变异函数结果表明：不同化学条件下,套合结构函数的各向异性比k(h)的变化幅度在0.3816-2.4117之间,可以认为PFC-HA絮体空间形貌具有各向异性特征。基于变异函数法确定的分形维数(D)值处于1.30-1.50之间,符合一维分形维数的取值范围(1-2),相应的R2值也较高,表明该方法计算的分形维数偏差较小,是一种可行的表面轮廓分形维数的计算方法。并且不同方向的D值呈现上下波动的趋势,与混凝pH值、PFC投药量没有形成某种相关性。
PFC-HA絮体一维空间的频谱分布表明：不同方向上的高度分布、高度斜率分布和功率谱分布差异显著,表现出明显的各向异性特征。高度分布体现了PFC-HA絮体空间形貌不同方向的粗糙不平的性质；斜率分布中含有多种频率成分,说明了PFC-HA絮体空间形貌不同方向上组成的复杂性;另外,能谱密度高的区域普遍集中在频率(f)<1mm-1的部分。因此,分别计算了不同pH下,f<1mm-1部分的累积功率谱密度指数(psd*),其数值绝大部分集中在0.6-0.9之间,显示PFC-HA絮体空间形貌高程的斜率分布中低频信号所占的比重较大,含有较多某种低阶的形状参量,这种参量在空间上更多的表现为一种形状上的起伏。此外,psd*并没有与PFC投药量形成某种相关性。另外,还考察了测量间距对PFC-HA絮体空间形貌不同方向的功率谱密度的影响,当测量间距从0.0128mm逐步增大到0.1024mm时,平均功率谱密度急剧减小。
PFC-HA絮体一维空间不同方向上的自仿射分形维数(D1)表明：不同混凝化学条件下不同方向上D1呈波动变化,说明PFC-HA絮体空间形貌是各向异性的。并且在低pH(pH=5.00±0.05和pH=6.00±0.05)时,D1随PFC投药量的增加变化幅度较大；在低PFC投药量(以Fe3+计,为2.02×10-4 mol.L-1)时,D1随pH的升高变化幅度较大。不同方向上D1值与1.0的较大差别表明,在弱酸性条件下和低投药量下PFC-HA絮体空间形貌不同方向上的曲线较粗糙。
PFC-HA絮体二维空间中形貌涨落的分形维数(Ds)表明：不同混凝条件下,利用TPSAM、PCM、CCM和ICCM等方法确定的Ds均大于2.0,符合分形维数的定义。其中,ICCM法能够获取更为详细、准确的形貌涨落信息,计算出的Ds值稍高一些,但总体上看,4种方法计算出的Ds值都比较小,表明PFC-HA絮体的空间填充能力较低,不存在大的形貌高程的涨落。
在混凝pH=5.00±0.05、6.00±0.05和7.00±0.05时,PFC-HA絮体Ds值随PFC投药量的增加变化区间较大,ICCM法确定的Ds值分别处于2.0017-2.0057、2.0025-2.0065和2.0029-2.0067之间；当PFC投药量(以Fe3+计)分别为1.01×10-4mol·L-1和2.02×10-4mol·L-1时,Ds值随pH的升高变化区间较大,ICCM法确定的Ds值分别处于2.0025-2.0067和2.0037～2.0054之间,表明在弱酸性和低投药量下,PFC-HA絮体空间填充能力稍强,空间形貌涨落趋势明显。
PFC-HA絮体空间形貌的各向异性特征对形貌高程的敏感性分析结果表明：PFC-HA絮体空间形貌的变异函数值和频谱分布均随形貌高程的增加而升高,但各向异性程度不变；Hurst指数对形貌高程的变化不敏感；二维分形维数Ds随形貌高程的增大逐渐升高,不同算法确定Ds值的处于2.0000～2.2609之间。
The morphological gray of PFC-HA flocs two-dimensional images was analyzed through Anisotropy analysis software, and the height corresponding to the gray was calibrated. Then, the spatial morphological height distribution matrixes of typical flocs produced under different coagulation-flocculation conditions were identified as well. Then, the parameters including variograms, Hurst indices, fractal dimensions, spectral distribution in one-dimensional space and fractal characteristics of spatial morphological fluctuation in two-dimensional space, were employed to describe the anisotropy of spatial morphology PFC-HA flocs formed under various chemical conditions. In addition, effects of the scale dependence and spatial morphological height for certain parameters on space anisotropy of PFC-HA flocs were analyzed. And a first attempt was made to study the relation between space heterogeneity and flocculation process.
The flocs images were taken with a charged coupled device (CCD) sensor and the results indicated that the flocs, being different from any simple geometric body, were irregular and unsmooth and many pores with various sizes and morphologies were found in them. The three-dimensional curved surface figure and three-dimensional grid figure directly showed the space-filling capacity and fluctuation of spatial morphological height for the flocs as well.
Particle distribution and average particle size for the PFC-HA flocs under different coagulation-flocculation conditions changed significantly with PFC dosage and pH. With the increasing of PFC dosage, the particle size reduced gradually and tended to be stable. With an increase in pH, the changing range for the particle size decreased and it became steady as well.
Results of variograms in different directions of PFC-HA flocs in one-dimensional space showed that under various chemical conditions, the anisotropic ratio of nested model variograms k(h) varied between 0.3816 to 2.4117, which indicated the anisotropy of spatial morphology for the PFC-HA flocs. The fractal dimension (D) calculated by variogram was between 1.30 and 1.50 with a high R2 value, which is consistentwith the definition of one-dimensional fractal dimension (1-2). This suggested fractal dimension deviations calculated by the method were relatively small and therefore the method was feasible for working out surface profile fractal dimension. Further, D in different directions fluctuated and showed no relation with coagulation-flocculation pH and PFC dosage.
Spectral distribution of PFC-HA flocs in one-dimensional space indicated that height distribution, slope distribution and power spectral density in different directions varied significantly and space anisotropy can be observed obviously. Height distribution showed roughness and unsmooth in different directions for spatial morphology of PFC-HA flocs, while slope distribution gave various kinds of frequency components, indicating complexity of spatial morphology composition in different directions for PFC-HA flocs. Moreover, area with high power spectral density mainly focused in the frequency range (f)<1mm-1. Therefore, the indexes for accumulated power spectral density (psd) were calculated under different pHs when f<1mm-1 and most data were found between 0.6 to 0.9, demonstrating that low frequency signal occupied most of the area in the slope distribution of spatial morphological height of PFC-HA flocs and there were a lot of low stage shape parameters which mostly exhibited fluctuation in space. In addition, the accumulated psd was not clearly related to PFC dosage. Effects of measurement interval on psd for spatial morphology of PFC-HA flocs in different directions were also investigated and the results showed that average psd reduced drastically when the measurement interval increased from 0.0128mm to 0.1024mm.
One-dimensional self-affine fractal dimension (D1) of PFC-HA flocs in different directions fluctuated under different coagulation-flocculation conditions, which indicated the space anisotropy of PFC-HA flocs. D1 changed widely with the increasing of PFC dosage at low pH (pH=5.00±0.05 and pH=6.00±0.05) and with the increasing of pH at low PFC dosage ([Fe3+]=2.02×10-4 mol·L-1). D1 in different directions varied largely from 1.0, suggesting that the profile of spatial morphology of PFC-HA flocs in different directions was rough under weak acid condition and low dosage.
The results showed that all the Ds vlues of PFC-HA flocs under different coagulation-flocculation conditions were greater than 2.0, which were calculated through the following four methods:Triangular Prism Surface Area Method(TPSAM), Projective Covering Method(PCM), Cubic Covering Method(CCM) and Improved Cubic Covering Method(ICCM). This agrees with the definition of fractal dimension.More detailed and accurate information on space morphological fluctuation can be obtained by ICCM with a slightly higher Ds value. However, Ds calculated by the four methods were generally low, which demonstrated low space-filling capacity and gentle fluctuation on morphological height for PFC-HA flocs.
Ds of PFC-HA flocs varied greatly with the increasing of PFC dosage at coagulation-flocculation pH=5.00±0.05,6.00±0.05 and 7.00±0.05. Ds calculated by ICCM were around 2.0017～2.0057, 2.0025～2.0065 and 2.0029～2.0067, respectively. Ds changed largly with increasing pH when the PFC dosage (by Fe3+) were 1.01×10-4mol·L-1 and 2.02×10-4mol·L-1. Ds calculated by ICCM were around 2.0025～2.0067 and 2.0037～2.0054. These indicated that PFC-HA flocs had a slightly larger space-filling capacity and showed stronger fluctuation under low pH and PFC dosage.
The influence of spatial anisotropy of PFC-HA floes on the sensitivity of spatial morphological height was studied. The spatial morphology variograms and spectral distribution of PFC-HA flocs increased with the increasing of spatial morphological height without a change in the extent of spaceanisotropy. Hurst indices were insensitive to morphological height. Two-dimensional fractal dimension Ds increased gradually with the increasing of morphological height. Ds calculated by different methods ranged between 2.0000 and 2.2609.
引文
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