High-frequency viscosity of a dilute polydisperse colloidal suspension

We consider a dilute polydisperse suspension of spherical colloidal particles and obtain an expression for the high frequency (short time) effective viscosity of the suspension. We show that the Huggins coefficient for such a suspension is sensitive to the degree and nature of the polydispersity. We present numerical calculations for hard sphere particles and for droplets to show that size polydispersity can either decrease or increase the Huggins coefficient of such a suspension relative to its value for a monodisperse system of the same type of particles. For suspensions of hard spheres or droplets with internal viscosity much different from that of the suspending liquid, the effect can be significant when there is a distribution of particle sizes such that there are appreciable volume fractions of both large and small particles. By choice of the spectrum of particle sizes and of the volume fraction of each size the Huggins coefficient can be tuned over an appreciable range