| 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.
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