Viscosity of a binary mixture: Approach to the hydrodynamic limit

We have used equilibrium and nonequilibrium molecular dynamics simulations to study the solute self-diffusion coefficient and the shear rate dependence of the solution viscosity in solutions of model nanocolloidal particles that range in mass ratio from mu=1 up to mu=50 and size ratio from s=1 up to s=4.03 at various concentrations. The zero shear rate viscosities and the initial rates of shear thinning were determined from data in the shear rate region in which the suspension is strongly shear thinning while the solvent remains Newtonian or is weakly shear thinning. The rate of shear thinning increased dramatically with solute volume fraction, regardless of whether the increase was due to increasing solute size or increasing the solute concentration. In a series of simulations in which the mass ratio was varied while keeping the size ratio fixed at s=1, we found that the approach of the viscosities and self-diffusion coefficients to their limiting mass ratio independent values was well described by a rather simple exponential dependence on mass ratio. The concentration dependence of the limiting infinite mass ratio values of the self-diffusion coefficients and zero shear rate viscosities were determined, and used to compute the hydrodynamic radius R-H of the solute particles by various methods. The values of R-H that were obtained by the different methods were reasonably consistent with each other, and indicated that the radius at which the slip boundary condition holds is slightly smaller than the cross-interaction radius between the solute and solvent particles.