Brownian Dynamics simulation of hard-sphere colloidal dispersions

Abstract

The rheology of hard-sphere suspensions in the absence of hydrodynamic interactions is examined by Brownian Dynamics. Simulations are performed over a wide range of volume fraction φ and Péclet number Pe=γ̇a2/D, where γ̇ is the shear rate and D=kT/6πηa is the Stokes-Einstein diffusivity of an isolated spherical particle of radius a and thermal energy kT in a fluid of viscosity η. At low Pe, the viscosity decreases as Pe increases—the suspension shear thins. The first normal stress difference is positive, while the second normal stress difference is negative. Each normal stress difference vanishes at very low Pe and increases in magnitude to an extremum at Pe≈3. The suspension pressure is proportional to kT and is found to grow as Pe2 from its equilibrium value. Long-time self-diffusivities scale as D and grow as Pe is increased in this regime. At Pe≈100, the suspension undergoes a disorder–order transition to a microstructure of hexagonally packed strings aligned in the flow direction, which is accompanie...