The initial values of the transport properties of colloidal dispersions depend on the equilibrium arrangement of particles, g(r), and the hydrodynamic in- teractions between the particles. This information is sufficient to calculate the high-frequency viscosity and the short-time self diffusion coefficient, D¡s. Colloidal forces only enter through their effect on the radial distribution func- tion. A further short-time property, the high-frequency modulus, G', contains an additional explicit dependence on the interparticle potential.

This talk will describe the different viscosities, moduli, and diffusion coefficients relevant to colloidal dispersions and outline the relation between stress and microstructure in concentrated suspensions. A high-frequency expansion of a nonequilibrium conservation equation then leads to an exact equation for G' . Approximations for the hydrodynamic interactions based on lubrication theory and far-field results allow calculations of G' . At high volume fraction the form of the high-frequency modulus is very sensitive to the interplay between colloidal and hydrodynamic forces near contact.

An example is the combination of the singular nature of the hard sphere potential with lubrication stresses near contact. Dilute theories demonstrate clearly that soft potentials and/or lubrication stresses that reduce the relative mobility to zero at contact lead to a well defined plateau in G' as w ~ inf, whereas a hard sphere potential without hydrodynamic interaction produces G' ~ w^0.5 in this limit. The former follows from a small, but afflne, deformation of the equilibrium structure by the oscillatory motion and the latter from a diffusional boundary layer near contact required to satisfy the no-flux boundary condition. Two sets of data that delineate the high frequency response for colloidal hard spheres at high volume fraction appear to differ in this regime, suggesting different physics for the interactions at small separations.

Our theory provides quantitative predictions of both limits and a possible interpretation for the experimental results. The two experimental systems only differ in the surface modification of the particles and the high-frequency modulus is the only rheological property sensitive to this difference. The predictions of our theory with varying extent of hydrodynamic interaction illustrate the link between the behavior of the high-frequency modulus and the fluid mechanics very near the particle surface.