Bubble flows in non-Newtonian fluids were analyzed using first-principles methods with the aim to compute and predict mass transfer coefficients in such fermentation media. The method we used is a Direct Numerical Simulation (DNS) of the reactive multiphase flow with deformable boundaries and interfaces. With this method, we are able for the first time to calculate mass transfer coefficients in non-Newtonian liquids of different rheologies without any experimental data. In the current article, shear-thinning fluids are considered. However, the results provide the basis for further investigations, such as the study of viscoelastic fluids.