At low frequencies ($\beta$ of the order of 1), the flow exhibits a viscous regime (the velocity profile is parabolic, the boundary layer is of the order of magnitude of the tube / pore radius ).

At high frequencies (Reynolds number $\beta$ higher than 100), the flow exhibits an inertial regime (the velocity is almost the same in the cross-section, the boundary layer is small compared to the tube / pore radius).

A quick numerical application leads to a variation of $\delta_v$ between 350 and 11 $\mu$m in the audible frequency range : [20 – 20 000] Hz.

Almost the same result is obtained for the thermal boundary layer ($\delta_t$ goes from 410 to 13 $\mu$m in the audible frequency range).

In other words, if you want to take advantage of these visco-inertial & thermal effects, pores & pore connections should have dimensions of the order of 10 to ~500 $\mu$m.

At high frequencies (Reynolds number $\beta$ higher than 100), the flow exhibits an inertial regime (the velocity is almost the same in the cross-section, the boundary layer is small compared to the tube / pore radius).

A quick numerical application leads to a variation of $\delta_v$ between 350 and 11 $\mu$m in the audible frequency range : [20 – 20 000] Hz.

Almost the same result is obtained for the thermal boundary layer ($\delta_t$ goes from 410 to 13 $\mu$m in the audible frequency range).

In other words, if you want to take advantage of these visco-inertial & thermal effects, pores & pore connections should have dimensions of the order of 10 to ~500 $\mu$m.

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Luc Jaouen (@ljaouen), ISSN 2606-4138.

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