A numerical scheme for treating viscous effects in three-fluid flows of Newtonian and non-Newtonian shear thinning fluids

Multi-fluid flows with Newtonian and non-Newtonian fluid interactions are encountered in many applications, including surfactant replacement therapy in prematurely born infants, bubbly flows, and wastewater treatment. Computational simulation of such complex fluid interaction requires solving additional constitutive equations to resolve the non-Newtonian fluid dynamics and capture the interactions with the Newtonian fluids. We present a novel numerical scheme for treating the viscous effects in three-fluid flows of two Newtonian fluids (liquid and gas) interacting with a shear thinning non-Newtonian liquid. In this work, the volume-of-fluid method is used to track fluid volumes, where an additional passive scalar is employed to distinguish between the Newtonian and non-Newtonian fluids. The non-Newtonian fluid viscosity is modeled by the Carreau-Yasuda equation. We demonstrate the accuracy of the proposed scheme and the overall flow solver performance using various test cases.