Environmental Engineering Program, Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona 85721, USA.
Biotechnol Bioeng. 1991 Aug 5;38(4):389-96. doi: 10.1002/bit.260380409.
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.
微生物聚集体的分形性质是微生物类型和用于开发聚集体的混合条件的函数。我们从长度-投影面积（D(2)）和长度-数量标度（D(3)）关系确定分形维数。在旋转试管中培养的动胶菌聚集体既是表面分形又是质量分形，分形维数分别为 D(2) = 1.69 +/- 0.11 和 D(3)= 1.79 +/- 0.28(+/-标准偏差)。当我们在台式发酵罐中培养这种细菌时，聚集体保持其表面分形特征（D(2) = 1.78 +/- 0.11），但失去了质量分形特征（D(3) = 2.99 +/- 0.36）。在旋转试验管中培养的酵母聚集体（酿酒酵母）比在物理条件相同的情况下培养的细菌聚集体具有更高的平均分形维数，也被认为是分形的（D(2) = 1.92 +/- 0.08 和 D(3) = 2.66 +/- 0.34）。聚集体的孔隙率可以用分形维数来表示，但平均孔隙率高于预期。酵母聚集体（0.9250-0.9966）的孔隙率与在相同物理条件下培养的细菌聚集体（0.9250-0.9966）的孔隙率相似，尽管在反应器中培养的细菌聚集体具有更高的平均孔隙率（0.9857-0.9980）。这些结果表明，基于分形几何的比例关系可能比基于欧几里得几何的方程更有助于量化不同流体力学环境对聚集体形态和特征（如密度、孔隙率和投影表面积）的影响。
