Modeling three-dimensional surface morphology of biocake layer in a membrane bioreactor based on fractal geometry

While the adsorptive fouling in membrane bioreactors (MBRs) is highly dependent of the surface morphology, little progress has been made on modeling biocake layer surface morphology. In this study, a novel method, which combined static light scattering method for fractal dimension (D_f) measurement with fractal method represented by the modified two-variable Weierstrass-Mandelbrot function, was proposed to model biocake layer surface in a MBR. Characterization by atomic force microscopy showed that the biocake surface was stochastic, disorder, self-similarity, and with non-integer dimension, illustrating obvious fractal features. Fractal dimension (D_f) of sludge suspension experienced a significant change with operation of the MBR. The constructed biocake layer surface by the proposed method was quite close to the real surface, showing the feasibility of the proposed method. It was found that D_f was the critical factor affecting surface morphology, while other factors exerted moderate or minor effects on the roughness of biocake layer.