(20d) Bill Russel's Quest for Understanding the Viscosity of Hard Sphere Colloidal Suspensions.

Hard sphere colloidal suspensions are the “hydrogen-atom” of colloid science, providing a baseline for understanding more complex systems with interparticle interactions. Hard sphere colloidal dispersions have excluded volume, Brownian and hydrodynamic forces, the many-body nature of which and the coupling between the latter by fluctuation-dissipation makes even the equilibrium viscosity calculation challenging beyond the two-particle limit. William Russel, building upon the seminal work of Einstein and Batchelor, pioneered the melding of the classical master equation approach (Smoluchowski) for the Brownian motion with methods of handling the many-body hydrodynamics in the Stokes limit. This formalism provided a method to calculate the elastic moduli as well as equilibrium viscosity in the 3-body limit (third virial coefficient for the viscosity) as well as explore the all-important divergence in the viscosity with packing fraction at the colloidal glass transition. In the presentation I will summarize the key features of the approach, review critical results, and show how this can be framed in a formal, nonequilibrium thermodynamics approach as well as review extensions by Russel to incorporate results from mode-coupling theory to formally identify the dynamical arrest transitions in colloidal suspensions.