Dynamics of short polymer chains in solution

We present numerical and analytical results describing the effect of hydrodynamic interactions on the dynamics of a short polymer chain in solution. A molecular dynamics algorithm for the polymer is coupled to a direct simulation Monte Carlo algorithm for the solvent. We give an explicit expression for the velocity autocorrelation function of the centre of mass of the polymer which agrees well with numerical results if Brownian dynamics, hydrodynamic correlations and sound wave scattering are included

Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology

For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together, leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and actions must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.Comment: Topical review, 31 pages, 10 figure

An optical fiber based interferometer to measure velocity profiles in sheared complex fluids

We describe an optical fiber based interferometer to measure velocity profiles in sheared complex fluids using Dynamic Light Scattering (DLS). After a review of the theoretical problem of DLS under shear, a detailed description of the setup is given. We outline the various experimental difficulties induced by refraction when using a Couette cell. We also show that homodyne DLS is not well suited to measure quantitative velocity profiles in narrow-gap Couette geometries. On the other hand, the heterodyne technique allows us to determine the velocity field inside the gap of a Couette cell. All the technical features of the setup, namely its spatial resolution ($\approx 50$--$100 \mu$m) and its temporal resolution ($\approx 1$ s per point, $\approx 1$ min per profile) are discussed, as well as the calibration procedure with a Newtonian fluid. As briefly shown on oil-in-water emulsions, such a setup permits one to record both velocity profiles and rheological data simultaneouslyComment: 13 pages, 16 figures, Submitted to Eur. Phys. J. A

Coexistence and Phase Separation in Sheared Complex Fluids

We demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken-symmetry order parameter (nematic, smectic, crystalline, etc.) are coupled to shear rate. Our construction relies on a selection criterion, the existence of a steady interface connecting two stable homogeneous states. We use the (generalized) Doi model of lyotropic nematic liquid crystals as a model system, but the method can be easily applied to other systems, provided non-local effects are included.Comment: 4 pages REVTEX, 5 figures using epsf macros. To appear in Physical Review E (Rapid Communications

High-frequency ultrasonic speckle velocimetry in sheared complex fluids

High-frequency ultrasonic pulses at 36 MHz are used to measure velocity profiles in a complex fluid sheared in the Couette geometry. Our technique is based on time-domain cross-correlation of ultrasonic speckle signals backscattered by the moving medium. Post-processing of acoustic data allows us to record a velocity profile in 0.02--2 s with a spatial resolution of 40 $\mu$m over 1 mm. After a careful calibration using a Newtonian suspension, the technique is applied to a sheared lyotropic lamellar phase seeded with polystyrene spheres of diameter 3--10 $\mu$m. Time-averaged velocity profiles reveal the existence of inhomogeneous flows, with both wall slip and shear bands, in the vicinity of a shear-induced ``layering'' transition. Slow transient regimes and/or temporal fluctuations can also be resolved and exhibit complex spatio-temporal flow behaviors with sometimes more than two shear bands.Comment: 15 pages, 18 figures, submitted to Eur. Phys. J. A

Linear and nonlinear rheology of wormlike micelles

Several surfactant molecules self-assemble in solution to form long, cylindrical, flexible wormlike micelles. These micelles can be entangled with each other leading to viscoelastic phases. The rheological properties of such phases are very interesting and have been the subject of a large number of experimental and theoretical studies in recent years. We shall report on our recent work on the macrorheology, microrheology and nonlinear flow behaviour of dilute aqueous solutions of a surfactant CTAT (Cetyltrimethylammonium Tosilate). This system forms elongated micelles and exhibits strong viscoelasticity at low concentrations ($\sim$ 0.9 wt%) without the addition of electrolytes. Microrheology measurements of $G(\omega)$ have been done using diffusing wave spectroscopy which will be compared with the conventional frequency sweep measurements done using a cone and plate rheometer. The second part of the paper deals with the nonlinear rheology where the measured shear stress $\sigma$ is a nonmonotonic function of the shear rate $\dot{\gamma}$. In stress-controlled experiments, the shear stress shows a plateau for $\dot{\gamma}$ larger than some critical strain rate, similar to the earlier reports on CPyCl/NaSal system. Cates et al have proposed that the plateau is a signature of mechanical instability in the form of shear bands. We have carried out extensive experiments under controlled strain rate conditions, to study the time-dependence of shear stress. The measured time series of shear stress has been analysed in terms of correlation integrals and Lyapunov exponents to show unambiguously that the behaviour is typical of low dimensional dynamical systems.Comment: 15 pages, 10 eps figure

Numerical investigation of heat retention and warm-up with thermal encapsulation of powertrain

Powertrain thermal encapsulation has the potential to improve fuel consumption and CO2 via heat retention. Heat retained within the powertrain after a period of engine-off, can increase the temperature of the next engine start hours after key-off. This in turn reduces inefficiencies associated with sub-optimal temperatures such as friction. The Ambient Temperature Correction Test was adopted in the current work which contains two World-wide harmonised Light duty Test Procedure (WLTP) cycles separated by a 9-hour soak period. A coupled 1D - 3D computational approach was used to capture heat retention characteristics and subsequent warm-up effects. A 1-D powertrain warm-up model was developed in GT-Suite to capture the thermal warm-up characteristics of the powertrain. The model included a temperature dependent friction model, the thermal-hydraulic characteristics of the cooling and lubrication circuits as well as parasitic losses associated with pumps. A 23°C WLTP cycle was run via the 1D model, key fluids and solids temperatures around the engine bay calculated at the end of the 1st WLTP cycle were then imported into a 3D heat retention model, in which the transient 3D computational fluid dynamics and heat transfer coupled simulation was initiated to model the full-geometry vehicle for a 9 hours static soak period. The cool-down behaviors of the coolant and oils were predicted from the 3D model and the temperatures at the end of the soak were fed back to the 1D warm-up model to carry out the second WLTP cycle simulation at 14°C ambient condition. A coupled 1D-3D heat retention modelling method predicted both warm-up and cooldown characteristics to within circa ±3 °C of vehicle test data over the entire ATCT test. The impact of thermal encapsulation was clearly shown, whereby coolant and oil temperatures at the end of the 9 hour soak period were 6°C and 10°C higher with encapsulation respectively, which led to a fuel consumption improvement in the order 1% over the post-soak 14°C WLTP through retaining heat

Vorticity Banding During the Lamellar-to-Onion Transition in a Lyotropic Surfactant Solution in Shear Flow

We report on the rheology of a lamellar lyotropic surfactant solution (SDS/dodecane/pentanol/water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low stress lamellar phase and the more viscous shear induced multi-lamellar vesicle, or ``onion'' phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.Comment: 10 pages, 10 figure

Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress \sigma is driven at a constant shear rate \dot\gamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(\sigma_1) and a linear decay at rate \lambda\sigma_2. Here \sigma_{1,2}(t) = \tau_{1,2}^{-1}\int_0^t\sigma(t')\exp[-(t-t')/\tau_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when \tau_2>\tau_1 and 0>R'(\sigma)>-\lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case \tau_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.Comment: Reference added; typos corrected. To appear in PRE Rap. Com

The Johnson-Segalman model with a diffusion term in Couette flow

We study the Johnson-Segalman (JS) model as a paradigm for some complex fluids which are observed to phase separate, or ``shear-band'' in flow. We analyze the behavior of this model in cylindrical Couette flow and demonstrate the history dependence inherent in the local JS model. We add a simple gradient term to the stress dynamics and demonstrate how this term breaks the degeneracy of the local model and prescribes a much smaller (discrete, rather than continuous) set of banded steady state solutions. We investigate some of the effects of the curvature of Couette flow on the observable steady state behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog