Time efficient way to calculate oxygen transfer areas and power input in cylindrical disposable shaken bioreactors

Disposable orbitally shaken bioreactors are a promising alternative to stirred or wave agitated systems for mammalian and plant cell cultivation, because they provide a homogeneous and well defined liquid distribution together with a simple and cost-efficient design. Cultivation conditions in the surface-aerated bioreactors are mainly affected by the size of the volumetric oxygen transfer area (a) and the volumetric power input (P/VL) that both result from the liquid distribution during shaking. Since Computational Fluid Dynamics (CFD)-commonly applied to simulate the liquid distribution in such bioreactors-needs high computing power, this technique is poorly suited to investigate the influence of many different operating conditions in various scales. Thus, the aim of this paper is to introduce a new mathematical model for calculating the values of a and P/VL for liquids with water-like viscosities. The model equations were derived from the balance of centrifugal and gravitational forces exerted during shaking. A good agreement was found among calculated values for a and P/VL, CFD simulation values and empirical results. The newly proposed model enables a time efficient way to calculate the oxygen transfer areas and power input for various shaking frequencies, filling volumes and shaking and reactor diameters. All these parameters can be calculated fast and with little computing power.