This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Dedicated to Prof. Dr.-Ing. Matthias Kraume on the occasion of his 65th birthday Oxygen supply in aerobic bioprocesses is of crucial importance. For this reason, this paper presents the oxygen demand of different cells and summarizes experimental and numerical possibilities for the determination of oxygen transfer in bioreactors. The focus lies on the volumetric oxygen mass transfer coefficient (k L a) calculation using computational fluid dynamics and state-of-the-art models for surface-aerated and forced-aerated bioreactors. In addition, experimental methods for the determination of the k L a value and the gas bubble size distribution are presented.

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Plant cell and tissue cultivations are of growing interest for the production of structurally complex and expensive plant-derived products, especially in pharmaceutical production. Problems with up-scaling, low yields, and high-priced process conditions result in an increased demand for models to provide comprehension, simulation, and optimization of production processes. In the last 25 years, many models have evolved in plant biotechnology; the majority of them are specialized models for a few selected products or nutritional conditions. In this article we review, delineate, and discuss the concepts and characteristics of the most commonly used models. Therefore, the authors focus on models for plant suspension and submerged hairy root cultures. The article includes a short overview of modeling and mathematics and integrated parameters, as well as the application scope for each model. The review is meant to help researchers better understand and utilize the numerous models published for plant cultures, and to select the most suitable model for their purposes.