A Minimal Model for Vorticity and Gradient Banding in Complex Fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relations for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady-state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions.Comment: 11 pages, submitted to Eur Phys J

Dynamic Response of Block Copolymer Wormlike Micelles to Shear Flow

The linear and non-linear dynamic response to an oscillatory shear flow of giant wormlike micelles consisting of Pb-Peo block copolymers is studied by means of Fourier transform rheology. Experiments are performed in the vicinity of the isotropic-nematic phase transition concentration, where the location of isotropic-nematic phase transition lines is determined independently. Strong shear-thinning behaviour is observed due to critical slowing down of orientational diffusion as a result of the vicinity of the isotropic- nematic spinodal. This severe shear-thinning behaviour is shown to result in gradient shear banding. Time-resolved Small angle neutron scattering experiments are used to obtain insight in the microscopic phenomena that underly the observed rheological response. An equation of motion for the order-parameter tensor and an expression of the stress tensor in terms of the order-parameter tensor are used to interpret the experimental data, both in the linear and non-linear regime. Scaling of the dynamic behaviour of the orientational order parameter and the stress is found when critical slowing down due to the vicinity of the isotropic-nematic spinodal is accounted for.Comment: Accepted by J. Phys.: Condens. Matter, CODEF II Special Issue. 20 pages, 9 figure

Dynamic Response of Block Copolymer Wormlike Micelles to Shear Flow

The linear and non-linear dynamic response to an oscillatory shear flow of giant wormlike micelles consisting of Pb-Peo block copolymers is studied by means of Fourier transform rheology. Experiments are performed in the vicinity of the isotropic-nematic phase transition concentration, where the location of isotropic-nematic phase transition lines is determined independently. Strong shear-thinning behaviour is observed due to critical slowing down of orientational diffusion as a result of the vicinity of the isotropic- nematic spinodal. This severe shear-thinning behaviour is shown to result in gradient shear banding. Time-resolved Small angle neutron scattering experiments are used to obtain insight in the microscopic phenomena that underly the observed rheological response. An equation of motion for the order-parameter tensor and an expression of the stress tensor in terms of the order-parameter tensor are used to interpret the experimental data, both in the linear and non-linear regime. Scaling of the dynamic behaviour of the orientational order parameter and the stress is found when critical slowing down due to the vicinity of the isotropic-nematic spinodal is accounted for.Comment: Accepted by J. Phys.: Condens. Matter, CODEF II Special Issue. 20 pages, 9 figure

Stress response and structural transitions in sheared gyroidal and lamellar amphiphilic mesophases: lattice-Boltzmann simulations

We report on the stress response of gyroidal and lamellar amphiphilic mesophases to steady shear simulated using a bottom-up lattice-Boltzmann model for amphiphilic fluids and sliding periodic (Lees-Edwards) boundary conditions. We study the gyroid per se (above the sponge-gyroid transition, of high crystallinity) and the molten gyroid (within such a transition, of shorter-range order). We find that both mesophases exhibit shear-thinning, more pronounced and at lower strain rates for the molten gyroid. At late times after the onset of shear, the skeleton of the crystalline gyroid becomes a structure of interconnected irregular tubes and toroidal rings, mostly oriented along the velocity ramp imposed by the shear, in contradistinction with free-energy Langevin-diffusion studies which yield a much simpler structure of disentangled tubes. We also compare the shear stress and deformation of lamellar mesophases with and without amphiphile when subjected to the same shear flow applied normal to the lamellae. We find that the presence of amphiphile allows (a) the shear stress at late times to be higher than in the case without amphiphile, and (b) the formation of rich patterns on the sheared interface, characterised by alternating regions of high and low curvature.Comment: 15 pages, 10 figures, Physical Review E, in pres

Generality of shear thickening in suspensions

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response.Comment: 11 pages, 9 figures, accepted for publication in Nature Material

Glass transitions and shear thickening suspension rheology

We introduce a class of simple models for shear thickening and/ or `jamming' in colloidal suspensions. These are based on schematic mode coupling theory (MCT) of the glass transition, having a memory term that depends on a density variable, and on both the shear stress and the shear rate. (Tensorial aspects of the rheology, such as normal stresses, are ignored for simplicity.) We calculate steady-state flow curves and correlation functions. Depending on model parameters, we find a range of rheological behaviours, including `S-shaped' flow curves, indicating discontinuous shear thickening, and stress-induced transitions from a fluid to a nonergodic (jammed) state, showing zero flow rate in an interval of applied stress. The shear thickening and jamming scenarios that we explore appear broadly consistent with experiments on dense colloids close to the glass transition, despite the fact that we ignore hydrodynamic interactions. In particular, the jamming transition we propose is conceptually quite different from various hydrodynamic mechanisms of shear thickening in the literature, although the latter might remain pertinent at lower colloid densities. Our jammed state is a stress-induced glass, but its nonergodicity transitions have an analytical structure distinct from that of the conventional MCT glass transition.Comment: 33 pages; 19 figure