Projekte

We discuss pressure-driven channel flow for a model of shear-thinning glass-forming fluids, employing a modified lattice-Boltzmann (LB) simulation scheme. The model is motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions and captures a nonvanishing dynamical yield stress and the appearance of normal-stress differences and a flow-induced pressure contribution. The standard LB algorithm is extended to deal with tensorial, nonlinear constitutive equations of this class. The new LB scheme is tested in 2D pressure-driven channel flow and reproduces the analytical steady-state solution. The transient dynamics after startup and removal of the pressure gradient reproduce a finite stopping time for the cessation flow of yield-stress fluids in agreement with previous analytical estimates.

We present results from microscopic mode coupling theory generalized to colloidal dispersions under shear in an integration-through-transients formalism. Stress-strain curves in start-up shear, flow curves, and normal stresses are calculated with the equilibrium static structure factor as only input. Hard spheres close to their glass transition are considered, as are hard spheres with a short-ranged square-well attraction at their attraction dominated glass transition. The consequences of steric packing and physical bond formation on the linear elastic response, the stress release during yielding, and the steady plastic flow are discussed and compared to experimental data from concentrated model dispersions.

The stress vs strain curves in dense colloidal dispersions under start-up shear flow are investigated combining experiments on model core-shell microgels, computer simulations of hard disk mixtures, and mode coupling theory. In dense fluid and glassy states, the transient stresses exhibit first a linear increase with the accumulated strain, then a maximum (stress overshoot) for strain values around 5%, before finally approaching the stationary value, which makes up the flow curve. These phenomena arise in well-equilibrated systems and for homogeneous flows, indicating that they are generic phenomena of the shear-driven transient structural relaxation. Microscopic mode coupling theory (generalized to flowing states by integration through the transients) derives them from the transient stress correlations, which first exhibit a plateau (corresponding to the solid-like elastic shear modulus) at intermediate times, and then negative stress correlations during the final decay. We introduce and validate a schematic model within mode coupling theory which captures all of these phenomena and handily can be used to jointly analyze linear and large-amplitude moduli, flow curves, and stress-strain curves. This is done by introducing a new strain- and time-dependent vertex into the relation between the generalized shear modulus and the transient density correlator.

Mode coupling theory (MCT) has had notable successes in addressing the rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such as star-polymers. Here, we explore the properties of a recently developed MCT-based schematic constitutive equation under idealized experimental protocols involving single and then double step strains. We find strong deviations from expectations based on factorable, BKZ-type constitutive models. Specifically, a nonvanishing stress remains long after the application of two equal and opposite step strains; this residual stress is a signature of plastic deformation. We also discuss the distinction between hypothetically instantaneous step strains and fast ramps. These are not generally equivalent in our MCT approach, with the latter more likely to capture the physics of experimental ‘step’ strains. The distinction points to the different role played by reversible anelastic, and irreversible plastic rearrangements.

We discuss the concept of a glass-transition line in the temperature-shear-stress plane in the context of recent simulation data for a metallic melt and dense-packed granular systems. Analyzing these data within a schematic model of the mode-coupling theory for dense glass formers under shear, values for the critical dynamic yield stress (the stress resulting in the limit of arbitrarily slow shear, at the glass transition) are estimated. We discuss two possible scenarios, that of a continuous rise in the dynamic yield stress at the transition, and that of a discontinuous transition, and discuss the data range that needs to be covered to decide between the two cases. A connection is made to the two commonly drawn versions of the jamming diagram, one convex and one concave regarding to the shape of the solid region.