Numerical Investigation of Rigid Zone Evolution in Herschel–Bulkley Fluids Under Unsteady Flow

Abstract

Understanding and predicting the formation of rigid zones in viscoplastic flows is essential for optimizing the casting and structural performance of fresh concrete. This study investigates the unsteady-state evolution of rigid zones in concrete modeled as a Herschel–Bulkley fluid. A two-dimensional numerical model was developed using the Papanastasiou regularization method and implemented in COMSOL Multiphysics 6.0 to simulate viscoplastic flow within a plate domain. The simulations reveal that rigid zones emerge and expand as the yield stress and consistency coefficient increase, significantly altering the flow behavior. At low yield stress, the material behaves predominantly as a fluid, while higher yield stress and consistency values promote the formation and growth of rigid zones over time. Conversely, increasing the applied pressure reduces rigid zone formation, leading to a more continuous, Power-law-type flow. Mathematical expressions are proposed to predict the rigid zone area and stagnation time based on yield stress, consistency, and pressure. These findings enhance the understanding of viscoplastic flow dynamics and offer practical tools for predicting and controlling rigid zone development in concrete casting processes.