Advances in understanding and modeling the gas–liquid mass transfer in shake flasks

Abstract

The gas–liquid mass transfer in 250 ml shake flasks has previously been sucessfully modelled on basis of Higbie’s penetration theory. The current contribution presents advances in understanding and modelling the gas–liquid mass transfer in shake flasks at waterlike liquid viscosity in flask sizes between 50 and 1000 ml. An experimental investigation of the maximum gas–liquid mass transfer capacity OTR max using the sodium sulphite system was extended to relative filling volumes of 4–16%, shaking diameters of 1.25, 2.5, 5, 7, 10 cm and shaking frequencies of 50–500 rpm for the above flask sizes. Simultaneously, the previous model of the gas–liquid mass transfer was extended to a “two sub-reactor model” to account for different mechanisms of mass transfer in the liquid film on the flask wall and the bulk of the liquid rotating within the flask. The shake flask is for the first time considered to be a two-reactor system consisting of a stirred tank reactor (bulk liquid) and a film reactor (film on flask wall and base). The mass transfer into the film on the flask wall and base at “in-phase” operating conditions is described by Higbie’s penetration theory. Two different mass transfer theories were applied to successfully describe the mass transfer into the bulk liquid: a model by Kawase and Moo-Young and a model by Gnielinski. The agreement between the new modelling approach, which requires absolutely no fitting parameters and the experimental is within ±30%. The applicability of the models to a biological system was shown using a Pichia pastoris culture. This is particularly notable since geometrically non-similar liquid distributions in very different sizes of shaking flasks are covered. A comparable description of the gas–liquid mass transfer in bubble aerated reactors like stirred tanks is absolutely out of reach. A spatially- and time-resolved consideration of the mass transfer in the liquid film on the flask wall and base has shown that the validity of Higbie’s theory sensitively depends on the film thickness and contact time.