SPECTRUM OF DENSITY-FLUCTUATIONS IN A PARTICLE FLUID SYSTEM .2. POLYDISPERSE SPHERES

This paper presents an extension of the analysis shown in Part I to a polydisperse particle-fluid system. The density autocorrelation is sho wn to be a function of two quantities, a generalized Overlap function for which an analytical expression is derived, and the radial distribu tion function (RDF). In Fourier transform space, the density spectrum again appears to be a strong function of the mean particle size, and s econdarily the mean particle separation distance. One unusual result i s previously observed oscillations in the density spectrum of a monodi sperse system of particles are severely dampened or even eliminated in the polydisperse case, depending on the width of the particle size di stribution. Apparently contributions from different particle correlati ons interfere with each other, thereby reducing the coherent oscillati ons seen in the monodisperse particle-fluid system. Furthermore at lar ge wavenumbers, the spectrum decays with a -2 power-law, independent o f the shape of the particle size distribution. This behavior can be tr aced to the Overlap function which controls the behavior of the spectr um beyond the first peak. Remarkably the -2 power-law spectrum is dete rmined by the shape of the particles (i.e. spheres) rather than their spatial distribution (RDF). The effect of an asymptotically large pres sure gradient on the correlation of several important higher-order mom ents is revisited for the polydisperse system. The relatively simple r elationships developed for the monodisperse system are lost in the pol ydisperse case because particles of different sizes will be influenced differently by an applied pressure gradient. The result is moments th at are of different order in velocity can no longer be related to each other (as they were in the monodisperse system), even in this idealiz ed flow. A more comprehensive understanding of this phenomenon can onl y be achieved through direct numerical simulation or experiment.