We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli [$G^{\prime }\left(\omega \right)$ and $G^{″}\left(\omega \right)$, respectively], from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise.

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.

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behavior and, for steady shear, gives rise to stress-mediated long-range interactions.

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalized Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers.

Microrheology is a branch of rheology having the same principles as conventional bulk rheology, but working on micron length scales and micro-litre volumes. Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining fluid viscosity. Conversely, when optical tweezers are used to measure the viscoelastic properties of complex fluids the results are either limited to the material's high-frequency response, discarding important information related to the low-frequency behavior, or they are supplemented by low-frequency measurements performed with different techniques, often without presenting an overlapping region of clear agreement between the sets of results. We present a simple experimental procedure to perform microrheological measurements over the widest frequency range possible with optical tweezers. A generalised Langevin equation is used to relate the frequency-dependent moduli of the complex fluid to the time-dependent trajectory of a probe particle as it flips between two optical traps that alternately switch on and off.