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

Lamir Djaaroun; Farid Messelmi; Hadi Taibi; Hamidréza Adib Ramézani; Mabrouk Meflah; Abdelaziz Rabehi; Takele Ferede Agajie; Abdullah K. Alanazi

doi:10.1063/5.0298769

journal article·2025-11-01Open access

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

Lamir Djaaroun, Farid Messelmi, Hadi Taibi, Hamidréza Adib Ramézani, Mabrouk Meflah, Abdelaziz Rabehi, Takele Ferede Agajie, Abdullah K. Alanazi

AIP Advances· Volume 15· Issue 11

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Abstract

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.

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Research context

OpenAlex topics: Rheology and Fluid Dynamics Studies · Fluid Dynamics and Thin Films · Nanofluid Flow and Heat Transfer

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Laboratory of Applied Mathematics, Kasdi Merbah University, Ouargla University 1 , B.P. 511, Ouargla 30000,

Department of Mathematics and Laboratory of Development in Mechanic and Materials, Zian Achour University 2 , 17000 Djelfa,

Laboratory of Development in Mechanic and Materials, Zian Achour University 3 , 17000 Djelfa,

Ecole Polytechnique de I’Universitée d’Orléans, Université d’Orléans 4 , 8 rue Léonrad de Vinci, 45072 Orléans,

Department of Mathematics, Ouargla University 5 , 30000 Ouargla,

Laboratory of Telecommunications and Smart Systems, Faculty of Sciences and Technologies, Zian Achour University 6 , BP 3117, 17000 Djelfa,

Department of Electrical and Computer Engineering, Faculty of Technology, Debre Markos University 7 , P. BOX 269, Debre Markos,

Department of Chemistry, College of Science, Taif University 8 , Taif,

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