Non-uniform flow of colloidal glasses and gels: The “shear-gradient concentration coupling instability”

There are several types of shear-induced instabilities in soft-matter systems, like vorticity- and gradient-banding, that are by now well-understood. There is, however, an instability that can be referred to as “the Shear-gradient Concentration Coupling instability” (the SCC-instability) that has been largely ignored due to the lack of understanding of its microscopic origin, since its phenomenological description a few decades ago. This instability is due to a postulated shear-gradient induced mass flux together with a strong coupling of the stress to concentration. The origin of the shear-induced mass flux resulting from direct interactions is so far not understood, and explicit expressions for the corresponding transport coefficient have therefore not been derived. In this presentation, the origin of this mass flux is discussed, an explicit expression for the transport coefficient is presented, and numerical results are discussed for the stationary non-uniform flow profiles and concentration profiles of an initially SCC-unstable system, which will be compared to experiments on hard-sphere glasses H. Jin, K. Kang, A.K. Hyun, J.K.G. Dhont, Soft Matter 10 (2014) 9470

Temperature-induced migration of electro-neutral interacting colloidal particles

Migration of colloidal particles induced by temperature gradients is commonly referred to as thermodiffusion, thermal diffusion, or the (Ludwig-)Soret effect. The thermophoretic force experienced by a colloidal particle that drives thermodiffusion consists of two distinct contributions: a contribution resulting from internal degrees of freedom of single colloidal particles, and a contribution due to the interactions between the colloids. We present an irreversible thermodynamics based theory for the latter collective contribution to the thermophoretic force. The present theory leads to a novel “thermophoretic interaction force” (for uncharged colloids), which has not been identified in earlier approaches. In addition, an N-particle Smoluchowski equation including temperature gradients is proposed, which complies with the irreversible thermodynamics approach.A comparison with experiments on colloids with a temperature dependent attractive interaction potential over a large concentration and temperature range is presented. The comparison shows that the novel thermophoretic interaction force is essential to describe data on the Soret coefficient and the thermodiffusion coefficient

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Electric-field-induced polarization of the layer of condensed ions on cylindrical colloids

In concentrated suspensions of charged colloids, interactions between colloids can be induced by an external electric field through the polarization of charge distributions (within the diffusive double layer and the layer of condensed ions) and/or electro-osmotic flow. In case of rod-like colloids, these field-induced inter-colloidal interactions have recently been shown to lead to anomalous orientation perpendicular to the external field, and to phase/state transitions and dynamical states, depending on the field amplitude and frequency of the external field. As a first step towards a (semi-) quantitative understanding of these phenomena, we present a linear-response analysis of the frequency-dependent polarization of the layer of condensed ions on a single, long and thin cylindrical colloid. The in-phase and out-phase response functions for the charge distribution and the electric potential are calculated for arbitrary orientation of the cylindrical colloid. The frequency-dependent degree of alignment, which is proportional to the electric-field-induced birefringence, is calculated as well, and compared to experiments on dilute fd virus suspensions

A constitutive relation describing the shear-banding transition

An additional contribution to the standard expression for the shear stress must be considered in order to describe shear banding. A possible extension of the standard constitutive relation is proposed. Its physical, purely hydrodynamic origin is discussed. The corresponding Navier-Stokes equation is analyzed for the two-plate geometry, where flow gradients are assumed to exist only in the direction perpendicular to the two plates. The linearized Navier-Stokes equation is shown to be very similar to the Cahn-Hilliard equation for spinodal decomposition, with a similar term that stabilizes rapid spatial variations. Only slowly varying flow gradients are unstable. Just as in the initial stage of spinodal decomposition there is a most rapidly growing wavelength in the initial stage of the shear-banding transition, leading to a predictable number of shear bands. A modified Maxwell equal area construction is derived, which dictates the stress and the shear rates in the bands under controlled shear conditions, and which shows that under controlled stress conditions no true shear bands can coexist. The kinetics of the shear-banding transition is studied numerically. For the two-plate geometry it is found that there exist multiple stationary states under controlled shear conditions, depending on the initial state of the flow profile. Shear banding occurs not only when the system is initially unstable, but can also be induced outside the unstable region when the amplitude of the initial perturbation is large enough. The shear-banding transition can thus proceed via “spinodal demixing” (from an unstable initial state) or via “condensation.” Under controlled stress conditions no stationary state is found. Here, coupling with flow gradients extending in other directions, not perpendicular to the two plates, should probably be taken into account