Settling velocities of multifractal flocs formed in chemical coagulation process

• All well-known floc settling models are based on inaccurate fundamental assumptions.
• Lime softening flocs are multifractal.
• There is more than one relationship between the size and volume of life softening flocs.
• Lime softening flocs cannot be adequately described by the morphological information.

A number of different flocculation mechanisms are involved in the formation of chemical coagulation flocs. Consequently, two flocs with the same size may have been formed by different mechanisms of aggregation and therefore have different arrangement of primary particles. As a result, two flocs with the same size may have different masses or mass distributions and therefore, different settling velocities. Although the correct estimation of the floc mass and density is critical for the development of the floc settling model, none of the suggested floc settling models incorporate the information on mass distribution and variable density of flocs. A probability-based method is used to determine the floc fractal dimensions on floc images. The results demonstrated that flocs formed in lime softening coagulation are multifractal. The multifractal spectra indicated the existence of a multiple fractal dimensions as opposed to the unique box-counting dimension which is a morphology-based fractal dimensions typically introduced into the Stokes' Law. These fractal dimensions may provide information on the flocs' aggregation mechanism, floc's structure, and the distribution of mass inside the floc. More research is required to investigate how to utilize the information obtained from the multifractal spectra to incorporate the variable floc density and nonhomogeneous mass distribution of flocs into the floc settling models.