Photon correlation spectroscopy on flowing polydisperse fluid-particle systems: theory

We develop an analytical expression for the homodyne autocorrelation function of laser light scattered by a laminar flow of a polydisperse particle-fluid system. In contrast to the already existing literature on the development of autocorrelation functions, we explicitly begin with the effects of the finite linewidth of the light source, the spatial and temporal intensity averaging that is due to the detection process, the Brownian particle movement on the amplitudes of the scattered light waves as well as on the degree of resolution that we introduce in this paper, and a general system velocity v = (v(x), v(y), v(z)). One main result is a new physical interpretation of the well-known, generally empirically introduced coherence factor. Quantities that are comparable to the well-known degree of coherence, coherence area, and number of coherence areas have also been obtained. Finally the investigations are simplified to an autocorrelation function that can be used for the analysis of fluid-particle systems in the low Knudsen number regime. It is shown that in this case particle size or size distribution, system velocity, and particle concentration can be obtained simultaneously. The developed autocorrelation function is related to frequently analyzed special cases and compared with expressions from the literature.