Numerical determination of bubble size distribution in Newtonian and non-Newtonian fluid flows based on the complete turbulence spectrum

Abstract

Gas-liquid mass transfer in non-Newtonian fluids is a crucial aspect of the bioprocess industry. Mass transfer is analyzed using the coefficient kLa, which is limited by the rheology since it exerts a barrier to the fluid deformation, significantly affecting the oxygen diffusivity and the bubble breakup and coalescence. However, the traditional mathematical expressions to model the bubble size distribution from bubble breakup and coalescence in turbulent flows of Newtonian fluids are restricted to the inertial sub-range of turbulence where the kinetic energy is dominated only by the microscales. Application of the Newtonian models to non-Newtonian fluids could result in inaccurate predictions by not considering the continuous phase rheology. The main goal of this research is the numerical determination and experimental comparison of bubble sizes in different axial positions of a bioreactor stirred by a Rushton turbine. Emphasis was placed on the viscosity effects on simulating bubble dispersion in a Newtonian fluid (water) and its comparison with a non-Newtonian fluid (0.4 % CMC). The mathematical framework is constructed by coupling the hydrodynamics (through computational fluid dynamics CFD) and bubble breakup and coalescence from a turbulence perspective using the complete energy spectrum that considers the contributions from the energy containing, inertial, and dissipation sub-ranges. This is achieved by including the second-order structure–function. The results of bubble sizes and kLa were compared with experimental data, and acceptable agreement was achieved. Therefore, it is shown that the viscous effects were captured numerically by the entire energy spectrum and improved the predictions of the kLa and bubble sizes compared to the traditional structure function turbulence models.