Hydromechanical stress in shake flasks: correlation for the maximum local energy dissipation rate

Shake flasks are widely used in biotechnological process research. Bioprocesses for which hydromechanical stress may become the rate controlling parameter include those where oils are applied as carbon sources, biotransformation of compounds with low solubility in the aqueous phase, or processes employing animal, plant, or filamentous microorganisms. In this study, the maximum local energy dissipation rate as the measure for hydromechanical stress is characterized in shake flasks by measuring the maximum stable drop size. The theoretical basis for the method is that the maximum stable drop diameter in a coalescence inhibited liquid/liquid dispersion is only a function of the maximum local energy dissipation rate and not of the dispersing apparatus. The maximum local energy dissipation rate is obtained by comparing the drop diameters in shake flasks to those in a stirred tank reactor. At the same volumetric power consumption, the maximum energy dissipation rate in shake flasks is about 10 times lower than in stirred tank reactors explaining the common observation of considerable differences in the morphology of hydromechanically sensitive cells between these two reactor types. At the same volumetric power consumption, the maximum local energy dissipation rate in baffled and in unbaffled shake flasks is very similar. A correlation is presented to quantify the maximum local energy dissipation rate in shake flasks as a function of the operating conditions. Non-negligible drop viscosity may be considered by known literature correlations. Further, from dispersion experiments a critical Reynolds number of about 60,000 is proposed for turbulent flow in unbaffled shake flasks.