Theoretical Model for Velocity Profile and Pressure Drop in Perfect Core-annular Flow of Immiscible Herschel–Bulkley Fluids in a Horizontal Pipe

This study investigates an axisymmetric perfect core-annular flow (PCAF) scenario where two incompressible and immiscible Herschel–Bulkley fluids flow in a horizontal pipe. A theoretical model is developed for steady and fully developed PCAF to predict the velocity profiles and pressure drops for different yield stress and power law characteristics of both the fluids. The model presented in this study clearly demonstrates that the velocity profiles and pressure drops in a PCAF arrangement depend on the power law characteristics of both the core and annular fluids, as well as on the respective yield stress values. As the consistency index of the core fluid increases, it behaves more like a solid, leading to a reduced dependency on its flow behaviour index. However, when there are smaller viscosity differences between the core and annular fluids, the flow behaviour index of the core fluid plays a significant role in determining velocity profiles. The yield stresses of the core and annular fluids are also found to significantly affect the velocity profiles and pressure drop in the PCAF arrangement, even at comparable values of actual shear stresses of the co-flow system. Lastly, the validation of the theoretical model is presented through experimental data and numerical simulations available in the literature.