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Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary

 

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Opened Access Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary
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Author: Anguiano Moreno, María
Suárez Grau, Francisco Javier
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2019
Published in: IMA Journal of Applied Mathematics, 84 (1), 63-95.
Document type: Article
Abstract: We consider a non-Newtonian fluid flow in a thin domain with thickness ηε and an oscillating top boundary of period ε. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index p, with 9/5 < p < +∞. We consider the limit when the thickness tends to zero and we prove that the three characteristic regimes for Newtonian fluids are still valid for non-Newtonian fluids, i.e. Stokes roughness (ηε ≈ ε), Reynolds roughness (ηε << ε) and high-frequency roughness (ηε >> ε) regime. Moreover, we obtain different nonlinear Reynolds-type equations in each case.
Size: 584.9Kb
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URI: https://hdl.handle.net/11441/83194

DOI: 10.1093/imamat/hxy052

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