In recent years optical tracer techniques have been developed to determine the micro-rheology of soft viscoelastic materials. Recent theoretical arguments (Levine A J and Lubensky T C 2001 Phys. Rev. E 65 011501) suggest that the correlated fluctuations of a pair of widely separated probe particles should reflect the bulk rheology of the medium that they are embedded in more accurately than the motion of a single particle. We present a experimental test of these arguments. Using optical tweezers techniques (Henderson S, Mitchell S and Bartlett P 2002 Phys. Rev. Lett. 88 088302), we measure at high spatial and temporal resolution the thermal motion of a pair of colloidal particles suspended in a semi-dilute viscoelastic solution of non-adsorbing polystyrene in decalin. From the measured particle trajectories we determine both the one- and two-particle correlations and extract the local and bulk rheology. A comparison of the two measurements shows significant differences which are interpreted in terms of the depletion of polymer molecules from the particle surface.

We present an extension of the two-point optical microrheology technique introduced by Crocker et al. [J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh and D. A.Weitz, Phys. Rev. Lett., 2000, 85, 888] to high frequencies. The correlated fluctuations of two probe spheres held by a pair of optical tweezers within a viscoelastic medium are determined using optical interferometry. A theoretical model is developed to yield the frequency-dependent one- and two-particle response functions from the correlated motion. We demonstrate the validity of this method by determining the one- and two-particle correlations in a semi-dilute solution of polystyrene in decalin. We find that the ratio of the one- and two-particle response functions is anomalous which we interpret as evidence for a slip boundary condition caused by depletion of polymer from the surface of the particle.

Following a quench, colloidal systems with strong, short-ranged, attractive interactions can exhibit transient gelation, instead of the classical phase-ordering mechanisms of spinodal decomposition or nucleation. The particles aggregate into a tenuous, system-spanning network, which, for a time, remains robust to mechanical disturbance. Eventually, the network's ability to recover from destructive deformations becomes compromised, and the gel collapses. A detailed experimental study of gel collapse was reported in the preceding, companion article, leaving several open questions regarding the processes involved. We present a theoretical investigation into the factors affecting a gel's lifetime, concentrating in particular on the surprising influence of the size and shape of the container. We construct a model in which solvent dynamics are replaced by a dissipative coupling of the particulate network to a fixed frame and show that, in the absence of zero-frequency elasticity, such a coupling results in a novel class of matter in which stresses cannot propagate beyond a finite distance. We find our prediction of the characteristic length to be in quantitative agreement with the experimental data, and show how its ratio to the dimensions of the container controls the sedimentation. We discuss some aspects of the ageing mechanism, and suggest that a sudden collapse is ultimately due to erosion with positive feedback.

Transient gelation in colloid-polymer mixtures is an interesting but poorly understood non-equilibrium phenomenon which has recently attracted the attention of experiment and theory. In a transient gel the particles aggregate, by the depletion interaction, to form a space-spanning network which maintains its structural integrity for a finite period before suddenly collapsing. In this paper we present a study of the collapse process which provides new information on the way in which transient gels collapse. We have studied gel collapse in three ways. Firstly, we have observed the gel throughout its lifetime using dark-field optics and time-lapsed video recording. In a second experiment we have measured the concentration of gels throughout their entire height before, during and after collapse. This was performed using a non-intrusive ultrasonic technique which measures the speed of sound in the suspension. Finally, we have studied the effect of varying sample height and width on the lifetime of a gel. Our observations provide new information on the collapse process and have important implications for the formulation of a theoretical model. In discussing the effects of height and width we refer to the following companion paper which describes this particular effect.

The addition of enough non-adsorbing polymer to a hard-sphere suspension causes the particles to aggregate to form a space-filling gel. The integrity of the gel persists for a finite period of time, and then the space-filling structure collapses suddenly to form a denser sediment. This phenomenon of 'delayed sedimentation' is ubiquitous in many weakly-flocculated suspensions. In this work, we observe the processes occurring in the bulk of a colloid-polymer gel using dark-field imaging, and probe the arrangement and dynamics of the particles in the system using two-colour dynamic light scattering. The effect of shear is also studied. A number of physical mechanisms relevant to a comprehensive explanation of delayed sedimentation are proposed and discussed.