Viscosity renormalization in the Brinkman equation
作者:
Joel Koplik,
Herbert Levine,
A. Zee,
期刊:
Physics of Fluids(00319171)
(AIP Available online 1983)
卷期:
Volume 26,
issue 10
页码: 2864-2870
ISSN:0031-9171
年代: 1983
DOI:10.1063/1.864050
出版商: AIP
数据来源: AIP
摘要:
The Brinkman equation purports to describe low‐Reynolds‐number flow in porous media in situations where velocity gradients are non‐negligible. The equation involves modifying the usual Darcy law by the addition of a standard viscosity term whose coefficient is usually identified with the pure‐fluid viscosity. It is argued instead that the porous medium induces a renormalization of viscosity, which is calculated in the dilute limit and separately in a self‐consistent approximation. The effective Brinkman viscosity is found todecreasefrom the pore‐fluid value. The calculation fails at low porosity but agrees at least in part with experiment. In addition, the relationship between the Brinkman equation and the phenomenological boundary condition of Beavers and Joseph is discussed and it is pointed out that their experimental configuration provides a simple means of measuring viscosity renormalization.
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