Theory of Microstructure and Rheology of Nonequilibrium Colloidal Dispersions: Shear Flow and Active Microrheology

A theory based on the Smoluchowski equation has been developed to predict the non-equilibrium microstructure and rheology of hard sphere colloidal suspensions as a function of Peclet number, Pe (ratio of shear to Brownian motion) and solid volume fraction.  The theory is based on the observation that particles near contact are the controlling configuration in concentrated sheared suspensions, allowing use of pair-wise additive interactions.  The pair distribution function, g(r), is determined from an integro-differential equation solved by iterative numerical methods.  The focus of the discussion will be on the structure and rheology determined in simple shear flow, but extensional and rotational kinematics will also be considered.   The prediced rheology is developed through use of g(r) and well-known hydrodynamic functions for pairs of particles, with good agreement with Stokesian Dynamics simulation for 0.1<Pe<100.  The developed theoretical framework is extended to predict structure in active microrheology, i.e. when a single probe particle is subjected to a constant external force. A comparison of experimental and simulation results to the theory is provided.