Determination of the Fractal Dimension of Microbial Flocs from the Change in Their Size Distribution after Breakage

The fractal dimension is of ultimate importance in the description of the properties and behavior of microbial flocs in biological wastewater treatment systems. However, the methods for the measurement of the fractal dimension have not been well-established. In this study, a new method is developed to determine the fractal dimension of biological flocs in activated sludge (AS) suspensions. The new method utilizes the particle size distribution (PSD) of the sludge flocs measured by image processing under a microscope. Mechanical breakage is conducted for the sludge sample to create a change in the PSD. On the basis of the self-similarity of fractal aggregates, the fractal dimension of the AS flocs can be calculated from a comparison between the original PSD and the altered PSD by breakage. It is determined that the sludge flocs grown in laboratory bioreactors with sludge ages of 5, 10, and 20 days have fractal dimensions of 2.07, 2.21, and 2.36. The sludge collected from a full-scale AS treatment plant has a fractal dimension of 1.99. This new method overcomes the deficiencies of other existing methods. It is easier to use and provides more reliable results in the determination of the fractal dimension of biological flocs and other similar aggregate samples.