Numerical investigation of the Herschel–Bulkley fluid flow through thin layers

The purpose of the present paper is to numerically investigate the steady flow of Herschel–Bulkley fluid through thin layers in order to analyze the behavior of the rigid zones. This study establishes correlations between the measure of rigid zones, the yield stress, and the layer thickness. The results show that the increase in the yield stress leads to a large expansion of rigid zones, which becomes larger as the layer becomes thinner. Moreover, the occupancy rate and the spatial distribution of the unyielded regions within the flow domain are illustrated, showing the trend of growth of these areas until reaching an upper limit. In addition, the flow is examined under both velocity and pressure boundary conditions, which allows us to demonstrate that the blocking phenomenon corresponding to the total solidification of the flow domain occurs in the pressure-driven case, while it cannot be reached when the flow is governed by imposed velocity.