BROWNIAN DYNAMICS SIMULATIONS OF CONCENTRATED DISPERSIONS - VISCOELASTICITY AND NEAR-NEWTONIAN BEHAVIOR

We make a detailed study of the viscoelastic and shear-thinning proper ties of the popular r-36 pair potential model for stable colloidal dis persions, particularly in the near-Newtonian regime, using the Brownia n dynamics (BD) technique. Calculations were performed with a simple B D algorithm which uses a free-draining model for the hydrodynamic inte ractions. The linear or Newtonian behaviour of the liquid was obtained using the Green-Kubo formula which makes use of the stress relaxation autocorrelation function calculated from the stress fluctuations of a n unsheared model colloidal liquid. The viscoelastic behaviour, charac terised in terms of the complex dynamic modulus (G', G'') and complex dynamic viscosity (eta(r)', eta(r)'') of the liquid was obtained by Fo urier transformation of the stress autocorrelation function. We also c arried out non-equilibrium BD calculations of the non-Newtonian rheolo gy, using Lees-Edwards periodic boundary conditions to impose a homoge neous shear rate, gamma, on the model colloidal liquid. The shear-thin ning behaviour was calculated and the Newtonian viscosity, eta(o), was obtained by extrapolation to zero shear rate. Near-Newtonian behaviou r was explored using steady-shear simulations and also by applying an oscillating shear strain at constant strain amplitude to obtain the dy namic moduli directly. Two methods were used, one applying a series of widely spaced discrete oscillation frequencies applied progressively (descending from high to low frequency). Another more efficient approa ch was also used, employing a continuously varying sweep through frequ ency space with a broad Gaussian smoothing window function. This route avoids problems associated with equilibration at each frequency. We f ound that the Green-Kubo method gives better statistics for the Newton ian viscosity than the non-equilibrium steady-state shear technique. T he viscosities obtained are in reasonable agreement with the Krieger-D ougherty equation. Low-frequency dynamic moduli are best obtained via the Green-Kubo approach, whereas the high-frequency moduli showed bett er statistics when calculated by the direct non-equilibrium oscillatin g shear strain method.