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Scaling bioprocesses remains a major challenge. Since it is physically impossible to increase all process parameters equally, a suitable scale-up strategy must be selected for a successful bioprocess. One of the most widely used criteria when scaling up bioprocesses is the specific power input. However, this represents only an average value. This study aims to determine the Kolmogorov length scale distribution by means of computational fluid dynamics (CFD) and to use it as an alternative scale-up criterion for geometrically non-similar bioreactors for the first time. In order to obtain a comparable Kolmogorov length scale distribution, an automated geometry and process parameter optimization was carried out using the open-source tools OpenFOAM and DAKOTA. The Kolmogorov–Smirnov test statistic was used for optimization. A HEK293-F cell expansion (batch mode) from benchtop (Infors Minifors 2 with 4 L working volume) to pilot scale (D-DCU from Sartorius with 30 L working volume) was carried out. As a reference cultivation, the classical scale-up approach with constant specific power input (233 W m−3) was used, where a maximum viable cell density (VCDmaxmax) of 5.02·1065.02·106 cells mL−1 was achieved (VCDmaxmax at laboratory scale 5.77·1065.77·106 cells mL−1). Through the automated optimization of the stirrer geometry (three parameters), position and speed, comparable cultivation results were achieved as in the small scale with a maximum VCD of 5.60·1065.60·106 cells mL−1. In addition, even on the pilot scale, cell aggregate size distribution was seen to strictly follow a geometric distribution and can be predicted with the help of CFD with the previously published correlation.

In this study, a first approach to model drop size distributions in agitated nanoparticle-stabilized liquid/liquid systems with population balance equations is presented. Established coalescence efficiency models fail to predict the effect of steric hindrance of nanoparticles at the liquid/liquid interface during the film drainage process. A novel modified coalescence efficiency is developed for the population balance framework based on the film drainage model. The elaborate submodel considers the desorption energy required to detach a particle from the interface, representing an energy barrier against coalescence. With an additional implemented function in the population balance framework, the interface coverage rate by particles is calculated for each time step. The transient change of the coverage degree of the phase interface by particles is thereby considered in the submodel. Validation of the modified submodel was performed with experimental data of agitated water-in-oil (w/o) dispersions, stabilized by well-defined spherical silica nanoparticles. The nanospheres with a size of 28 nm are positively charged and were hydrophobized by silanization with dimethyloctadecyl[3-(trimethoxysilyl)propyl]ammoniumchloride. This modeling approach is a first step toward predicting time-resolved dynamic drop size distributions of nanoparticle-stabilized liquid/liquid systems.