Gradient and vorticity banding

"Banded structures" of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the gradient or vorticity direction, the banding transition is referred to as "gradient banding" or "vorticity banding," respectively. The main features of gradient banding can be understood on the basis of a relatively simple constitutive equation. This minimal model for gradient banding will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient banding is sometimes also observed in glassy- and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient banding can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity banding is less well understood and less extensively investigated experimentally as compared to gradient banding. Possible scenarios that are at the origin of vorticity banding will be discussed. Among other systems, the observed vorticity-banding transition in rod-like colloids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain vorticity banding in discontinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Comment: 95 pages, 48 figure

Local Interfacial Migration of Clay Particles within an Oil Droplet in an Aqueous Environment

We discuss the interfacial migration due to Marangoni forces of clay particles within an oil droplet that is immersed in water, which is relevant for the formation kinetics of Pickering emulsions. Hydrophilic (MMT) and hydrophobic (OMT) clays are studied, where the hydrophilic clay particles adsorb in the oil–water interface, contrary to the hydrophobic clays. The feasibility of an “image–time correlation technique” is discussed, in order to probe the local interfacial migration velocities of clay particles in the oil droplet. Here, correlation functions are constructed from time-resolved images, in order to quantify the local migration of clay particles. Correlation functions are measured at different waiting times, that is, the time after formation of the droplet. The initial decay rate and the baseline of these correlation functions depend on the waiting time in a qualitatively different way for the two clays, which is attributed to the different interfacial migration behavior for the hydrophilic, adsorbing clays and the nonadsorbing, hydrophobic clays as a result of the Marangoni effect

Viscoelasticity of suspensions of long, rigid rods

A microscopic theory for the viscoelastic behaviour of suspensions of rigid rods with excluded volume interactions is presented, which is valid in the asymptotic limit of very long and thin rods. Stresses arising from translational and rotational Brownian motion and direct interactions are calculated for concentrations up to (L/D) (with L the length; D, the thickness of the rods; and their volume fraction). It is argued that for very long and thin rods, contributions to the stress arising from hydrodynamic interactions vanish asymptotically with increasing aspect ratio relative to the single particle contribution. As will be discussed, this is supported by calculations of Shaqfeh and Fredrickson (Phys. Fluids A2 (1990) 7), although convergence to negligible hydrodynamics interactions with increasing aspect ratio is very slow (for aspect ratios larger than ≈50, the contribution of hydrodynamic interactions to the stress is at most ≈20%). It is argued that the pair-correlation function is in good approximation given by the Boltzmann exponential of the pair-interaction potential. The neglect of hydrodynamic interactions and the use of the Boltzmann exponential approximation for the pair-correlation function allows the microscopic evaluation of stresses in terms of concentration and the orientation order parameter tensor to within a Ginzburg–Landau expansion up to third order, without having to resort to thermodynamic arguments. The orientational order parameter tensor in turn is obtained from an equation of motion that is derived from the N-particle Smoluchowski equation. The resulting expression for the stress tensor and the equation of motion are similar to, but also in some respects significantly differing from, the well known theory due to Doi, Edward and Kuzuu. Analytic expressions are derived for linear and leading order non-linear, viscoelastic response functions. It is found that the zero shear viscosity varies linearly in concentration. The Huggins coefficient vanishes like the square of the shear-rate. Such a linear concentration dependence of the zero shear viscosity for very long and thin rods is also found in simulations by Claeys and Brady (J. Fluid Mech. 251 (1993) 443) and Yamane et al. (J. Non-Newtonian Fluid Mech. 54 (1994) 405) for the long rods, but is in contradiction with the Berry–Russel theory (J. Fluid Mech. 180 (1987) 475), where interactions are treated in an approximate, orientationally pre-averaged fashion. In addition, we find a Maxwellian frequency dependence of response functions at zero shear-rate. Highly non-linear viscoelastic response functions at higher shear-rates are computed numerically. Among other things, we find normal stress differences that do not change sign as a function of shear-rate and higher order harmonic response functions that are qualitatively different for the paranematic and nematic states

Nonuniform flow in soft glasses of colloidal rods

Despite our reasonably advanced understanding of the dynamics and flow of glasses made of spherical colloids, the role of shape, i.e., the respective behavior of glasses formed by rodlike, particles is virtually unexplored. Recently, long, thin and highly charged rods (fd-virus particles) were found to vitrify in aqueous suspensions at low ionic strength [Phys. Rev. Lett. 110, 015901 (2013)]. The glass transition of these long-ranged repulsive rods occurs at a concentration far above the isotropic-nematic coexistence region and is characterized by the unique arrest of both the dynamics of domains that constitute the chiral-nematic orientational texture, as well as individual rods inside the domains. Hence, two relevant length scales exist: the domain size of a few hundreds of microns, and the rod-cage size of a few microns, inside the domains. We show that the unique dual dynamic arrest and the existing of two widely separated length scales imparts an unprecedented, highly heterogeneous flow behavior with three distinct signatures. Beyond a weak stress plateau at very small shear rates that characterizes the glass, the kinetic arrest of the domain dynamics gives rise to internal fracture, as a result of domain-domain interactions, as well as wall partial slip. It is shown that, on increasing the shear rate, the fractured plug flow changes to a shear-banded flow profile due to the stress response of the kinetically arrested aligned rods within the domains. Shear-gradient banding occurs due to the strong thinning of the uniform chiral-nematic phase within the domains, i.e., complying with the classic shear-banding scenario, giving rise to a stress plateau in the flow curve. Finally, a linear (uniform) velocity profile is found at the highest shear rates. Vorticity banding is also observed at intermediate and high shear rates. These results point to the crucial role of particle shape in tailoring the flow properties of dense colloidal suspensions. Moreover, they strongly support the argument that the origin of shear banding in soft-particle glasses with long-ranged repulsive interactions is fundamentally different from that of hard-particle glasses with short-ranged repulsive interactions