Volume 56, Issue 6, November 2012
Index of content:
56(2012); http://dx.doi.org/10.1122/1.4739067View Description Hide Description
One of the challenges in the study of cocontinuous blends is to relate their rheological behavior with their morphology. This is due to the inherent instability of cocontinuous structures. We have studied the morphological and rheological time evolution of cocontinuous blends with different interfacial tension and viscosity ratio during annealing. In general, the presence of an interface generates an extra contribution to the elastic modulus,. We have found that both the initial value of and its rate of evolution during coarsening are proportional to the ratio between interfacial tension and blend viscosity. We have related time evolution of the elastic modulus to that of the interfacial area via a simplification of Doi–Ohta model for the case of small amplitude oscillatory shear flow. This simplification is based on the experimental evidence that the degree of anisotropy generated during small amplitude oscillations is negligible [López-Barrón and Macosko, Langmuir 26, 14284–14293 (2010b)]. The simplification gives a linear relation between the characteristic size and time and an asymptotic decrease of the elastic modulus with a limit behavior at long times: . This behavior was observed on blends with low interfacial tension. However, blends with high interfacial tension underwent a transition toward a decrease in the rate of coarsening, which is accompanied by a slower decrease of the elastic modulus. Doi–Ohta model is not sensitive to this transition and fails in predicting the time evolution of the characteristic length and elasticity of high interfacial tension blends.
Numerical description of elastic flow instability and its dependence on liquid viscoelasticity in planar contraction56(2012); http://dx.doi.org/10.1122/1.4739926View Description Hide Description
In the finite element framework, we employ decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow and then investigate highly nonlinear behavior in 2D creeping contraction flow. In the analysis of steady solutions as a preliminary study, the results are shown to be free from frustrating mesh dependence when we incorporate the tensor-logarithmic formulation [Fattal and Kupferman, J. Non-Newtonian Fluid Mech. 123, 281–285 (2004)]. Two kinds of elastic fluid have been chosen, that is, highly shear thinning and Boger-type liquids. According to each liquid property, the transient computational modeling has revealed qualitatively distinct dynamics of instability. With pressure difference imposed slightly below the steady convergence limit, the numerical scheme demonstrates fluctuating solution without approaching steady state for the shear thinning fluid. When the pressure fairly higher than the limit is enforced, severe fluctuation of flowrate, oscillation of corner vortices, and also asymmetric irregular stress wave propagation along the downstream channel wall are expressed. In addition, flowdynamics seems quite stochastic with scanty temporal correlation. For the Boger-type fluid, under the traction higher than steady limit, the flowrate and corner vortices exhibit periodic variation with asymmetry added to the dynamics. These express elasticflow instability in this inertialess flow approximation.
56(2012); http://dx.doi.org/10.1122/1.4739066View Description Hide Description
The average length of threadlike micelles in a semidilute solution has been inferred from the ratio of loss to storage modulus at a local minimum in loss modulus, which occurs at frequencies well above terminal. This method has yielded average micelle lengths of less than 1 μm or so for cetyltrimethylammonium surfactants at concentrations of around 0.1 to 1 M [Khatory et al., Langmuir 9, 1456–1464 (1993)]. Here, I use established correlations for polymer semidilute solutions to show that this estimate of micelle length is likely too small by around an order of magnitude. More accurate estimates can be obtained from the terminal relaxation time and the viscosity near the cross-over from dilute to semidilute, which show typical micelle average lengths that are well above 1 μm in length, for cetyltrimethylammonium solutions.
The investigation on the nonlinearity of plasticine-like magnetorheological material under oscillatory shear rheometry56(2012); http://dx.doi.org/10.1122/1.4739263View Description Hide Description
To fully understand the structure dependent mechanical property, the harmonic strain loadings were applied to the magnetorheological plastomer (MRP) to study their dynamic properties. Under different test conditions, nonlinearity which was induced by strain amplitude and driving frequency was generated. In order to investigate the mechanism of nonlinearity, a facile and effective strategy by analyzing the response stress and actuating strain within an oscillatory cycle was introduced. In addition, the microstructures of isotropic and anisotropic MRP were observed and the time dependence of dynamic properties for MRP (from isotropic to anisotropic) under an 800 mT magnetic field was also investigated, which were helpful to further understand the structure dependent dynamic properties depending on actuating strain amplitude.
Modeling of the influence of matrix elasticity on coalescence probability of colliding droplets in shear flow56(2012); http://dx.doi.org/10.1122/1.4739930View Description Hide Description
The theory of shear-flow-induced coalescence of monodisperse Newtonian droplets in Newtonian and viscoelastic (described by the Maxwell model) matrices has been derived. Changes in flattening of droplets during coalescence are considered. Calculated dependences on the system parameters of probability, P c, that the droplet collision is followed by their fusion for Newtonian systems agree qualitatively with the Rother–Davis theory [Phys. Fluids 13, 1178–1190, (2001)]. Values of P c for a certain set of parameters are substantially affected by the model used to describe mobility of the interface. It has been found that increasing elasticity(relaxation time) of the matrix leads to decreasing P c irrespective of mobility of the interface. This decrease is small for short relaxation times but pronounced for long relaxation times. The shapes of the dependences of P c on the droplet radii and the shear rate are similar for systems with a Newtonian matrix but differ qualitatively for systems with a viscoelastic matrix. Results of the theory show that P c for viscous and viscoelastic matrices can be semiquantitatively approximated by a product of probability for spherical droplets and probability for highly flattened droplets, calculated from Janssen’s theory [“Dynamics of liquid–liquid mixing,” Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1993] for a viscous system.
56(2012); http://dx.doi.org/10.1122/1.4740264View Description Hide Description
Using simultaneous rheometric and particle-tracking velocimetric measurements, we show that the long-time rheological states of well-entangled polymer solutions are not unique in simple shear. Shear banding emerges upon a sudden startup shear as well as during conventional large amplitude oscillatory shear at rates higher than the overall chain relaxation rate. However, shear homogeneity prevails when the final conditions of continuous shear and oscillatory shear are approached gradually from rates lower than the terminal relaxation rate. This suggests that the observed shear banding as nonlinear response to sudden large deformation is only metastable and not unique.
Nonlinear viscoelasticity and two-step yielding in magnetorheology: A colloidal gel approach to understand the effect of particle concentration56(2012); http://dx.doi.org/10.1122/1.4742186View Description Hide Description
The yielding behavior of conventional magnetorheological (MR) fluids is revisited for a wide range of magnetic fields and particle concentrations under a colloidalgel perspective. A two-step yielding behavior is found at intermediate magnetic fields (∼10 kA/m) that can be explained as a transition from a strong-link to a weak-link (or transition) regime upon increasing the particle concentration in the MR fluid. This two-step yielding behavior is reminiscent of the classical concepts of static (frictional) and dynamic (Bingham) yield stress. By relating macroscopic elastic properties to a scaling fractal model, we could identify the prevalent gelation regime in MR fluids.
56(2012); http://dx.doi.org/10.1122/1.4746781View Description Hide Description
A method is presented to obtain rheological information from capillary velocimetry experiments coupled with pressure drop measurements. The method is based on rescaling the velocity profile with the wall shear stress. The stress-rescaled velocity curve generated depends only on the rheological properties of the fluid, and not on other experimental variables such as tube dimensions, flow rates or pressure drops employed, thus providing a direct means for rheological characterization. We also present transformed functions of the rescaled velocity that facilitate the interpretation of the rheological information via plots that resemble conventional rheograms. In contrast with previous data processing methods that require differentiation, model fitting, or smoothing, the proposed rescaling approach does not require the introduction of additional data processing parameters, such as smoothing factors, that may affect reproducibility of the results. The rescaling method should be useful for robust measurements in low signal-to-noise conditions such as rapid measurements required for process control.
56(2012); http://dx.doi.org/10.1122/1.4751871View Description Hide Description
This paper is concerned with a direct experimental and modeling comparison of the rheology of carbon black (CB) and multiwalled carbon nanotube(CNT)suspensions within a Newtonian epoxy matrix. Experimental observations of the effect of shear on CB and CNT microstructure are reported for a range of CB and CNTsuspension concentrations. Steady shear, time dependent shear behavior, and oscillatory linear viscoelasticity (LVE) of the suspensions are reported and remarkably strong similarities were observed between the CB and CNTsuspension rheology, for example, 4 wt. % CB and 0.4 wt. % CNTsuspensions. Optical observations showed that both the CB and CNT microstructures were shear rate sensitive and a structure-dependent hybrid Maxwell-Voigt phenomenological model with a yield stress was developed that gave a reasonable fit to the rheological data. The structure model parameters for both systems were found to be of a similar order of magnitude, although the onset of rheology development for the two systems occurred with a decade difference of concentration. The experimental rheological results and model fit indicated that for both CB and CNTsuspensions, the observed rheology changes were dominantly controlled by aggregate size and interaction, rather than the respective particulate and filament morphology of the CB and CNT microstructures. The critical concentration for the onset of rheology development was, however, dependant on the basic morphology of the CB and CNTsuspensions.
The matching of polymer solution fast filament stretching, relaxation, and break up experimental results with 1D and 2D numerical viscoelastic simulation56(2012); http://dx.doi.org/10.1122/1.4749828View Description Hide Description
This paper is concerned with the comparison of two numerical viscoelastic strategies for predicting the fast filament stretching, relaxation, and break up of low viscosity, weakly elastic polymeric fluids. Experimental data on stretch, relaxation, and breakup were obtained using a Cambridge Trimaster for a Newtonian solvent (diethyl phthalate) and three monodisperse polystyrene polymer solutions. Two numerical codes were tested to simulate the flow numerically. One code used a one-dimensional approximation coupled with the arbitrary Lagrangian–Eulerian approach and the other a two-dimensional axisymmetric approximation for the flow. In both cases, the same constitutive equations and mono and multimode parameter fitting were used, thereby enabling a direct comparison on both codes and their respective fit to the experimental data. Both simulations fitted the experimental data well and surprisingly the one-dimensional code closely matched that of the two-dimensional. In both cases, it was found necessary to utilize a multimode approach to obtain a realistic match to the experimental data. The sensitivity of the simulation to the choice of constitutive equation (Oldroyd-B and FENE-CR) and the magnitude of nonlinear parameters were also investigated. The results are of particular relevance to ink-jet processing and demonstrate that high shear rate, low viscosityviscoelasticpolymeric flows can be simulated with reasonable accuracy.
56(2012); http://dx.doi.org/10.1122/1.4752193View Description Hide Description
Pulp suspensions possess a yield stress that varies with concentration and fibre type, and understanding of this property is important to the pulp and paper industry. Unfortunately, pulp suspensions are highly susceptible to wall slip, which greatly complicates many rheological measurements including determination of the apparent yield stress. Using the vane method as a starting point, a slip-free method for measuring the apparent yield stress of pulp suspensions is developed. The findings from this method development are also used to assess the likelihood of slip having interfered with previous pulp rheometry studies and to offer some guidelines for the design of future experiments. Finally, the apparent yield stresses of suspensions of two National Institute of Standards and Technology reference pulps are determined for concentrations between 1% and 5% w/w, and the results contrasted with previous studies.
56(2012); http://dx.doi.org/10.1122/1.4752759View Description Hide Description
The extensional dynamics of two low-density polyethylene melts Lupolen 3020D and Lupolen 1840D, both showing a stress overshoot in start-up of uniaxial extension [Rasmussen, H. K., J. K. Nielsen, A. Bach, and O. Hassager, “Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts,” J. Rheol. 49(2), 369–381 (2005)], have been further investigated in stress relaxation and reversed flow. After the overshoot, the stress relaxation has a remarkably faster decrease of the transient stress than when the relaxation is initiated before the overshoot. The measurements from the reversed flow also show that the melts appear less elastic after the overshoot. Multi mode versions of the pom-pom and interchain pressure model fit the data quantitatively up to the stress maximum, but neither model captures the qualitative behavior after the maximum.
The effect of interfacial slip on the rheology of a dilute emulsion of drops for small capillary numbers56(2012); http://dx.doi.org/10.1122/1.4749836View Description Hide Description
We present the constitutive equation for the volume-averaged hydrodynamic stress for a dilute emulsion in a linear ambient flow, when there is slip at the liquid-liquid interface between the Newtonian drop and the suspending fluids. Slip is modeled using a simple Navier slip boundary condition. We provide analytical solutions in the limit of small capillary numbers for the shape deformation, viscosity, and normal stresses. Slip moderates these quantities, with changes from the no-slip case being more pronounced for large viscosity ratios of the drop relative to the suspending fluid. It has been suggested in the past that slip can explain the anomalously low viscosities of certain polymeric blends. Our analysis indicates that slip can only partially account for these deviations, and that other mechanisms should be explored to explain the residual discrepancy.