Nonlinear microrheology of dense colloidal suspensions: A mode-coupling theory

摘要

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension isnpresented. Starting point is the Smoluchowski equation forN bath and a single probe particle. The probe performsnBrownian motion under the influence of a strong constant and uniform external force Fex. It is immersed in a densenhomogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered;nsolvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode couplingnapproximations are performed and an integration through transients approach applied. A microscopic theory fornthe nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe inna glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motionnand describes active microrheology experiments. A force threshold is identified which needs to be overcome tonpull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for thenthreshold force and the probability density of the localized probe are solved numerically. Neglecting the spatialnstructure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transitionnand the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss itsnphase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The modelnwas successfully applied to simulations and experiments on colloidal hard sphere systems [Gazuz et al., Phys.nRev. Lett. 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.