Constitutive equation for colloidal suspensions
Dr. Joseph Brader (Universität Konstanz)

We present a first principles approach to the time-dependent non-linear rheology of dense colloidal suspensions. Starting from the Smoluchowski equation for interacting Brownian particles under flow we derive exact results for time dependent averages. We focus here on the resulting generalized Green-Kubo relation for the stress tensor, which is of particular interest for rheological studies. This exact result may be approximated using projection operator techniques and yields a constitutive equation with an unexpected dependence on the flow history.
As the approximations are tailored to treat high density systems our final equations allow the time dependent rheology of both fluid and glassy arrested states to be investigated within a unified theory.
Numerical results will be presented for several flows of interest.