No Arabic abstract
A Molecular Dynamics approach has been used to compute the shear force resulting from the shearing of disks. Two-dimensional monodisperse disks have been put in an horizontal and rectangular shearing cell with periodic boundary conditions on right and left hand sides. The shear is applied by pulling the cover of the cell either at a constant rate or by pulling a spring, linked to the cover, with a constant force. Depending on the rate of shearing and on the elasticity of the whole set up, we showed that the measured shear force signal is either irregular in time, regular in time but not in shape, or regular in shape.
We provide a quantitative analysis of all kinds of topological defects present in 2D passive and active repulsive disk systems. We show that the passage from the solid to the hexatic is driven by the unbinding of dislocations. Instead, although we see dissociation of disclinations as soon as the liquid phase appears, extended clusters of defects largely dominate below the solid-hexatic critical line. The latter percolate at the hexatic-liquid transition in continuous cases or within the coexistence region in discontinuous ones, and their form gets more ramified for increasing activity.
We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.
The effect of excluded volume interactions on the structure of a polymer in shear flow is investigated by Brownian Dynamics simulations for chains with size $30leq Nleq 300$. The main results concern the structure factor $S({bf q})$ of chains of N=300 Kuhn segments, observed at a reduced shear rate $beta=dot{gamma}tau=3.2$, where $dot{gamma}$ is the bare shear rate and $tau$ is the longest relaxation time of the chain. At low q, where anisotropic global deformation is probed, the chain form factor is shown to match the form factor of the continuous Rouse model under shear at the same reduced shear rate, computed here for the first time in a wide range of wave vectors. At high q, the chain structure factor evolves towards the isotropic equilibrium power law $q^{-1/ u}$ typical of self-avoiding walk statistics. The matching between excluded volume and ideal chains at small q, and the excluded volume power law behavior at large q are observed for ${bf q}$ orthogonal to the main elongation axis but not yet for ${bf q}$ along the elongation direction itself, as a result of interferences with finite extensibility effects. Our simulations support the existence of anisotropic shear blobs for polymers in good solvent under shear flow for $beta>1$ provided chains are sufficiently long.
Steady-state pair correlations between inelastic granular beads in a vertically shaken, quasi two-dimensional cell can be mapped onto the particle correlations in a truly two-dimensional reference fluid in thermodynamic equilibrium. Using Granular Dynamics simulations and Iterative Ornstein--Zernike Inversion, we demonstrate that this mapping applies in a wide range of particle packing fractions and restitution coefficients, and that the conservative reference particle interactions are simpler than it has been reported earlier. The effective potential appears to be a smooth, concave function of the particle distance $r$. At low packing fraction, the shape of the effective potential is compatible with a one-parametric fit function proportional to $r^{-2}$.
We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two-dimensions, and the deposition front, or growth line, varies spatio-temporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang (KPZ) universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by KPZ fluctuations in the presence of quenched disorder.