Fluctuations in dispersion rheology

On the basis of the mesoscopic fluctuations of excess density, an experimentally verified model is developed to describe the effective shear viscosity and modulus of complex dispersions as a function of concentration, frequency, and temperature. A stochastic differential equation is used in the derivation of the zero-shear viscosity that shows large viscosity enhancement over a broad range of concentrations. The scaling behavior of shear thinning is determined from an anomalous diffusion equation. We obtain the shear-thinning exponent 1>β>1 / 2, which depends on the tenuous fractal structure of the complex systems. The divergence of the shear viscosity in the vicinity of a critical temperature is derived as a dynamic critical phenomenon due to thermal fluctuations, and the critical exponent relates directly to the shear-thinning exponent.