Volume 54, Issue 5, September 2010
Index of content:
54(2010); http://dx.doi.org/10.1122/1.3460800View Description Hide Description
Dilute Laponite suspensions in water at low salt concentration form repulsive colloidal glasses which display physical aging. This phenomenon is still not completely understood and, in particular, little is known about the connection between the flow history, as a determinant of the initial state of the system, and the subsequent agingdynamics. Using a stress controlled rheometer, we perform stress jump experiments to observe the elastic component of the flow stress that remains on cessation of flow or flow quenching. We investigate the connection between the dynamics of these residual stresses and the rate of physical aging upon quenching from different points on the steady-state flow curve. Quenching from high rates produces a fluid state, , with small, fast relaxing residual stresses and rapid, sigmoidal aging of the complex modulus. Conversely, quenching from lower shear rates produces increasingly jammed states featuring slowly relaxing stresses and a slow increase of the complex modulus with system age. Flow cessation from a fixed shear rate with varying quench durations shows that slower quenches produce smaller residual stresses at short times which relax at long times by smaller extents, by comparison with faster quenches. These smaller stresses are correlated with a higher modulus but slower physical aging of the system. The characteristic time for the residual stress relaxation scales inversely with the quench rate. This implies a frustrated approach to any ideal stress-free state that succinctly reflects the frustrated nature of these glassy systems.
Measurement of fluid properties using an acoustically excited atomic force microscope micro-cantilever54(2010); http://dx.doi.org/10.1122/1.3460907View Description Hide Description
In this study, we develop a technique that can be used for extracting the properties of high viscosity Newtonian liquids at the microliter scale using an atomic force microscope. We obtained the responses of two different cantilevers in solutions of glycerin and water using thermal and acoustic frequency sweep excitations. The thermal excitation method cannot be used for liquids with viscosity substantially higher than because of the existence of a noise floor which obscures the cantilever response. The acoustic frequency sweep excitation can overcome this limitation. The fluid properties were extracted by combining a theoretical model with the experimentally obtained results for the frequency sweep excitation. By using the cantilever phase response, errors of less than 14% in viscosity and density were achieved. This error can be explained by a local increase in fluid temperature of due to the laser energy.
54(2010); http://dx.doi.org/10.1122/1.3462306View Description Hide Description
In this paper, we experimentally study the deformation and break-up of a micron-sized polydimethylsiloxanedrop in a refractive-index-matched suspension of polymethylmethacrylate particles undergoing a planar hyperbolic flow. The particles produce both short-ranged stochastic effects and macroscopic mean-field effects on the deformation and break-up of the drops. In our experiments, the relative influence of these effects was varied by changing the particle to drop-size ratio . At small , the mean-field effects dominate and the drop deformation and break-up are only influenced by an increased effective viscosity of the suspension. At large , the local flowfluctuations and the direct interactions with particles have the dominant effect on drop dynamics. This leads to pronounced fluctuations in the drop deformation and a higher polydispersity in the drop size after break-up.
54(2010); http://dx.doi.org/10.1122/1.3473811View Description Hide Description
Poisson’s ratio is defined as the ratio of the lateral contraction to the elongation in the infinitesimal uniaxial extension of a homogeneous isotropic body. In a viscoelastic material, Poisson’s ratio is a function of time (or frequency). In this paper, the time-dependence of the Poisson’s ratio is analytically evaluated from the bulk and shear responses using the relations between the viscoelastic functions in the Laplace domain. It has been found that, in the region of -relaxation, Poisson’s ratio may be a nonmonotonic function of time, with a weak minimum at short times, when the shear response is broader than bulk response such that the ratio is much larger than 1, or a monotonically increasing function of time if the shear and bulk responses share similar timescales and relaxation time distributions. The latter case is verified using experimental data from the literature for a cross-linked polymer, whereas the former case is verified for two linear polymers.
54(2010); http://dx.doi.org/10.1122/1.3474580View Description Hide Description
We investigate confined shear thickeningsuspensions for which the sample thickness is comparable to the particle dimensions. Rheometrymeasurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed-shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.
54(2010); http://dx.doi.org/10.1122/1.3473924View Description Hide Description
The breakup of confined drops in shear flow between parallel plates is investigated as a function of viscosity ratio and confinement ratio. Using a boundary-integral method for numerical simulations and a counter-rotating experimental device, critical capillary numbers in shear flow are obtained. It is observed that different viscosity ratios yield different trends with increasing confinement ratio: a low viscosity ratio drop shows an increase in critical capillary number, at a viscosity ratio of unity no major trend is seen, and the critical capillary number for a high viscosity ratio drop decreases significantly. A generalized explanation for all viscosity ratios is that confinement affects the orientation of the drop with respect to the direction of the local strain field. At moderate confinement ratios, the drop orients more toward the strain direction, where it experiences a stronger flow and hence, the critical capillary number is decreased. As the drop gets more confined, it aligns more in the flow direction. Hence, the drop experiences a weaker flow and thus, additionally stabilized by wall effects, it breaks at a higher critical capillary number. In principle, this behavior is the same for all viscosity ratios, but transitions occur at different confinement ratios. Most of the breakup is of a binary nature, but ternary breakup can occur if the drop length is larger than 6 undeformed drop radii, consistent with arguments based on the Rayleigh–Plateau instability.
Brownian dynamics simulations of single polymer chains with and without self-entanglements in theta and good solvents under imposed flow fields54(2010); http://dx.doi.org/10.1122/1.3473925View Description Hide Description
The effects of self-entanglements (spring-spring uncrossability) and solvent quality on the static and dynamic properties of a polymer chain in shear and extensional flows are investigated using Brownian dynamics simulations. We model the polymer chain by a sequence of beads connected by finitely extensible non-linear elastic springs, and spring-spring uncrossability is enforced by applying a spring-spring repulsive potential together with an adaptive time-stepping. Our findings suggest that chain uncrossability has an insignificant effect on the dynamics of a polymer chain. Furthermore, we considered four different combinations of intramolecular interactions: (i) no interactions, (ii) repulsive spring-spring and attractive bead-bead interactions, (iii) only repulsive bead-bead interactions, and (iv) only repulsive spring-spring interactions. The first two cases model “theta” solvents, where the radius-of-gyration of a polymer chain, , where is the number of beads. For appropriately chosen parameters of interaction potentials, the last two cases model good solvents, where . In the presence of a simple shear flow, the stretching behavior is alike in all the cases except case (ii). In case (ii), the polymer chain forms “pearl-necklace-like” structures at zero Weissenberg number, . With an increase in , first increases due to stretching of bonds between neighboring “pearls,” and then decreases when the decrease in the number of pearls becomes limiting. In the presence of an extensional flow, normal stretching behavior is observed even in case (ii); the number of pearls increases with increasing extension rate because larger pearls break into smaller “pearls.” The results show that even for fixed overall solvent quality for a chain at rest (e.g., a theta solvent), the ability of the chain to stretch in a shear flow is sensitive to the nature of intramolecular interactions. A chain with short-range attraction (between beads) and a long-range repulsion (between springs) tuned to balance each other and so create a theta condition at rest does not stretch much in a shear flow, while a chain for which the theta condition is achieved by applying no interactions at all does stretch in a shear flow.
Continuous lubricated squeezing flow: A novel technique for equibiaxial elongational viscosity measurements on polymer melts54(2010); http://dx.doi.org/10.1122/1.3474599View Description Hide Description
A novel experimental technique to study the rheological behavior of polymer melts and other viscous fluids in equibiaxial elongational deformations is described. The new technique is a modification of lubricated squeezing flow (LSF) wherein deformation is induced by compression of the sample between parallel plates having a thin film of a low-viscosity fluid or lubricant. In previous work, we have demonstrated that despite its simplicity, LSF is limited to rather small strains because of uncontrolled lubricant film thinning. The new technique, which we call continuous lubricated squeezing flow (CLSF), resolves the lubricant thinning problem by replenishing the lubricant films with a continuous and uniform flow of lubricant through porous plates. The CLSF technique is validated in constant strain-rate deformations by direct comparison with published data obtained using a considerably more complicated device developed by Meissner and co-workers [Hachmann, P., and J. Meissner, “Rheometer for equibiaxial and planar elongations of polymer melts,” J. Rheol.47, 989–1010 (2003)].
An investigation into the constriction flow of a particle reinforced polystyrene melt using a combination of flow visualization and finite element simulations54(2010); http://dx.doi.org/10.1122/1.3478307View Description Hide Description
This paper investigates the flow of a particle filled polystyrene melt through a constriction zone using a combination of experimental techniques and computer simulation. A special blend, containing cross-linked polystyrene beads mixed into a polydispersed polystyrene matrix, was produced for this study. This closely refractive index matched blend allowed visualization of the flow birefringence up to an equivalent particle loading of around 15 vol %. Flow birefringence through a 10:1.4 contraction, measured using a multi-pass rheometer (MPR), was compared with that predicted from finite element simulations, in a similar way to that already published for unfilled polymer melts [Collis et al., J. Rheol.49(2), 501–522 (2005)]. Numerical predictions were obtained using the finite element solver “EUFLOW” and ranked against the experimental processing data from the MPR. An extensive study of the rheology of the particle filled polystyrene blend was conducted which provided the input to the simulations. The addition of the particles was seen to enhance the shear thinning of the melt, while debonding between the particles and the polystyrene melt during extension testing had the effect of reducing strain hardening. EUFLOW was used to evaluate how these two important aspects could affect the flow birefringence of the filled polystyrene melt.
Normal stresses in a shear flow of magnetorheological suspensions: Viscoelastic versus Maxwell stresses54(2010); http://dx.doi.org/10.1122/1.3479043View Description Hide Description
This work reports an experimental and theoretical study on the normal force developed by suspensions of magnetic microparticles subjected to magnetic fields. Experimental values of the normal force were obtained using a rotational rheometer, for a broad range of particle concentration in the suspensions. Applied magnetic fields up to 343 kA/m were generated in the plate-plate measuring geometry. It was found that the normal force exhibited a high-value plateau at low shear, followed by a decrease as the suspensions started to flow and a final low-value plateau at high shear. These three regions in the normal force vs shear rate curve were well correlated with the microscopic regimes in the suspensions: field-aligned structures filling the gap, inclined structures still filling the gap, and structures non-filling the gap. The theoretical model developed is based on the equilibrium between hydrodynamic and magnetostatic torques and forces in a field-induced aggregate of particles subjected to shear. The stress tensor was obtained and the normal force calculated as the integral of the stress over the total surface of the rotational plate. A good correspondence among the theoretical and experimental values was obtained.
54(2010); http://dx.doi.org/10.1122/1.3473923View Description Hide Description
The apparent yield stress is one of the most important rheological properties of pulp suspensions in designing process equipment for the pulp and paper industry. Therefore, determining a reliable apparent yield stressmeasurement technique is of importance, not only for pulp suspensions but for any fluid exhibiting yielding behavior. In this work two established and extensively used methods for determining apparent yield stress are compared with a velocity profile determination technique using ultrasonicDopplervelocimetry. The apparent yield stresses are determined for various commercial pulp suspensions at fiber mass concentrations ranging from 0.5 to 5 wt %. The results are compared and models are proposed to represent the apparent yield stress of pulp suspensions as a function of fiber mass concentration. It is concluded that the apparent yield stressmeasurements obtained using the local velocity profile determination technique are the most reliable.
Linear and nonlinear viscoelastic properties of bidisperse linear polymers: Mixing law and tube pressure effect54(2010); http://dx.doi.org/10.1122/1.3478316View Description Hide Description
In this manuscript, we extend the tube-based model that we developed for predicting the linear viscoelasticity of entangled polymers [van Ruymbeke et al., J. Non-Newtonian Fluid Mech.128, 7–22 (2005)] to the prediction of the extensional rheology of monodisperse and bidisperse linear polymers and confront the results to experimental data. This model is based on the concepts of stretch-orientation separability [McLeish and Larson, J. Rheol.42, 81–110 (1998)] and inter-chain pressure [Marrucci and Ianniruberto, Macromolecules37, 3934–3942 (2004)]. In order to deal with polydisperse samples, a new mixing law is proposed. As it does not require knowledge of the full linear relaxation spectrum, the proposed model is a powerful predictive tool. Very good agreement is found between theoretical and experimental results. For bidisperse samples, the individual contribution of each component is determined, and it is shown that only few percent of long chains are enough to generate the strong strain hardening observed in the experimental data. Last, we discuss the value of the tube diameter relaxation time. For monodisperse samples, this parameter is found to scale with . However, for bidisperse samples, as it was already observed by Wagner et al. [J. Rheol.52, 67–86 (2008)], the tube diameter relaxation time of the long component must be rescaled, which is contrary to the inter-chain pressure model and opens several new questions.