For the aeration of highly viscous non-Newtonian fluids, prior studies have demonstrated the improved efficacy of dual coaxial mixing bioreactors fitted with two central impellers and a close clearance anchor. Evaluating the effectiveness of these bioreactors involves considering various mixing characteristics, with a specific emphasis on shear rate distribution. The study of shear rate distribution is critical due to its significant impact on the mixing performance, gas dispersion, and homogeneity in aerated mixing systems comprising shear-thinning fluids. Although yield-pseudoplastic fluids are commonly employed in various industries, there is a research gap when it comes to evaluating shear rate distribution in aerated mixing bioreactors that utilize this fluid type. This study aims to investigate shear rate distribution in an aerated double coaxial bioreactor that handles a 1 wt% xanthan gum solution, known as a Herschel–Bulkley fluid. To achieve this goal, we employed an experimentally validated computational fluid dynamics (CFD) model to assess the effect of different mixing configurations, including down-pumping and co-rotating (Down-Co), up-pumping and co-rotating (Up-Co), down-pumping and counter-rotating (Down-Counter), and up-pumping and counter-rotating (Up-Counter) modes, on the shear rate distribution within the coaxial mixing bioreactor. Our findings revealed that the Up-Co system led to a more uniform local shear distribution and improved mixing performance.