The Ageing and Rejuvenation of Soft, Glassy Complex Fluids

<p>Suspensions of multiarm star polymers are studied as models for soft colloidal interactionsin colloidal glasses. Establishing a pre-shearing protocol which ensures a reproducible initial state (the "rejuvenation" of the system), we report here the stress evolution from startup for two different concentrations for a range of shear rates using conventional rheological techniques. We show the existence of critical shear rateswhich are functions of the concentration. When the suspensions are sheared at rates below the critical rates, the stress rises to a common value which is also a function of the concentration. The system thus evolves into a yield stress-like fluid. This behavior manifests itself as an evolution from a monotonic, slightly shear-thinning flow curve to a flow curve dominated by a stress plateau. Complementary to the controlled-rate measurements, stress-controlled measurementsshow that for a stress below the critical stress, the rate at which strain is acquired drops several orders of magnitude, providing evidence of a lower branch of the flow curve. In stress-controlled ageing experiments, the material recovers an increasing fraction of the strain acquired under stress with waiting time upon cessation of the (less than critical) stress. The freshly rejuvenated suspension recovers a mere 2%of the acquired strain, while for a waiting time of 104 s the material recovers 97% of the acquired strain. The material thus appears to evolve from a nearly ideal fluid to a nearly ideal solid. We relate this bulk evolution to spatially and temporally resolved Rheo-NMR velocity profiles which clearly show an evolution to a strongly shear-banded state. The velocity of the suspension in the lower shear band is below the uncertainty of the experiment. The growth of the (assumed) zero-shear band is well described by a Gompertz relation. The effects of shear-rate, temperature and waiting time on the Gompertzparameters are investigated. Phenomenological understanding is provided through a scalar model that describes the stress-dependent free-energy landscape. Using a dual-minimum free-energy landscape, the model is able to replicate the behaviour of the stress after startup in shearratecontrolled experiments, the flow curve and the velocity profiles across the gap of a Couette geometry. The Large-Amplitude-Oscillatory-Shear (LAOS) response is reported along with discussions of current LAOS analysis techniques. The stress response to LAOS of the star suspensions is well described in a Cox-Merz manner by a modified Cross model. The modified Cross model highlights an asymmetry in the LAOS response. This constitutes the first ever report of asymmetric LAOS responses. The asymmetry is followed as a function of time using two complementary scalar variables. A speculativeinterpretation is given to account for the evolution of the asymmetry.</p>

The Ageing and Rejuvenation of Soft, Glassy Complex Fluids

<p>Suspensions of multiarm star polymers are studied as models for soft colloidal interactionsin colloidal glasses. Establishing a pre-shearing protocol which ensures a reproducible initial state (the "rejuvenation" of the system), we report here the stress evolution from startup for two different concentrations for a range of shear rates using conventional rheological techniques. We show the existence of critical shear rateswhich are functions of the concentration. When the suspensions are sheared at rates below the critical rates, the stress rises to a common value which is also a function of the concentration. The system thus evolves into a yield stress-like fluid. This behavior manifests itself as an evolution from a monotonic, slightly shear-thinning flow curve to a flow curve dominated by a stress plateau. Complementary to the controlled-rate measurements, stress-controlled measurementsshow that for a stress below the critical stress, the rate at which strain is acquired drops several orders of magnitude, providing evidence of a lower branch of the flow curve. In stress-controlled ageing experiments, the material recovers an increasing fraction of the strain acquired under stress with waiting time upon cessation of the (less than critical) stress. The freshly rejuvenated suspension recovers a mere 2%of the acquired strain, while for a waiting time of 104 s the material recovers 97% of the acquired strain. The material thus appears to evolve from a nearly ideal fluid to a nearly ideal solid. We relate this bulk evolution to spatially and temporally resolved Rheo-NMR velocity profiles which clearly show an evolution to a strongly shear-banded state. The velocity of the suspension in the lower shear band is below the uncertainty of the experiment. The growth of the (assumed) zero-shear band is well described by a Gompertz relation. The effects of shear-rate, temperature and waiting time on the Gompertzparameters are investigated. Phenomenological understanding is provided through a scalar model that describes the stress-dependent free-energy landscape. Using a dual-minimum free-energy landscape, the model is able to replicate the behaviour of the stress after startup in shearratecontrolled experiments, the flow curve and the velocity profiles across the gap of a Couette geometry. The Large-Amplitude-Oscillatory-Shear (LAOS) response is reported along with discussions of current LAOS analysis techniques. The stress response to LAOS of the star suspensions is well described in a Cox-Merz manner by a modified Cross model. The modified Cross model highlights an asymmetry in the LAOS response. This constitutes the first ever report of asymmetric LAOS responses. The asymmetry is followed as a function of time using two complementary scalar variables. A speculativeinterpretation is given to account for the evolution of the asymmetry.</p>

Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds

We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open curves we propose natural boundary conditions that respect the appropriate gradient flow structure. Based on suitable weak formulations we introduce finite element approximations using piecewise linear elements. For some of the schemes a stability result can be shown. The derived schemes can be employed in very different contexts. For example, we apply the schemes to the Angenent metric in order to numerically compute rotationally symmetric self-shrinkers for the mean curvature flow. Furthermore, we utilise the schemes to compute geodesics that are relevant for optimal interface profiles in multi-component phase field models.