Volume 52, Issue 6, November 2008
Index of content:
52(2008); http://dx.doi.org/10.1122/1.2995858View Description Hide Description
Using a well-entangled monodisperse styrene-butadiene random-copolymer (SBR) melt as a model system, we illustrate generic features of uniaxial extension behavior that may be shared by all well-entangled thermoplastic and elastomeric materials. Depending on the imposed extensional rate, the same sample may behave like a viscous liquid or an elastic “solid.” Analogous to the recently revealed shear inhomogeneity, the SBR melt inevitably undergoes cohesive failure in the form of sample breakage whenever the Weissenberg number is much greater than unity, making it challenging to reach steady state. In the elastic deformation regime where the external deformation rate is faster than Rouse relaxation rate, the sample undergoes a finite amount of uniform stretching before yielding occurs in a period much shorter than the terminal relaxation time. Steady flow can be achieved only in the terminal regime where entangled chains utilize directed molecular diffusion to achieve rearrangement and enable uniform flow.
52(2008); http://dx.doi.org/10.1122/1.2980013View Description Hide Description
When two equal-sized drops collide in a two-dimensional extensional flow of a second immiscible fluid, the time required to drain the thin film between the drops prior to coalescence is referred to as the drainage time. In a previously proposed scaling theory [H. Yang et al., Phys. Fluids13, 1087–1106 (2001)] we found that in the low Ca regime, the dimensionless product of the film drainage time and the applied shear rate should scale as . Yet, recent numerical simulations contradict this result and show that the dimensionless drainage time in this regime scales as Ca. Furthermore, the existing experiments suggest that the drainage time may become independent of Ca in the limit . In this paper, we attempt to address these apparent contradictions. First, we carry out coalescence experiments in a four-roll mill for significantly smaller drops than have heretofore been studied. Our results show that as is decreased for a fixed Ca range, the scaling exponent in the correlation falls in the range , but never exhibits a value smaller than 1. Thus, we corroborate the numerically predicted scaling of with Ca in the low Ca regime. We then reexamine the scaling theory. We find that the disagreement between scaling theories and the numerical simulations (as well as the present experiments) ultimately emanates from a fundamental limitation in the definition of the drainage time. Finally, our experiments show that the scaling exponent unexpectedly increases when the viscosity ratio is increased from to for a drop radius smaller than . We show that one must evidently account for interfacial “slip” between the drops and the surrounding film to account for this observed increase in . We define a slip parameter that gives an a priori estimate of the importance of slip in the experimental data.
52(2008); http://dx.doi.org/10.1122/1.2982932View Description Hide Description
This paper is concerned with the rheological modeling of untreated carbon nanotubes(CNTs) suspended within an epoxy resin. The untreated CNTsuspensions exhibited significant steady shear thinning and contained optically resolvable aggregate structures. A simple orientation model, based on a Fokker–Planck advection-diffusion description, failed to capture the experimentally observed rheological responses for untreated CNTsuspensions. A new model named the “aggregation∕orientation” (AO) model has been developed to describe the experimental findings. The model integrated elements of both a standard orientation model and aggregationmodeling concepts within the Fokker–Planck formalism. A hierarchy of states between CNTs that are free from entanglement and a complete CNT network was incorporated into the AO model, thereby enabling different microstructure populations to exist for different shear conditions. Using a small number of adjustable parameters, it was found that the experimental data could be fitted with reasonable precision.
52(2008); http://dx.doi.org/10.1122/1.2998219View Description Hide Description
In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference.
52(2008); http://dx.doi.org/10.1122/1.2982514View Description Hide Description
The inertialess three-dimensional (3D) flow of viscoelasticshear-thinning fluids in a 4:1 sudden square-square contraction was investigated experimentally and numerically and compared with the flow of inelastic fluids. Whereas for a Newtonian fluid the vortex length remains unchanged at low Reynolds numbers, with the non-Newtonian fluid there is a large increase in vortex length with fluid elasticity leading to unstable periodic flow at higher flow rates. In the steady flow regime the vortices are 3D and fluid particles enter the vortex at the middle plane, rotate towards its eye, drift sideways to the corner-plane vortex, rotate to its periphery, and exit to the downstream duct. Such dynamic process is reverse of that observed and predicted with Newtonian fluids. Numerical predictions using a multimode Phan-Thien–Tanner viscoelastic model are found to match the visualizations accurately and in particular are able to replicate the observed flow reversal. The effect of fluid rheology on flow reversal, vortex enhancement, and entry pressure drop is investigated in detail.
52(2008); http://dx.doi.org/10.1122/1.2992600View Description Hide Description
The dissipative behavior of model suspensions composed of non-Brownian, inertialess, rigid spheres immersed in Newtonian and viscoelastic matrices is investigated in the range of volumetric concentrations up to 10%, thus encompassing both the dilute and semidilute regimes. Polymethylmethacrylate beads are dispersed into polyisobutylene, characterized by a Newtonian rheology, and into two viscoelasticpolydimethylsiloxanes. Both steady state viscosity and oscillatory shear loss modulusmeasurements are performed. As expected, the presence of the filler increases both the viscosity and the loss modulus of all suspensions. Following the hydrodynamic calculations of Batchelor, the concentration dependence is described by a second order polynomial expansion in the volume fraction. For low concentrations, the linear Einstein and Palierne predictions for Newtonian and viscoelastic fluids are found to be well obeyed by both the Newtonian and the viscoelasticsuspensions. In the semidilute regime, the experimental data for the Newtonian suspension show an excellent quantitative agreement with Batchelor’s calculations. Conversely we find that, out of possible experimental errors, the viscoelasticsuspensions show more pronounced deviations from the linear dilute behavior, resulting in a second order polynomial coefficient substantially larger than that predicted by Batchelor for Newtonian systems.
Morphology and rheology of compatibilized polymer blends: Diblock compatibilizers vs crosslinked reactive compatibilizers52(2008); http://dx.doi.org/10.1122/1.2995857View Description Hide Description
Reactive compatibilization is commonly used when blending immiscible homopolymers. The compatibilizers formed from the interfacial coupling of two types of reactive chains often have a graft copolymer architecture. Here we consider the case where both reactive chains are multifunctional, leading to a crosslinked copolymer at the interface. Experiments were conducted on a model blend of polydimethylsiloxane drops in a polyisoprene matrix. Compatibilizer was formed by an interfacial reaction between amine-functional polydimethylsiloxane and maleic anhydride-functional polyisoprene. Both species were multifunctional, and therefore capable of interfacial crosslinking. Optical microscopy showed some unusual features including drop clusters, nonspherical drops, and some drops with apparently nonsmooth surfaces. All these features suggest that a crosslinked “skin” covers the interface of the drops. Rheologically, the reactively compatibilized blend showed gel-like behavior in oscillatory experiments, enhanced viscosity and elastic recovery at low stresses, and strong viscosity overshoots in creep experiments, all of which are likely attributable to drop clustering. At the highest stress studied , the viscosity of the reactively compatibilized blend is comparable to that of a similar blend compatibilized by diblock copolymer. This suggests that, in practical processing operations that occur at even higher stresses, interfacial crosslinking by multifunctional chains will not adversely affect processability.
52(2008); http://dx.doi.org/10.1122/1.2994729View Description Hide Description
The dynamics of dilute solutions of DNA flowing in a scaled down roll-knife coating flow are investigated on multiple scales. The flow is generated between a rotating roll and a stationary glass knife, and extension of fluorescently stained DNA molecules is measured at the minimum gap at low roll speeds. The macroscopic flow is computed by solving the continuum equations of motion with the finite element method; the microscale behavior of DNA molecules is predicted by Brownian dynamics combined with successive fine-graining. The simulations predict that the DNA should stretch almost to full extension near the roll surface in the region of minimum gap; this does not agree with experimental measurements. The assumption that the flow is nearly homogeneous on the length scale of the polymer molecules, commonly used in processing flows as well as Brownian dynamics simulations of simple flows, fails near free surfaces, and is the likely cause of the discrepancy. Evidence from the literature suggests that similar nonlocal effects may be present in coating and ink-jet printing flows of high molecular weight polymer solutions.
52(2008); http://dx.doi.org/10.1122/1.2970095View Description Hide Description
Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using rheometric tests such as steady shear or step strains. However, a definitive framework does not exist to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We define a robust and physically meaningful scheme to quantify such behavior, using an imposed large amplitude oscillatory shear (LAOS) strain. Our new framework includes new material measures and clearly defined terminology such as intra-/intercycle nonlinearities, strain-stiffening/softening, and shear-thinning/thickening. The method naturally lends a physical interpretation to the higher Fourier coefficients that are commonly reported to describe the nonlinear stress response. These nonlinear viscoelasticproperties can be used to provide a “rheological fingerprint” in a Pipkin diagram that characterizes the material response as a function of both imposed frequency and strain amplitude. We illustrate our new framework by first examining prototypical nonlinear constitutive models (including purely elastic and purely viscous models, and the nonlinear viscoelastic constitutive equation proposed by Giesekus). In addition, we use this new framework to study experimentally two representative nonlinear soft materials, a biopolymer hydrogel and a wormlike micelle solution. These new material measures can be used to characterize the rheology of any complex fluid or soft solid and clearly reveal important nonlinear materialproperties which are typically obscured by conventional test protocols.
Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow52(2008); http://dx.doi.org/10.1122/1.2978956View Description Hide Description
The deformation and orientation of droplets during transient shear flow is studied in a counterrotating device using microscopy. The effect of the degree of confinement and viscosity ratio is systematically investigated. The system consists of polydimethylsiloxane droplets of varying sizes and viscosities dispersed in a polyisobutylene matrix. The observations are compared with the predictions of an adapted version of the Maffettone and Minale model [Maffettone, and Minale, J. Non-Newtonian Fluid Mech.78, 227–241 (1998)] which includes confinement effects [Minale, Rheol. Acta47, 667–675 (2008)]. For flow start-up at low capillary numbers, the deformation of confined droplets and their orientation towards the flow direction are increased with respect to the unconfined situation for all viscosity ratios under investigation. The confined model results for start-up and the experimental data at low capillary numbers are in good agreement both showing similar monotonous transients. At high degrees of confinement and high shear rates, one or more overshoots in the dropletdeformation are experimentally observed, depending on the viscosity ratio. In addition, droplets become sigmoidal when highly confined. Under these conditions, the confined Maffettone and Minale model, which assumes an ellipsoidal droplet shape, cannot be used to predict the droplet behavior. The relaxation of confined droplets upon cessation of steady-state shear flow is also studied. It is experimentally observed that confinement only affects the relaxation at degrees of confinement above 60% of the gap spacing. Highly confined droplets experience a slightly slower relaxation with respect to bulk conditions. The relaxation predictions of the confined model are in rather good agreement with the experimental data.