Critical bubble size in shear-thinning non-newtonian fluids: toward rational aeration design for low-energy aeration in MBRs.

Membrane bioreactors (MBRs) are central to low-carbon wastewater treatment, yet membrane fouling control consumes the majority of aeration energy. Classical bubble dynamics (Clift diagram) fail in the shear-thinning non-Newtonian fluids typical of high-MLSS mixed liquor, leaving the definition of "large bubbles" ambiguous and aeration design empirical. Here, we report a previously unrecognized second growth regime in the bubble diameter-velocity relationship. High-frame-rate imaging and dimensionless analysis revealed that bubble rise velocity exhibits a sharp rheological decoupling at a critical equivalent diameter of ∼10 cm. Below this threshold, shear-thinning rheology (0-1.0% CMC) strongly modulates velocity in a non-monotonic manner; above it, buoyancy and inertia dominate, rendering velocities insensitive to fluid viscoelasticity and converging toward a universal scaling law shared with Newtonian systems. This transition arises from inertial forces overwhelming the local reduction in viscosity at the bubble rim. These findings establish a physically based criterion for defining large bubbles in shear-thinning fluids and provide a rational framework for designing energy-efficient large-bubble aeration strategies that may reduce scouring-related aeration demand in MBRs. The underlying hydrodynamic mechanism may also inform the design and optimization of gas-liquid multiphase systems involving shear-thinning non-Newtonian fluids, such as chemical reactors, fermentation systems, and polymer-processing operations.