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Modified Brinkman equation for a free flow problem at the interface of porous surfaces: The Cantor‐Taylor brush configuration case
Author(s) -
Shavit U.,
BarYosef G.,
Rosenzweig R.,
Assouline S.
Publication year - 2002
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2001wr001142
Subject(s) - microscale chemistry , taylor microscale , stokes flow , flow (mathematics) , viscosity , mathematics , mechanics , porous medium , mathematical analysis , physics , porosity , materials science , thermodynamics , turbulence , reynolds number , composite material , mathematics education
The free flow problem above, at the surface interface, and inside a Cantor‐Taylor brush configuration (CTB), simulating a porous medium, was studied. Particle image velocimetry (PIV) measurements confirm that the microscale Stokes equation provides an accurate solution to the CTB microscale flow problem. A comparison between the results of the averaged microscale Stokes equation and that of the Brinkman equation using an apparent viscosity shows that the concept of “apparent viscosity” did not provide a satisfactory agreement between the two approaches. In order to develop a description of the average velocity profile across the interface flow region, theoretical and numerical analyses were performed. An averaging procedure of the Navier Stokes equations provided a set of three equations, which were used to predict the average velocity in the fluid phase 〈 u 〉 f . This set of equations is the suggested modified Brinkman equation (MBE). The comparison between the results of the Stokes equation and the MBE shows that optimizing the size of the averaging representative volume provides a good fit between the flow problem and the solution of the modified Brinkman equation.