Non-Gaussian Diffusion Near Surfaces.

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

Numerical simulations of confined Brownian-yet-non-Gaussian motion.

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.

Nonequilibrium Dynamics Induced by Scattering Forces for Optically Trapped Nanoparticles in Strongly Inertial Regimes.

The forces acting on optically trapped particles are commonly assumed to be conservative. Nonconservative scattering forces induce toroidal currents in overdamped liquid environments, with negligible effects on position fluctuations. However, their impact in the underdamped regime remains unexplored. Here, we study the effect of nonconservative scattering forces on the underdamped nonlinear dynamics of trapped nanoparticles at various air pressures. These forces induce significant low-frequency position fluctuations along the optical axis and the emergence of toroidal currents in both position and velocity variables. Our experimental and theoretical results provide fundamental insights into the functioning of optical tweezers and a means for investigating nonequilibrium steady states induced by nonconservative forces.

Drop formation in non-Newtonian fluids.

We study the pinch-off dynamics of droplets of yield stress and shear thinning fluids. To separate the two non-Newtonian effects, we use a yield stress material for which the yield stress can be tuned without changing the shear thinning behavior, and a shear thinning system (without a yield stress) for which the shear thinning can be controlled over a large range, without introducing too much elasticity into the system. We find that the pinch-off remains very similar to that of constant viscosity Newtonian liquids, and consequently thinning in shear flow does not imply a thinning in elongational flow.

Role of nonconservative scattering forces and damping on Brownian particles in optical traps.

We consider a model of a particle trapped in a harmonic optical trap but with the addition of a nonconservative radiation induced force. This model is known to correctly describe experimentally observed trapped particle statistics for a wide range of physical parameters, such as temperature and pressure. We theoretically analyze the effect of nonconservative force on the underlying steady state distribution as well as the power spectrum for the particle position. We compute perturbatively the probability distribution of the resulting nonequilibrium steady states for all dynamical regimes underdamped through to overdamped and give expressions for the associated currents in phase space (position and velocity). We also give the spectral density of the trapped particle's position in all dynamical regimes and for any value of the nonconservative force. Signatures of the presence of nonconservative forces are shown to be particularly strong for the underdamped regime at low frequencies.

Sedimentation of granular columns in the viscous and weakly inertial regimes.

We investigate the dynamics of granular columns of point particles that interact via long-range hydrodynamic interactions and fall under the action of gravity. We investigate the influence of inertia using the Green's function for the Oseen equation. The initial conditions (density and aspect ratio) are systematically varied. Our results suggest that universal self-similar laws may be sufficient to characterize the temporal and structural evolution of the granular columns. A characteristic time above which an instability is triggered (which may enable the formation of clusters) is also retrieved and discussed.

Capillarylike fluctuations at the interface of falling granular jets.

We study the interface fluctuations of a granular jet falling under gravity and show that for small scales they are the analog of the thermally induced capillary waves. Experimental results from radial height and velocity fluctuations, static correlation functions and capillary ripple velocities allow us to estimate a granular surface tension. The ultralow interfacial tensions measured (of the order of 100 microN/m) can be rationalized using a simple model.