Homogenization of Bingham flow in thin porous media

María Anguiano; Renata Bunoiu

doi:10.3934/nhm.2020004

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2020, Volume 15, Issue 1: 87-110. Doi: 10.3934/nhm.2020004

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Homogenization of Bingham flow in thin porous media

María Anguiano^1, and
Renata Bunoiu^2, ,

1.
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, 41012, Spain
2.
Université de Lorraine, CNRS, IECL, Metz, 57000, France

^* Corresponding author: Renata Bunoiu
^* Corresponding author: Renata Bunoiu

Received: March 2019

Published: December 2019

María Anguiano is supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466.

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Abstract

By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham fluid on the small parameters describing the geometry of the thin porous medium under consideration. Three different problems are obtained in the limit when the small parameter $ \varepsilon $ tends to zero, following the ratio between the height $ \varepsilon $ of the porous medium and the relative dimension $ a_\varepsilon $ of its periodically distributed pores. We conclude with the interpretation of these limit problems, which all preserve the nonlinear character of the flow.

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Mathematics Subject Classification: Primary: 76A05, 76A20; Secondary: 76M50, 35B27.

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Figure 1. View of the domain $ \Omega_\varepsilon $

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