Calculating liquid distribution in shake flasks on rotary shakers at waterlike viscosities

Screening projects in biotechnological industry performed in shake flasks risk unwanted development if not failure, when operating conditions are not suitable. Limited knowledge, however, is available for the mechanistical design of operating conditions in this type of bioreactor. The fundamental engineering variables are influenced by the geometry of the rotating bulk liquid: for momentum transfer, the contact area between the liquid and the flask inner wall is the friction area, and for mass transfer, the wetted wall exposed to the surrounding air is the mass exchange area. To assess the geometry of the rotating bulk liquid moving inside a shaken Erlenmeyer flask, with respect to the mentioned important engineering variables mentioned, a mechanistical model for the liquid distribution in shake flasks is described in this work. The model is based on a superposition of two individual movements: a circular translatoric movement and a rotation of the flask counteracting the first motion to keep the shake flasks’ spatial orientation. If the effect of viscosity is neglected, the liquid distribution results in an exactly symmetrical paraboloid. A comparison of the calculated liquid distribution with photographs shows very good qualitative agreement of the real liquid distributions by the model equations. Quantitative agreement has been demonstrated by comparison of the liquid height. Furthermore, model equations are presented for the calculation of the contact area between the liquid and the flask wall. This may eventually lead to a prediction of the volumetric power consumption. Similarly, the calculation of the mass transfer area (i.e. liquid surface area and wetted flask wall) is presented.