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Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates
Author(s) -
Logan Bruce E.,
Wilkinson Daniel B.
Publication year - 1991
Publication title -
biotechnology and bioengineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.136
H-Index - 189
eISSN - 1097-0290
pISSN - 0006-3592
DOI - 10.1002/bit.260380409
Subject(s) - fractal , fractal dimension , porosity , scaling , morphology (biology) , materials science , chemistry , geometry , mineralogy , composite material , mathematics , geology , mathematical analysis , paleontology
The fractal nature microbial aggregates is a function of the type of microorganism and mixing conditions used to develop aggregates. We determined fractal dimensions from length‐projected area ( D 2 ) and length‐number scaling ( D 3 ) relationships. Aggregates of Zoogloea ramigera developed in rotating test tubes were both surface and mass fractals, with fractal dimensions of D 2 = 1.69 ± 0.11 and D 3 = 1.79 ± 0.28 (±standard deviation), respectively. When we grew this bacteria in a bench‐top fermentor, aggregates maintained their surface fractal characteristics ( D 2 = 1.78 ± 0.11) but lost their mass fractal characteristics ( D 3 = 2.99 ± 0.36). Yeast aggregates ( Saccharomyces cerevisae ) grown in rotating tests tubes had higher average fractal dimensions than bacterial aggregates grown under physically identical conditions, and were also considered fractal ( D 2 = 1.92 ± 0.08 and D 3 = 2.66 ± 0.34). Aggregates porosity can be expressed in term of a fractal dimensions, but average porosities are higher than expected. The porosities of yeast aggregates (0.9250–0.9966) were similar to porosities of bacterial aggregates (0.9250‐0.9966) cultured under the same physical conditions, although bacterial aggregates developed in the reactor had higher average porosities (0.9857‐0.9980). These results suggest that that scaling relationships based on fractal geometry may be more useful than equations derived from Euclidean geometry for quantifying the effects of different fluid mechanical environments on aggregates morphology and characteristics such as density, porosity, and projected surface area.