Asymptotic behavior of a non-Newtonian flow in a thin domain with Navier law on a rough boundary

We consider a non-Newtonian flow in a thin domain of thickness $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes (Stokes) system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $p$. The bottom of the domain is irregular by the present o...

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Detalles Bibliográficos
Autor: Suárez Grau, Francisco Javier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/162340
Acceso en línea:https://hdl.handle.net/11441/162340
https://doi.org/10.1016/j.na.2015.01.013
Access Level:acceso abierto
Palabra clave:non-Newtonian flow
thin fluid films
rough boundary
Navier condition
adherence condition
asymptotic behavior
Descripción
Sumario:We consider a non-Newtonian flow in a thin domain of thickness $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes (Stokes) system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $p$. The bottom of the domain is irregular by the present of slight roughness of amplitude $\varepsilon^\delta$ and period $\varepsilon^\beta$, satisfying the relation $1<\beta<\delta$. Assuming pure slip or partial slip with a friction coefficient $\varepsilon^{-\gamma}$, with $\gamma>0$, on the rough boundary, we consider the limit when domain thickness tends to zero and we obtain different models depending on the magnitude $\delta$ with respect to ${2p-1\over p}\beta-{p-1\over p}$, and the magnitude $\gamma$ with respect to ${1\over p-1}$.