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Scaling up bioprocesses from the experimental to the pilot or industrial scale involves heuristics and scale relationships that are far from the specific phenomena and are usually not connected to the experimental data. In complex systems, the scaling-up methodology must connect the experimental data with the tools of engineering design. In this work, a two-stage gold bioleaching process was used as a case study to develop a mathematical model of bioprocess scaling that combines the design of experiments with dimensional analysis using the Buckingham Pi theorem to formulate a predictive model that allows scaling up bioprocesses. It was found that the C/N, C/K, and T/C ratios are dimensionless factors that can explain the behavior of a system. Using the Pearson Product–Moment bivariate analysis, it was found that the dimensionless factors C/N and C/K were correlated with the leaching potential of the fermented broth at 1060 cm−1. With these results, a non-linear logarithmic model based on dimensionless parameters was proposed to explain the behavior of the system with a correlation coefficient of R2 = 0.9889, showing that the optimal conditions to produce fermented broth comprised a C/N ratio close to 50 and a C/K ratio close to 800, which allows predicting the scaling of the bioprocess.

Extracellular synthesis of silica particles was carried out by Fusarium oxysporum mycelia using rice husk ash (RHA) as raw material. RHA before and after bioprocessing was analyzed by SEM and specific surface area. Dissolved silica was quantified using colorimetry. Incubation of rice husk ash with F. Oxysporum at 28°C and pH 6.8 indicated that 80% silica was dissolved and micrographs of RHA before and after reaction with fungi showed that the morphology of silica particles changed and the average size decreased (~600 to ~5 µm). Moreover, specific volume pore of particles was reduced from 0.026 to 0.013 cm3/g and surface area increased from 115 to 125 m2/g. Dissolved silica corresponds to 177 m2/g. It is concluded that synthesis of oxide materials using fungal biotransformation is a viable process to obtain added value products from agro-industrial waste materials.