A numerical study on regularization and key rheological parameters in the evolution of rigid zones in Herschel–Bulkley fluids

Regulating the formation of rigid zones in viscoplastic fluids is essential for accurate numerical modeling and practical applications. This paper presents a numerical study on the control and minimization of rigid zones in Herschel–Bulkley fluids during flow at the yield stress threshold within a confined square domain. The Papanastasiou regularization method is employed to ensure a smooth transition between fluid and rigid-like zones. This study systematically analyzes the influence of key rheological parameters and the regularization approach on the suppression and reduction of these zones. The influence of the regularization parameter on rigid zone formation during flow is investigated, along with the effect of the critical shear rate for different values of this parameter. Additionally, the impact of inlet pressure on the rigid zone area is examined, followed by an in-depth analysis of its effect for various critical shear rate values to explore their combined influence. Furthermore, the study explores the influence of the consistency factor and the power-law index on rigid zones during flow. The findings highlight optimal parameter selection strategies to suppress or minimize rigid zones at the yield stress threshold, ensuring improved numerical accuracy in viscoplastic fluid simulations.