Shavit, U., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Bar-Yosef, G., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Rosenzweig, R., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Assouline, S., Inst. of Soil, Water/Environ. Sci., Volcani Center, Bet Dagan, Israel, Inst. of Soil, Water/Environ. Sci., Volcani Center, A.R.O., Bet Dagan 50250, Israel

Bar-Yosef, G., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Rosenzweig, R., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Assouline, S., Inst. of Soil, Water/Environ. Sci., Volcani Center, Bet Dagan, Israel, Inst. of Soil, Water/Environ. Sci., Volcani Center, A.R.O., Bet Dagan 50250, Israel

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.

Modified Brinkman equation for a free flow problem at the interface of porous surfaces: The Cantor-Taylor brush configuration case

38

Shavit, U., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Bar-Yosef, G., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Rosenzweig, R., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Assouline, S., Inst. of Soil, Water/Environ. Sci., Volcani Center, Bet Dagan, Israel, Inst. of Soil, Water/Environ. Sci., Volcani Center, A.R.O., Bet Dagan 50250, Israel

Bar-Yosef, G., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Rosenzweig, R., Agricultural Engineering, Technion, Haifa, Israel, Agricultural Engineering, Technion, Haifa 32000, Israel

Assouline, S., Inst. of Soil, Water/Environ. Sci., Volcani Center, Bet Dagan, Israel, Inst. of Soil, Water/Environ. Sci., Volcani Center, A.R.O., Bet Dagan 50250, Israel

Modified Brinkman equation for a free flow problem at the interface of porous surfaces: The Cantor-Taylor brush configuration case

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.

Scientific Publication

You may also be interested in