Index of content:
Volume 53, Issue 6, November 2009
53(2009); http://dx.doi.org/10.1122/1.3238480View Description Hide Description
Closure seems to be something rheologists would prefer to avoid. Here, the story of closure is told in such a way that one should enduringly forget any improper undertone of “uncontrolled approximation” or “necessary evil,” which might arise, for example, in reducing a diffusion equation in configuration space to moment equations. In its widest sense, closure is associated with the search for self-contained levels of description on which time-evolution equations can be formulated in a closed or autonomous form. Proper closure requires the identification of the relevant structural variables participating in the dominant processes in a system of interest and closure hence is synonymous with focusing on the essence of a problem and consequently with deep understanding. The derivation of closed equations may or may not be accompanied by the elimination of fast processes in favor of dissipation. As a general requirement, any closed set of evolution equations should be thermodynamically admissible. Thermodynamic admissibility comprises much more than the second law of thermodynamics, most notably, a clear separation of reversible and irreversible effects and a profound geometric structure of the reversible terms as a hallmark of reversibility. We discuss some implications of the intimate relationship between nonequilibrium thermodynamics and the principles of closure for rheology, and we illustrate the abstract ideas for the rod model of liquid crystal polymers, bead-spring models of dilute polymer solutions, and the reptationmodel of melts of entangled linear polymers.
53(2009); http://dx.doi.org/10.1122/1.3236517View Description Hide Description
Many liquid metals exposed to air develop an oxide film on their outer surface. This film is sufficiently solid-like to provide mechanical stability to small liquid metal droplets, yet weak enough to allow the droplets to be malleable. These properties are useful in both micro-electronics and microfluidics; however, little is known about how to characterize them. Here we probe the elastic, yielding, and relaxationproperties of oxide-coated gallium and eutectic gallium indium using a rheometer equipped with a parallel-plate geometry. By using parallel plates of different size, we show that surface stresses dominate bulk stresses. These experiments also demonstrate that the apparent elastic properties of the oxide film are highly sensitive to its strain history. Moreover, the apparent elasticity is sensitive to the stresses stored in the oxide skin. We probe these stresses and their time-dependence, with both torque and normal force measurements. We also characterize the time-dependence of the elasticity by observing free vibrations of the rheometer. We rationalize the strain history and time-dependence in terms of oxidation and show that despite this dependence, reproducible elasticitymeasurements can be obtained due to the ability of shear to produce a state that is independent of the strain history.
Observing the chain stretch transition in a highly entangled polyisoprene melt using transient extensional rheometry53(2009); http://dx.doi.org/10.1122/1.3208073View Description Hide Description
We measure the viscoelastic properties of a highly entangled narrow molecular weight polyisoprene melt with approximately 280 entanglements per chain in steady and transient shear and in elongational flows. The storage and loss moduli of the melt are found to be well described by the Milner and McLeish model. The relaxation modulus is measured using stress relaxation after a sudden shearing displacement and we experimentally determine the Rouse time by observing strain-time separability for . The transient elongational properties are measured using three distinct instruments: the Sentmanat extensional rheometer (SER) universal testing platform from Xpansion Instruments, its counterpart, the extensional viscosity fixture (EVF) from TA Instruments, and a filament stretching rheometer (FSR). The kinematics obtained in each device is sensitive to the aspect ratio of the sample and care must be taken to achieve homogeneous deformation conditions. Especially for the SER and EVF instruments, a second aspect ratio associated with the rectangular cross-section of the sample is also important. We find that the initial growth in the tensile stress follows the prediction given by the Doi–Edwards reptation model for Deborah numbers based on the Rouse time less than about . For , the stress difference follows more or less the Doi–Edwards prediction in the limit of infinite stretch rates and, for , the measured stresses are well above those that can be predicted by the basic Doi–Edwards model. When , the stress difference also exceeds the linear viscoelastic prediction. In conjunction with this strain-hardening response, a stabilization is obtained whereby the limiting Hencky strain before sample rupture is markedly increased. We compare our observations in the regime with available experiments and theories. The stabilization for is interpreted as a signature of chain stretching for elongational deformation rates faster than the inverse Rouse time.
53(2009); http://dx.doi.org/10.1122/1.3216942View Description Hide Description
Shear flows of wormlike micellar solutions between parallel plates were experimentally investigated using aqueous solutions of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) as test fluids. The solution having a molar concentration ratio of NaSal to CTAB of 2.0 was primarily considered. The velocity between the plates was measured by particle tracking velocimetry. In addition, flow-induced birefringence and shear stress were measured using a parallel-plate rheometer. The measurements were carried out for shear rates at which shear thinning or shear thickening was observed. Banded velocity profiles were found at every shear rate considered in the present experiments, and the profile was stable at relatively low shear rates but fluctuated with time at high shear rates. Furthermore, multi-band velocity profiles were observed in the shear-thinning region. The results of velocity measurements in the shear-thickening region suggest that the velocity profile largely varies with time, accompanying the movement of the position of a band interface. Moreover, both birefringence and shear stress fluctuated with time at high shear rates. These results suggest that the fluctuation of the velocity profile is related to the structural change in the micellar network that leads to the change in the thickness fraction of oriented and isotropic layers or to three-dimensional flows induced by material instabilities.
53(2009); http://dx.doi.org/10.1122/1.3237024View Description Hide Description
A simple method to measure the local extensional properties of polymer melts using a modified Münstedt extensional rheometer is demonstrated. Real time imaging of the specimen during the extension process provides the local rates of strain as a function of the coordinate along the specimen. Simultaneously, the local stresses are assessed by measurements of the sample diameter along the sample and synchronous measurements of the force exerted on the bottom plate of the rheometer. The method provides a quantitative measure of the homogeneity of the deformation states via a kinematic and a dynamic fingerprint of the process. Test experiments using geometrically homogeneous samples reveal a good level of agreement between local and integral measurements of the transient extensional viscosity and thus validate the method. Furthermore, this technique is employed to assess quantitatively the impact of inhomogeneities of the deformation on measurements of the transient extensional viscosity. It is concluded that in the case of initially inhomogeneous samples, the extensional properties depend strongly on the position along the specimen and the usual integral measurements of the transient extensional viscosity are highly unreliable and unrepeatable. Higher Hencky strain measurements indicate that, although the sample inhomogeneity increases systematically during experiments, the integral viscosity data remain reliable as long as the samples were reasonably homogeneous in their initial state.
On time-temperature-concentration superposition principle for dynamic rheology of carbon black filled polymers53(2009); http://dx.doi.org/10.1122/1.3216923View Description Hide Description
Time-temperature-concentration superposition principle is disclosed to linear dynamic rheology of carbon black (CB) filled high-density polyethylene (HDPE) with a wide range of CB volume fraction. The time-concentration superposition (TCS) principle is also validated in CB filled ethylene-tetrafluoroethylene (ETFE) alternating copolymer at . The frequency-dependent viscoelastic functions can be superposed onto universal master curves with the reference of the unfilled HDPE and ETFE. The filler network and strain amplification concepts are used for accounting for the TCS principle.
Exploring stress overshoot phenomenon upon startup deformation of entangled linear polymeric liquids53(2009); http://dx.doi.org/10.1122/1.3208063View Description Hide Description
This work explores the picture associated with stress overshoot during sudden continual (i.e., startup) external deformation of entangled polymeric liquids and proposes a specific scaling form to depict the intermolecular interactions responsible for chain deformation. Following a previously proposed idea that the stress overshoot in startup deformation is a signature of yielding, we search for ingredients that should go into the description of the force imbalance at the yield point and show that the expression for the intermolecular locking force , derived from the characteristics associated with the yield point, can be tested against experiment. New rate-switching experiments support the proposed formula for .
Influence of confinement on the steady state behavior of single droplets in shear flow for immiscible blends with one viscoelastic component53(2009); http://dx.doi.org/10.1122/1.3236837View Description Hide Description
By using a counter rotating plate-plate device, single droplets in shear flow have been microscopically studied at confinement ratios ranging from 0.1 to 0.75. The droplet-to-matrix viscosity ratio was fixed at 0.45 and 1.5. Results are presented for systems with a viscoelastic Boger fluid matrix or a viscoelastic Boger fluid droplet, at a Deborah number of 1. Although the separate effects of confinement and component viscoelasticity on dropletdynamics in shear flow are widely studied, we present the first systematic experimental results on confined dropletdeformation and orientation in systems with viscoelastic components. Above a confinement ratio of 0.3, wall effects cause an increase in dropletdeformation and orientation, similar to fully Newtonian systems. To describe the experimental data, the Shapira–Haber theory [Shapira, M., and S. Haber, Int. J. Multiph. Flow16, 305–321 (1990)] for confined slightly deformeddroplets in Newtonian-Newtonian systems is combined with phenomenological bulk models for systems containing viscoelastic components [Maffettone, P. L., and F. Greco, J. Rheol48, 83–100 (2004); M. Minale, J. Non-Newtonian Fluid Mech.123, 151–160 (2004)]. The experimental results are also compared to a recent model for confined dropletdynamics in fully Newtonian systems [M. Minale, Rheol. Acta47, 667–675 (2008)]. For different values of the viscosity ratio, component viscoelasticity and Ca-number, good agreement was generally obtained between experimental results and predictions of one or more models. However, none of the models can accurately describe all experimental data for the whole range of parameter values.
Nature of steady flow in entangled fluids revealed by superimposed small amplitude oscillatory shear53(2009); http://dx.doi.org/10.1122/1.3236523View Description Hide Description
We carry out a systematic investigation into steady-state shear behavior of six entangled solutions based on a superposition of continuous shear and small amplitude oscillatory shear (SAOS). During steady shear in the shear thinning regime, the superimposed SAOS frequency sweep measurements reveal characteristics of viscous liquids, e.g., terminal dynamics, on the experimental time scale of the reciprocal shear rate. The residual entanglement network retains the same level of elastic stiffness as the equilibrium system does. Consistent with the convective constraint release idea, chains in the network are forced to pass around each other as they must do so to undergo steady flow. When such a sample is examined at significantly short time scales, chains are unable to pass around and the signature of this residual entanglement is that the storage modulus is greater than the loss modulus at higher frequencies than the applied shear rate. The particle-tracking velocimetric observations confirm that whether shear banding is present or not does not affect the basic “terminal flow” character revealed by the superimposed SAOS.
53(2009); http://dx.doi.org/10.1122/1.3237154View Description Hide Description
Colloidalgels can undergo a solid to liquid transition, and the yielding and subsequent microstructural reorganizations are responsible for the complex rheological properties of these materials. In the present work, video microscopy is used to study the details of the microstructure during the yielding transition, using planar monolayers of model aggregated suspensions subjected to homogeneous interfacial shear flows. The microstructural heterogeneity of the quiescent structure on both local and larger length scales is characterized in detail. The pertinent length scales can be directly linked to the aggregation pathway. The large scale heterogeneity in the microstructure, rather than the local scale properties, determines the length scales observed during the initial yielding of the gelstructure. The break-up and subsequent reaggregation leads to a local compaction and increasingly more heterogeneous structure. As the surface coverage increases, the heterogeneity and deformations become more and more localized. The experiments shed light on the pertinent length scales in colloidalgels and how they evolve upon initial yielding, which should be relevant for understanding the thixotropic response and guiding modeling efforts of the macroscopic rheological behavior of flocculated suspensions.
53(2009); http://dx.doi.org/10.1122/1.3213090View Description Hide Description
We present measurement of wall slip velocity in concentrated suspension of non-colloidal particles. The slip in non-colloidal concentrated suspension mainly arises from wall depletion effect since the non-hydrodynamic effects such as those arising from particle-wall interactions can be small. In this work, we provide a simple methodology for the determination of slip velocity, which requires less experimental work compared to other methods available for slip corrections. The experiments were carried out in a cylindrical Couette geometry of a rheometer. The rheological measurements were carried out first with serrated cup and serrated rotor geometry. Next, the serrated rotor was made smooth by a wax coating while the cup remained serrated. The serrated geometry offers no-slip boundary and the measuredviscosity is the true viscosity of suspension, whereas smooth rotor showed significant slip at a higher concentration of particles and the measuredviscosity was significantly lower. Comparing the wall shear stresses from the two measurements, we have determined the slip velocity at low shear rates. We have also carried out Stokesian dynamics simulation of simple shear flow of suspension bounded between smooth and serrated walls. The slip velocities from the simulations were calculated by similar analysis as done in the experiments. The simulation and experimental results are in qualitative agreement. It is observed that the wall slip velocity varies linearly with the apparent shear rate. The slip velocity determined from experiments is found to increase with the decrease in viscosity of continuous phase. These observations are in agreement with the previous experimental studies on non-colloidal suspensions.
53(2009); http://dx.doi.org/10.1122/1.3238546View Description Hide Description
This paper is motivated by experiments in which time series of tracer particles in viscoelastic liquids are recorded using advanced microscopy. The experiments seek to infer either viscoelastic properties of the sample [Mason and Weitz, Phys. Rev. Lett. 74, 1250–1253 (1995)] or diffusive properties of the specific tracer particle in the host medium [Suh et al., Adv. Drug Delivery Rev. 57, 63–78 (2005); Matsui et al., Proc. Natl. Acad. Sci. U.S.A. 103, 18131–18136 (2006); Lai et al., Proc. Natl. Acad. Sci. U.S.A. 104, 1482–1487 (2007); Fricks et al., SIAM J. Appl. Math. 69, 1277–1308 (2009)]. Our focus is the latter. Experimentalists often fit data to transient anomalous diffusion: a sub-diffusive power law scaling (, with ) of mean-squared displacement (MSD) over a finite time interval, with longtime viscous scaling . The time scales of sub-diffusion and exponents are observed to vary with particle size, particle surface chemistry, and viscoelastic properties of the host material. Until now, explicit models for transient sub-diffusive MSD scaling behavior [Doi and Edwards, The Theory of Polymer Physics (Oxford University Press, New York, 1986); Kremer and Grest, J. Chem. Phys. 92, 5057–5086 (1990); Rubinstein and Colby, Polymer Physics (Oxford University Press, New York, 2003)] are limited to precisely three exponents: monomerdiffusion in Rouse chain melts , in Zimm chain solutions, and in reptating chains . In this paper, we present an explicit parametrized family of stochastic processes (generalized Langevin equations with prescribed memory kernels) and derive their closed-form solutions which (1) span the complete range of transient sub-diffusive behavior and (2) possess the flexibility to tune both the time window of sub-diffusive scaling and the power law exponent . These results establish a robust family of sub-diffusive models, for which the inverse problem of parameter inference from experimental data [Fricks et al., SIAM J. Appl. Math. 69, 1277–1308 (2009)] remains to be developed.