Oscillatory shear tests are widely used in rheology to characterize the linear and non-linear mechanical response of complex fluids, including the yielding transition. There is an increasing urge to acquire...

The simultaneous presence of normal (Brownian) diffusion and non-Gaussian statistics of particle displacements has been identified as a recurring motif for a broad spectrum of physical and biological systems. While not yet fully understood, it is generally accepted that a key ingredient for observing this Brownian yet non-Gaussian (BNG) diffusion is that the environment hosting the particles appears stationary and homogenous on the small length and time scales, while displaying significant fluctuations on larger distances and/or longer time scales. To date, most of the experimental studies on systems displaying BNG diffusion have been performed in direct space, usually via a combination of optical microscopy and particle tracking to quantify the particle’s self-diffusion. Here, we demonstrate that a reciprocal space analysis of the density fluctuations caused by the particle motion as a function of the wave vector enables the investigation of BNG diffusion in situations where single-particle tracking is impossible. To accomplish this aim, we use confocal differential dynamic microscopy (ConDDM) to study the BNG dynamics of diluted sub-resolution tracers diffusing in a glassy matrix of larger hard spheres. We first elucidate the nontrivial connection between the tracer self-diffusion and collective relaxation of the resulting density fluctuations. We find that the experimentally determined intermediate scattering functions are in excellent agreement with the recent predictions of a “diffusing diffusivity” model of BNG diffusion, whose analytical predictions are available only in reciprocal space. Our results show that studying BNG diffusion in reciprocal space can be an invaluable strategy to access the fast, anomalous dynamics occurring at very small scales in crowded environments.

Direct observation of the microscopic material structure and dynamics during rheological shear tests is the goal of rheo-microscopy experiments. Microscopically, they shed light on the many mechanisms and processes that determine the mechanical properties at the macroscopic scale. Moreover, they permit for the determination of the actual deformation field, which is particularly relevant to assess shear banding or wall slip. While microscopic observation of the sample during mechanical probing is achieved by a variety of custom and commercial instruments, the possibility of performing quantitative rheology is not commonly available. Here, we describe a flexible rheo-microscopy setup that is built around a parallel-sliding-plate, stress-controlled shear cell, optimized to be mounted horizontally on a commercial microscope. Mechanically, soft materials with moduli ranging from few tens of Pa up to tens of kPa can be subjected to a variety of waveforms, ranging from standard step stress and oscillatory stress to more peculiar signals, such as triangular waves or any other signal of interest. Optically, the shear cell is designed to be compatible with different imaging methods (e.g. bright field or confocal microscopy). Most of the components of the shear cell are commercially available, and those that are not can be reproduced by a standard machine shop, easing the implementation of the rheo-microscopy setup in interested laboratories.