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Steady flows of Cosserat–Bingham fluids
Author(s) -
Růžička Michael,
Shelukhin Vladimir,
Santos Marcelo Martins
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4195
Subject(s) - bingham plastic , mathematics , constitutive equation , limiting , newtonian fluid , non newtonian fluid , lipschitz continuity , generalized newtonian fluid , truncation (statistics) , boundary value problem , mathematical analysis , flow (mathematics) , herschel–bulkley fluid , viscosity , rheology , classical mechanics , mechanics , geometry , physics , thermodynamics , finite element method , mechanical engineering , shear rate , statistics , engineering
The equations describing the steady flow of Cosserat–Bingham fluids are considered, and existence of weak solution is proved for the three‐dimensional boundary‐value problem with the use of the Lipschitz truncation argument. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro‐rotations and two types of plug zones. Our approach is based on an approximation of the constitutive relation by a generalized Newtonian constitutive relation and a subsequent limiting process. Copyright © 2016 John Wiley & Sons, Ltd.