Nonlinear rheology of dense colloidal dispersions: A phenomenological model and its connection to mode coupling theory

Rheology of colloidal and metallic glass formers

Colloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.

Shear-induced deconfinement of hard disks

Using Brownian dynamics simulations, we investigate the response to shear of a two-dimensional system of quasi-hard disks that are confined in the velocity gradient direction by a smooth external potential. Shearing the confined system leads to a homogenization of the one-body density profile. In order to rationalize this deconfinement effect, we split the internal one-body force field into adiabatic and superadiabatic contributions. We demonstrate that the superadiabatic force field consists of viscous and of structural contributions. We give an empirical scaling law that yields results for the superadiabatic force profiles both in the flow and in the gradient direction, in excellent agreement with the simulation data.

Multi-scale lattice Boltzmann and mode-coupling theory calculations of the flow of a glass-forming liquid

We present a hybrid-lattice Boltzmann (LB) algorithm for calculating the flow of glass-forming fluids that are governed by integral constitutive equations with pronounced nonlinear, non-Markovian dependence of the stresses on the flow history. The LB simulation for the macroscopic flow fields is combined with the mode-coupling theory (MCT) of the glass transition as a microscopic theory, in the framework of the integration-through transients formalism. Using the combined LB-MCT algorithm, pressure-driven planar channel flow is studied for a schematic MCT model neglecting spatial correlations in the microscopic dynamics. The cessation dynamics after removal of the driving pressure gradient shows strong signatures of oscillatory flow both in the macroscopic fields and the microscopic correlation functions.

Linear and nonlinear rheology of dense emulsions across the glass and the jamming regimes

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid.

Yield stresses and flow curves in metallic glass formers and granular systems

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.

Thermosensitive core-shell particles as model systems for studying the flow behavior of concentrated colloidal dispersions

We report on a comprehensive investigation of the flow behavior of colloidal thermosensitive core-shell particles at high densities. The particles consist of a solid core of poly(styrene) onto which a network of cross-linked poly(N-isopropylacrylamide) is affixed. Immersed in water the shell of these particles will swell if the temperature is low. Raising the temperature above 32 degrees C leads to a volume transition within this shell which leads to a marked shrinking of the shell. The particles have well-defined core-shell structure and a narrow size distribution. The remaining electrostatic interactions due to a small number of charges affixed to the core particles can be screened by adding 0.05M KCl to the suspensions. Below the lower critical solution temperature at 32 degrees C the particles are purely repulsive. Above this transition, a thermoreversible coagulation takes place. Lowering the temperature again leads to full dissociation of the aggregates formed by this process. The particles crystallize for effective volume fractions between 0.48 and 0.55. The crystallites can be molten by shear in order to reach a fluid sample again. The reduced shear stress measured in this metastable disordered state was found to be a unique function of the shear rate and the effective volume fraction. These reduced flow curves thus obtained can be described quantitatively by the theory of Fuchs and Cates [Phys. Rev. Lett. 89, 248304 (2002)] which is based on the mode-coupling theory of the glass transition.