Effective shear rates in shake flasks

• A correlation for effective shear rates in shake flasks is developed.
• The correlation is derived from dimensional analysis and experimental data.
• Effective shear rates are calculated for three different shake flask fermentations.
• Apparent viscosities in shake flasks are now accessible for non-Newtonian broths.
• Shear rates and viscosities in shake flasks are compared to those in stirred tanks.

In bioprocess development and scale-up and scale-down consistent fermentation conditions in shake flasks and stirred tank reactors are crucial. Fermentation broths at elevated viscosities generally show a non-Newtonian flow behavior. The effective shear rate is known to influence apparent viscosity, and, as a consequence, mixing as well as mass and heat transfer. Unknown effective shear rates pose the risk of screening and producing under unfavorable conditions. The present study is the first to systematically investigate the effective shear rate in shake flasks. Based on Buckingham׳s π-theorem a shear rate correlation for 50 mL to 1000 mL shake flasks as a function of viscosity and volumetric power input is developed. Viscosity and power input measurements for a wide range of pseudo-plastic flow behaviors and a broad spectrum of commonly applied operating conditions were applied. Effective shear rates in shake flasks cover a range from 20 s−1 to 2000 s−1. To demonstrate the value of the obtained shear rate correlation, effective shear rates over time were calculated for three different exemplary fermentation systems in shake flasks generating elevated viscosities. With the aid of this new source of information the specific courses of the individual fermentations could now be interpreted. Depending on the broth׳s flow behavior, the effective shear rate in shake flasks is at least 1.55 times higher than that in stirred tank reactors operated at the same volumetric power input, leading to a potentially 50% lower apparent viscosity in shake flasks. The obtained shear rate correlation is a valuable tool to explain existing deviations in screening and production results, ultimately assisting bioprocesses development by means of consistent scale-up or scale-down procedures.