Brownian dynamics simulations of concentrated dispersions: viscoelasticity and near-Newtonian behaviour

Abstract

We make a detailed study of the viscoelastic and shear-thinning properties of the popular r^–36 pair potential model for stable colloidal dispersions, particularly in the near-Newtonian regime, using the Brownian dynamics (BD) technique. Calculations were performed with a simple BD algorithm which uses a free-draining model for the hydrodynamic interactions. 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 an unsheared model colloidal liquid. The viscoelastic behaviour, characterised in terms of the complex dynamic modulus (G′, G″) and complex dynamic viscosity (η′_r, η″_r) of the liquid was obtained by Fourier transformation of the stress autocorrelation function.

We also carried out non-equilibrium BD calculations of the non-Newtonian rheology, using Lees–Edwards periodic boundary conditions to impose a homogeneous shear rate, , on the model colloidal liquid. The sheart-hinning behaviour was calculated and the Newtonian viscosity, η_o, was obtained by extrapolation to zero shear rate. Near-Newtonian behaviour was explored using steady-shear simulations and also by applying an oscillating shear strain at constant strain amplitude to obtain the dynamic 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 approach was also used, employing a continuously varying sweep through frequency space with a broad Gaussian smoothing window function. This route avoids problems associated with equilibration at each frequency.

We found that the Green–Kubo method gives better statistics for the Newtonian viscosity than the non-equilibrium steady-state shear technique. The viscosities obtained are in reasonable agreement with the Krieger–Dougherty equation. Low-frequency dynamic moduli are best obtained via the Green–Kubo approach, whereas the high-frequency moduli showed better statistics when calculated by the direct non-equilibrium oscillating shear strain method.