Rheology of colloidal suspensions. The isokinetic shear-flow hard-sphere model

The shear-flow rheology of the hard-sphere fluid under isokinetic conditions has been investigated by a computer-simulation method. Numerical results for the shear-rate dependence of the tensors of pressure and diffusivity are reported for four dense fluid states, each over a range of shear rate. The shear stress-shear rate flow curves are obtained initially in the isokinetic form by uniform velocity retardation. Results indicate that the onset of a non-linear stress response, and subsequent non-Newtonian phenomena at higher shear rate, can be understood as a shear perturbation of the equilibrium thermodynamic behaviour of the hard-sphere fluid and its phase transitions. The isokinetic flow curve has no direct experimental counterpart. Arguments based upon a renormalisation of the shear-rate scale, however, indicate that the isokinetic flow curve inverts to describe a general laboratory flow curve with the qualitative features of dense colloidal suspensions when seen against the body of experimental evidence. Other common non-Newtonian phenomena, including time-dependent effects (viscoelasticity, thixotropy, rheopexy) and anisotropic effects (normal differences in pressure, diffusivity and granular energy) are also seen in the isokinetic shear-flow model. The isokinetic pressure tensor-shear-rate flow curve may be used to predict experimental laboratory flow curves when the pressures and shear rates are renormalised to a time-scale corresponding to the 'granular temperature' of the experimental system at the same packing fraction.