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

Shaking bioreactors are the most frequently used reaction vessels in biotechnology and have been so for many decades. In spite of their large practical importance, very little is known about the characteristic properties of shaken cultures from an engineering point of view. The few publications available contain to some extent contradicting statements and conflicting advice concerning the correct operating conditions of shaking bioreactors. Depending on the investigated microbial system, the engineering parameters may more or less significantly influence the experimental results in a quantitative as well as in a qualitative manner. Unfortunately, these kind of interactions are often overlooked or ignored by scientists. Precise knowledge about the controlling hydrodynamic phenomena in shaking bioreactors and quantitative information about the physical parameters influencing the cultures are needed to assure reproducible and meaningful operating conditions. In this introduction, the state of the art of culturing microorganisms in shaking bioreactors is reviewed and some issues of their practical application in screening and process development projects are addressed.

The maximum gas-liquid mass transfer capacity of 250ml shaking flasks on orbital shaking machines has been experimentally investigated using the sulphite oxidation method under variation of the shaking frequency, shaking diameter, filling volume and viscosity of the medium. The distribution of the liquid within the flask has been modelled by the intersection between the rotational hyperboloid of the liquid and the inner wall of the shaking flask. This model allows for the calculation of the specific exchange area (a), the mass transfer coefficient (k(L)) and the maximum oxygen transfer capacity (OTR(max)) for given operating conditions and requires no fitting parameters. The model agrees well with the experimental results. It was furthermore shown that the liquid film on the flask wall contributes significantly to the specific mass transfer area (a) and to the oxygen transfer rate (OTR).

In this first article of a series a new method is introduced that enables the accurate determination of the power consumption in a shaking flask. The method is based on torque measurements in the drive and appropriate compensation of the friction losses. The results for unbaffled shaking flasks at low viscosities are presented after varying shaking frequency, flask size, filling volume, shaking diameter, and surface quality (hydrophilic and hydrophobic) of the inner flask walls. The order of magnitude of the values of power consumption in shaking flasks is equal to, or even higher than, the values typical for agitated tank bioreactors. A physically based model equation for shaking flasks is derived that introduces a modified power number and a resulting constant as the only fitting parameter. With this equation, the measured results are correlated with sufficient accuracy. For the first time, comprehensive data for the power consumption in unbaffled shaking flasks at low viscosity is available, giving a detailed picture of the influences of the different variables. Copyright 2000 John Wiley & Sons, Inc.