The laminar flow field at the interface of a Sierpinski carpet configuration

[1] The problem of laminar flow in a combined free and saturated porous domain was investigated using a Sierpinski carpet configuration. The three-dimensional steady state microscale velocities were measured using a particle image velocimeter and computed numerically. The macroscale velocity profiles were then obtained by averaging the microscale velocities. A comparison between the measured and computed velocities showed a good fit. The macroscale velocity profile was calculated using the modified Brinkman equation (MBE), which was recently derived for two-dimensional brush configurations. The MBE was developed for unidirectional, laminar flows, assuming that the porous medium planar porosity follows a step function. A new analytical solution of the MBE was developed and applied using no calibration or curve fitting. It was shown that although the MBE was originally derived for a unidirectional microscopic flow field, the macroscopic representation of the complex microscopic flow in the Sierpinski configuration can be well described by the solutions of the MBE.

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