Viscoelasticity and near-newtonian behaviour of concentrated dispersions by Brownian dynamics simulations

Abstract

We have developed the Brownian Dynamics simulation technique to calculate the viscoleastic behaviour of model colloidal dispersions. The linear or Newtonian behaviour of the liquid has been obtained using the Green-Kubo formula which incorporates the stress relaxation time autocorrelation function calculated from an unsheared model colloidal liquid. The viscoelastic behaviour, characterised in terms of the complex dynamic modulus (G′, G″) and complex dynamic viscosity (η′ _r ) of the liquid was obtained by Fourier transformation of the stress autocorrelation function. We also used the direct application of an oscillating shear strain at constant strain amplitude to obtain the dynamic moduli. Two variants on the method were used, one progressively (descending from high to low frequency) applying a series of widely spaced discrete oscillation frequencies. Another more efficient approach was also used, employing a continuously varying sweep through frequency space with a broad Gaussian smoothing window function. Results using the r ⁻³⁶ pair potential model for stable colloidal dispersions at high volume fractions are in agreement with experimental trends.