The fractal nature of Escherichia coli biological flocs

Abstract

The fractal structures of Escherichia coli biological flocs were characterised in terms of fractal dimension, which is a measurement of how the bacteria in the flocs occupy space. The dimensional analysis methods, based on power law correlations between floc perimeter, projected area and maximum length, were used to determine the one- and two-dimensional fractal dimensions ( D 1 and D 2) of E. coli flocs formed by flocculation in chitosan solution with a concentration of 10.0 mg chitosan per g dry cell weight (DCW), giving D 1=1.07±0.06 and D 2=1.70±0.08 (±S.D.). The three-dimensional fractal dimension ( D 3) of the E. coli flocs was determined by the two-slopes method, using cumulative size distributions of floc length and solid volume, to be 1.99±0.08 (±S.D.), which is close to the value of D 3=2.14±0.04 (±S.D.) measured by the small angle light scattering method. The results demonstrate that E. coli flocs flocculated with chitosan have a fractal nature, as their fractal dimensions D 1, D 2 and D 3 differ from the values of 1, 2 and 3 expected for the spherical Euclidean object, respectively.