Dissolved nutrient gas uptake and fluid mixing by bubble-mediated mass transfer in tall fermenters — a theoretical study

A laminar flow perturbation theory for small gas volume fraction in high aspect ratio bubble columns is developed. The model captures the approximate hydrodynamics, mass transfer, microbicidal gas consumption as well as the hydrostatic head appropriate to vessels in the range of 10–50 m heights. The model is validated against a finite element multiphysics two fluid bubbly flow model for limiting cases of low heights. The key parameter in the mixing is found to be the ratio between stripping length scale, and the hydro-static pressure variation. If this is small, the mixing efficiency in the unaerated region increases like the bubble radius to the -3rd power, but for large values it is independent of the bubble radius. The overall mass transfer continues to increase as the bubble radius decreases. We find that decreasing the bubble radius from 1 cm scale to 1 mm results in an order of magnitude increase in our mixing metric.