Acoustic waves in a halfspace material filled with random particulate

TL;DR

This paper develops a mathematical framework to relate acoustic wave reflection and transmission in a particulate-filled halfspace with different background media, enabling better non-destructive measurement of dense particulates.

Contribution

It extends the quasi-crystalline approximation to account for different background media in acoustic wave analysis of particulate materials.

Findings

Reflection coefficient can be calculated across various frequencies.

The extended model improves understanding of wave behavior in complex media.

Numerical results validate the approach's effectiveness.

Abstract

Particulate materials include powders, emulsions, composites, and many others. This is why measuring these has become important for both industry and scientific applications. For industrial applications, the greatest need is to measure dense particulates, in-situ, and non-destructively. In theory, this could be achieved with acoustics: the standard method is to send an acoustic wave through the particulate and then attempt to measure the effective wave speed and attenuation. A major obstacle here is that it is not clear how to relate the effective wave speed and attenuation to the reflection and transmission coefficients, which are far easier to measure. This is because it has been very difficult to mathematically account for different background mediums. In this paper we resolve this obstacle. We present how to account for different background mediums for a simple case, to help comprehension: a halfspace filled with a random particulate, where the background of the halfspace is different to the exterior medium. The key to solving this problem was to derive a systematic extension of a widely used closure approximation: the quasi-crystalline approximation (QCA). We present some numerical results to demonstrate that the reflection coefficient can be easily calculated for a broad range of frequencies and particle properties.