Lumped-element technique for the measurement of complex density.

Abstract

A novel lumped-element technique is employed to measure the complex density of a gas in circular pores. The complex density expresses the geometry-dependent viscous coupling between the gas and the pore walls and is related to the thermoacoustic function f(mu), or equivalently, F(lambdaV). The acoustic impedance of a compliant region coupled to a pore (or pore-array) is measured and the impedance of the compliant region is subtracted to yield the impedance of the pore(s) alone, which is directly related to F(lambdaV). Pores of different lengths are measured in order to eliminate end effects. Working down to very low frequencies achieves a wide range of values for the ratio of the viscous penetration depth to the mean pore size. The results agree very well with analytical solutions for circular pores. The technique is also applied to two porous foam materials. Comparing the results to previous measurements of the complex compressibility, it is shown that two different shape factors (or equivalently, characteristic dimensions) are required to account for the data.