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Computational-fluid-dynamics (CFD) analysis of mixing and gas–liquid mass transfer in shake flasks


Present address and address for correspondence: Process Engineering Center, Eli Lilly and Company, Lilly Corporate Center, DC 3127, Indianapolis, IN 46285, U.S.A. (email


CFD (computational fluid dynamics) techniques were used to predict mixing and gas-liquid mass transfer in a 250 ml shake flask operating over a range of shaking frequencies between 100 and 300 rev./min, shaking diameters between 20 and 60 mm, and fill volumes between 25 and 100 ml. Interfacial area, a, volumetric mass-transfer coeffcient, kLa, and the power input per unit volume, ηv, of the liquid were predicted to be 300<a<800 m2·m−3, 10<kLa<100 h−1 and 40<ηV<600 W·m−3 respectively. These values are significantly different from the reported range for laboratory and pilot-scale bioreactors used in the fermentation of bacterial and fungal micro-organisms (100<a<300 m2·m−3, 100<kLa<400 h−1 and 1000<ηV<3000 W·m−3). Our analysis showed that, at the highest shaking frequency and amplitude of operation, the specific power input in the shake flask was much lower than in laboratory bioreactors. Bacterial and fungal micro-organisms require dissolved oxygen concentrations typically in the range 50–250 mmol of O2·h−1·litre−1, corresponding to volumetric mass-transfer coefficients, kLa, in the range of 250–400 h−1. Poor mixing and dissolved-oxygen limitation in shake flasks may limit their use in process design and media optimization in fermentation. In contrast, mammalian cells have relatively low demand for oxygen and consequently require a lower specific power input, this being typically between 1 and 10 W·m−3, allowing efficient operation in shake flasks. Experimental data presented as part of the present study showed that mammalian cell growth in shake flasks was essentially independent of the specific power input, the maximum specific cell growth rate being 0.056 h−1. The corresponding maximum oxygen-uptake rate was 0.74 mmol of O2·h−1·litre−1 for a viable cell count of 1.3×106 cells·ml−1. These values are comparable with reported values for laboratory and pilotscale bioreactors. This analysis suggests that growth of mammalian cells in shake flasks (and hence in laboratory bioreactors) is not limited by the gas–liquid mass-transfer rate. In mammalian cell cultures, the requirement for good mixing is driven by other considerations, including the need for good cell suspension and reduction in heterogeneity, for example, in pH, temperature, nutrient concentration, osmolality and lactate/glucose ratio.