Index of content:
Volume 57, Issue 1, January 2013

This work analyses the highstrain extensional behavior of longchain branched polyethylenes, employing two novel extensional rheometer devices, the filament stretching rheometer and the crossslot extensional rheometer. The filament stretching rheometer uses an active feedback loop to control the imposed strain rate on a filament, allowing Hencky strains of around 7 to be reached. The crossslot extensional rheometer uses optical birefringence patterns to determine the steadystate extensional viscosity from planar stagnation point flow. The two methods probe different strainrate regimes and in this paper we demonstrate the agreement when the operating regimes overlap and explore the steadystate extensional viscosity in the full strainrate regime that these two complimentary techniques offer. For longchain branched materials, the crossslot birefringence images show a double cusp pattern around the outflow centre line (named Wcusps). Using constitutive modeling of the observed transient overshoot in extension seen in the filament stretching rheometer and using finite element simulations we show that the overshoot explains the Wcusps seen in the crossslot extensional rheometer, further confirming the agreement between the two experimental techniques.

Numerical simulation results of the nonlinear coefficient Q from FTRheology using a single mode pompom model
View Description Hide DescriptionIn previous experimental observations, Hyun and Wilhelm [Macromolecules 42, 411–422 (2009)] proposed a nonlinear coefficient Q (≡ I _{3/1}/γ _{0} ^{2}) that was determined from Fourier transform rheology experiments under dynamic oscillatory shear flow. Additionally an intrinsic zerostrain nonlinearity, Q _{0} ( ), was defined. It was found that this nonlinear coefficient Q(ω,γ _{0}), also given as Q _{0}(ω), is a very promising parameter to quantify nonlinear mechanical properties that are highly affected by polymer topology, e.g., branched structures. In this study, we systematically investigated the effect of polymer topology on the nonlinear parameters Q(ω,γ _{0}) and Q _{0}(ω) with a single mode differential pompom model. A number of parameters are affecting the topology of a pompom polymer, such as the number of dangling arms (q) and the dimensionless molecular weight of both the backbone (s _{b}) and the arms (s _{a}). In the here presented work, the linear viscoelastic properties G′(ω) and G″(ω) were compared with the nonlinear viscoelastic property Q _{0}(ω) for variety of molecular parameters. The intrinsic nonlinearity Q _{0}(ω) displayed two distinct relaxation processes for pompom architectures even though G′(ω) and G″(ω) could not distinguish two relaxation processes. Furthermore, the behavior of Q(γ _{0}) as a function of strain amplitude was also investigated in detail. From the results of these numerical simulations, it was concluded that polymer topology had a stronger influence on the nonlinear viscoelastic properties Q and Q _{0} than on the linear viscoelastic properties.

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)
View Description Hide DescriptionLarge amplitude oscillatory shear (LAOS) is used as a tool to probe the nonlinear rheological response of a model elastoviscoplastic material (a Carbopol microgel). In contrast to most recent studies, these large amplitude measurements are carried out in a stresscontrolled manner. We outline a descriptive framework of characterization measures for nonlinear rheology under stresscontrolled LAOS, and this is contrasted experimentally to the straincontrolled framework that is more commonly used. We show that this stresscontrolled methodology allows for a physically intuitive interpretation of the yielding behavior of elastoviscoplastic materials. The insight gained into the material behavior through these nonlinear measures is then used to develop two constitutive models that prescribe the rheological response of the Carbopol microgel. We show that these two successively more sophisticated constitutive models, which are based on the idea of strain decomposition, capture in a compact manner the important features of the nonlinear rheology of the microgel. The second constitutive model, which incorporates the concept of kinematic hardening, embodies all of the essential behaviors exhibited by Carbopol. These include elastoviscoplastic creep and timedependent viscosity plateaus below a critical stress, a viscosity bifurcation at the critical stress, and Herschel–Bulkley flow behavior at large stresses.

Normal stress measurements in sheared nonBrownian suspensions
View Description Hide DescriptionMeasurements in a cylindrical Taylor–Couette device of the shearinduced radial normal stress in a suspension of neutrally buoyant nonBrownian (noncolloidal) spheres immersed in a Newtonian viscous liquid are reported. The radial normal stress of the fluid phase was obtained by measurement of the grid pressure , i.e., the liquid pressure measured behind a grid which restrained the particles from crossing. The radial component of the total stress of the suspension was obtained by measurement of the pressure, , behind a membrane exposed to both phases. Pressure measurements, varying linearly with the shear rate, were obtained for shear rates low enough to insure a grid pressure below a particle size dependent capillary stress. Under these experimental conditions, the membrane pressure is shown to equal the second normal stress difference, , of the suspension stress whereas the difference between the grid pressure and the total pressure, , equals the radial normal stress of the particle phase, . The collected data show that is about 1 order of magnitude higher than the second normal stress difference of the suspension. The values obtained in this manner are independent of the particle size, and their ratio to the suspension shear stress increases quadratically with , in the range . This finding, in agreement with the theoretical particle pressure prediction of Brady and Morris [J. Fluid Mech. 348, 103–139 (1997)] for small , supports the contention that the particle phase normal stress is due to asymmetric pair interactions under dilute conditions, and may not require manybody effects. Moreover we show that the values of , normalized by the fluid shear stress, with the suspending fluid viscosity and the magnitude of the shear rate, are welldescribed by a simple analytic expression recently proposed for the particle pressure.

Studying the origin of “strain hardening”: Basic difference between extension and shear
View Description Hide DescriptionThis work studies the origin of the so called "strain hardening" observed when comparing the transient stress response of entangled melts to uniaxial extension with that to simple shear. Strain hardening occurs when the transient extensional viscosity measured from a startup uniaxial extension of finite rate deviates upward from the zerorate transient viscosity. Our theoretical analysis shows that polymer melts would always exhibit strain hardening at sufficient high Hencky rates because the entanglement network can be effectively strengthened during extension and can only be weakened during shear for linear chains. The kinematic difference between simple shear and uniaxial extension has two effects: (a) The force resulting from the startup deformation is measured from an increasingly shrinking area in uniaxial extension instead of a constant area as in simple shear; and (b) the tendency of the entanglement network to yield, i.e., to undergo chain disentanglement is partially suppressed during startup extension at high Hencky rates. In short, the phenomenon of strain hardening reflects the reality that entangled melts are not fluids but temporary solids and that the conventional description of their uniaxial extension in terms of the Cauchy stress contains a geometric condensation factor.

Increase of longchain branching by thermooxidative treatment of LDPE: Chromatographic, spectroscopic, and rheological evidence
View Description Hide DescriptionLowdensity polyethylene was thermooxidatively degraded at 170 °C, i.e., degraded in the presence of air, by a one thermal cycle (1C) treatment during times between 30 and 90 min, and by a two thermal cycles (2C) treatment, i.e., after storage at room temperature, an already previously degraded sample was further degraded during times between 15 and 45 min. Characterization methods include gel permeation chromatography (GPC), Fourier transform infrared (FTIR) spectroscopy, as well as linear and nonlinear rheology. A reduction of molar mass was detected for all degraded samples by GPC, as well as an increase of the high molar mass fraction of the 1C sample degraded for the longest time. Intrinsic viscosity measurements indicate also a reduction of molar mass with increasing degradation times for both 1C and 2C samples. Thermooxidation is confirmed for 1C and 2C samples by analyzing specific indices in FTIR. Linear viscoelasticity seems to be in general only marginally affected by thermooxidative exposure, while the enhanced strainhardening effect observed in uniaxial extension experiments presents a clear evidence for an increased longchain branching (LCB) content in both 1C and 2C samples. Elongational viscosity data were analyzed by the molecular stress function (MSF) model as well as the WagnerI model, and for both models, quantitative description of the experimental data for all samples was achieved by fit of only one nonlinear model parameter. Timedeformation separability was confirmed for all samples degraded, 1C as well as 2C, for cumulative degradation times of up to 90 min. The characterization by GPC was confronted with the characterization obtained from nonlinear rheology. It can be stated that elongational rheology is a powerful method to detect structural changes due to thermooxidative degradation, especially the formation of enhanced LCB. It has the further advantage that experimental data can be quantified by a single nonlinear model parameter of constitutive equations like the MSF or the WagnerI model.

Ageing, yielding, and rheology of nanocrystalline cellulose suspensions
View Description Hide DescriptionThis paper investigates yielding and flow of nanocrystalline cellulose (NCC) suspensions by combining rheological measurements with light scattering echo (LSecho). The NCC samples are characterized using static and dynamic light scattering as well as polarized optical microscopy coupled with a rotational rheometer. The storage modulus of the NCC suspensions is found to increase with waiting time after shear rejuvenation. The microscopic particle rearrangements of the NCC spindles are followed by LSecho at both short and long waiting times under oscillatory shear flow. We find that the onset of shearinduced irreversible microscopic particle rearrangements, coincide with the strain at which storage and loss moduli cross over in the nonlinear viscoelastic regime identified by the macroscopic yield point of the sample. The yielding transition is found to occur at a higher strain as the frequency of oscillation increases.

Overshoots in stressstrain curves: Colloid experiments and schematic mode coupling theory
View Description Hide DescriptionThe stress vs strain curves in dense colloidal dispersions under startup shear flow are investigated combining experiments on model coreshell microgels, computer simulations of hard disk mixtures, and mode coupling theory. In dense fluid and glassy states, the transient stresses exhibit first a linear increase with the accumulated strain, then a maximum (stress overshoot) for strain values around 5%, before finally approaching the stationary value, which makes up the flow curve. These phenomena arise in wellequilibrated systems and for homogeneous flows, indicating that they are generic phenomena of the sheardriven transient structural relaxation. Microscopic mode coupling theory (generalized to flowing states by integration through the transients) derives them from the transient stress correlations, which first exhibit a plateau (corresponding to the solidlike elastic shear modulus) at intermediate times, and then negative stress correlations during the final decay. We introduce and validate a schematic model within mode coupling theory which captures all of these phenomena and handily can be used to jointly analyze linear and largeamplitude moduli, flow curves, and stressstrain curves. This is done by introducing a new strain and timedependent vertex into the relation between the generalized shear modulus and the transient density correlator.

Defining nonlinear rheological material functions for oscillatory shear
View Description Hide DescriptionMaterial functions underlie our understanding of rheology. They form the descriptive language of rheologists and require clear definitions. Here, it is shown that the definitions of oscillatory material functions depend on how the oscillating input is mathematically referenced, as a sine or cosine. Depending on this seemingly arbitrary trigonometric reference choice, the (3rd, 7th, 11th, etc.) Fourier coefficients of a nonlinear shear response change sign. Additionally, the even harmonic coefficients of a shear normal stress response are transposed. This impacts largeamplitude oscillatory shear (LAOS) characterization in both shear straincontrol (LAOStrain) and shear stresscontrol (LAOStress) modes. It is important to resolve this issue, because it involves the leadingorder nonlinearities and the signs of these higher harmonics convey important information. This paper provides a resolution, in two parts. First, it is shown that the deformationdomain Chebyshev coefficients are immune to the arbitrary trigonometric reference in the time domain, and therefore the Chebyshevcoefficient material functions can be used and interpreted without risk of inconsistency. Second, this paper proposes the convention of referencing to a sine input for straincontrol tests (currently the typical convention) and using a cosine input for stresscontrol (where there is not currently a convention). Finally, clarity is brought to the practical issue of data processing a digital signal, which is required for numerical simulations and every instrument that performs oscillatory characterization.

High shear rheometry using hydrodynamic lubrication flows
View Description Hide DescriptionThis paper presents an analytical solution of Reynolds' equation for the hydrodynamic lubrication flow in a parallel plateonannulus configuration of a conventional rotational rheometer. In this triborheometrical configuration originally proposed by Kavehpour and McKinley [Tribol. Lett. 17, 327–335 (2004)], the shearing surfaces are pushed together by an externally applied normal force. This solution predicts quantitatively how lubrication forces are enlarging the gap h between the surfaces with increasing angular velocity Ω, depending solely on the unavoidable misalignment α of the surfaces. The predicted gap evolution as well as the predicted scaling of the shear stresses σ _{21} ∼ Ω^{2/3} for the hydrodynamic flow regime for Newtonian fluids are experimentally verified with polydimethyl siloxane melts of different viscosities. The analysis is extended to powerlaw fluids, and the consistency of theoretical predictions and experimental observation was shown for a strongly shear thinning polyisobutylene in pristane solution. Finally, it is shown that for a known misalignement α of the triborheometrical configuration the setup can be used to determine the high shear viscosity of an unknown sample, in the current setup up to shear rates of 10^{5} s^{−1}.

Mechanisms for different failure modes in startup uniaxial extension: Tensile (rupturelike) failure and necking
View Description Hide DescriptionThis work reports four different modes of failure during startup uniaxial extension of entangled polymer melts: Capillary, tensile decohesion, shearyieldinginduced necking, and rupture. Emphasis is placed on the identification of the critical condition separating tensile failure from necking and the molecular mechanisms for each type of failures. When Weissenberg number Wi is not vanishingly small, a startup extension terminates in a rupturelike failure where nonuniform extension takes place in a sharply localized manner. This decohesion event reflects the tensile yielding of the entanglement network that occurs due to insufficient intermolecular gripping force to balance the growing intrachain elastic retraction force. At higher rates, the failure mode switches from the tensile decohesion to necking as the entangled melts experience a Cauchy stress level in excess of twice the elastic plateau modulus (2 ). Since the minimum stress to produce shear yielding is on the order of , in these highrate extension tests the melts have the option to undergo shear yielding. Birefringence and particletracking velocimetric observations were carried out to reveal the first evidence for shear deformation as a precursor to the nonuniform extension: The necessarily localized shear yielding initiates nonuniformity of the stretched specimen sometimes termed “necking.”

Mechanical characterization and micromechanical modeling of bread dough
View Description Hide DescriptionThe mechanical behavior of dough, gluten, and starch was studied in an effort to investigate whether bread dough can be treated as a two phase (starch and gluten) composite material. Mechanical loading tests revealed ratedependent behavior for both the starch and the gluten constituents of dough. There is evidence from cryoscanning electron microscopy that damage in the form of debonding between starch and gluten occurs when the sample is stretched. In addition, the Lodge material model was found to deviate from the tension and shear stressstrain test data by a considerably larger amount than from the compression test data. This could indicate that “damage” is dominant along the glutenstarch interface, causing debonding; the latter occurs less under compression loading, but is more prevalent in tension and shear loading. A singleparticle finite element model was developed using starch as a filler contained in a gluten matrix. The interface between starch and gluten was modeled using cohesive zone elements with damage/debonding occurring under opening/tension and sliding/shear modes. The numerical results are compared to experimental stressstrain data obtained at various loading conditions. A comparison of stressstrain curves obtained from 2D and 3D singleparticle models and a 2D multiparticle model led to good agreement, indicating that the singleparticle model can be used to adequately represent the microstructure of the dough studied here.

Microstructure in sheared nonBrownian concentrated suspensions
View Description Hide DescriptionThe shearinduced microstructure in nonBrownian suspensions is studied. The pair distribution function (PDF) in the shear plane is experimentally determined for particle volume fractions ranging from 0.05 to 0.56. Transparent suspensions made of polymethylmetacrylate particles ( in diameter) dispersed in a fluorescent index matched Newtonian liquid are sheared in a widegap Couette rheometer. A thin laser sheet lights the shear plane. The particle positions are recorded and the PDF in the shear plane is computed. The PDF at contact is shown to be anisotropic, with a depleted area in the receding side of the reference particle. The angular position of the depleted zone, close to the velocity axis at low particle concentration, is tilted toward the dilatation axis as the volume fraction is increased. At high concentrations (larger than 0.45), the shape of the PDF changes qualitatively with a secondary depleted area in the compressional quadrant of the main flow and a probability peak in the velocity direction. These experimental results are in good agreement with numerical simulations in Stokesian dynamics where the interaction force between particles has been tuned to reproduce the particle roughness effects.

Transient overshoot extensional rheology of longchain branched polyethylenes: Experimental and numerical comparisons between filament stretching and crossslot flow
View Description Hide DescriptionThis work analyses the highstrain extensional behavior of longchain branched polyethylenes, employing two novel extensional rheometer devices, the filament stretching rheometer and the crossslot extensional rheometer. The filament stretching rheometer uses an active feedback loop to control the imposed strain rate on a filament, allowing Hencky strains of around 7 to be reached. The crossslot extensional rheometer uses optical birefringence patterns to determine the steadystate extensional viscosity from planar stagnation point flow. The two methods probe different strainrate regimes and in this paper we demonstrate the agreement when the operating regimes overlap and explore the steadystate extensional viscosity in the full strainrate regime that these two complimentary techniques offer. For longchain branched materials, the crossslot birefringence images show a double cusp pattern around the outflow centre line (named Wcusps). Using constitutive modeling of the observed transient overshoot in extension seen in the filament stretching rheometer and using finite element simulations we show that the overshoot explains the Wcusps seen in the crossslot extensional rheometer, further confirming the agreement between the two experimental techniques.

Newtonian Poiseuille flows with pressuredependent wall slip
View Description Hide DescriptionThe effect of pressuredependent slip at the wall in steady, isothermal, incompressible Poiseuille flows of a Newtonian liquid is investigated. Exponential dependence of the slip coefficient on the pressure is assumed and the flow problems are solved using a regular perturbation scheme in terms of the exponential decay parameter of the slip coefficient. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to second order. The twodimensional solution reveals the effects of the slip decay coefficient and the other dimensionless numbers and parameters, in the flow. The average pressure drop and the skin friction factor are also derived and discussed.

Shaping complex fluids—How foams stand up for themselves
View Description Hide DescriptionBeing able to model at what point a yield stress material starts to flow under its own weight is of great importance for many practical applications. However, describing the deformation of yield stress fluids under gravity is anything but a simple exercise due to the feedback between the shape of the deposited material and the locally acting stresses. In this article, we concentrate on a specific aspect of this problem: What is the maximum height of a pile of a yield stress fluid which can be obtained under gravity? For this purpose we use the example of liquid foams in which the yield stress is strongly coupled to the bubble size and the liquid fraction. We show that a good agreement between models and experiments is obtained over a wide parameter range in two limiting cases: When the yield stress is either higher or much lower than the normal stresses encountered in the material.

Exploring shear yielding and strain localization at the die entry during extrusion of entangled melts
View Description Hide DescriptionThis work applied a particletracking velocimetric technique to observe the deformation field in the die entry pressuredriven extrusion, motivated by insights gained from previous studies of entangled melts in simple shear. Based on several styrenebutadiene rubbers and a polybutadiene melt, we show that shear yielding takes place to result in (shear bandinglike) strain localization in the die entry. The degree of strain discontinuity is shown to grow with the level of chain entanglement. The critical pressure for shear yielding corresponds to a level of shear stress at a 45° inclined plane that is comparable to the melt plateau modulus, and therefore can be predicted based on our recent understanding of yielding and strain localization in startup shear. The unstable (i.e., timedependent) shear strain localization in the die entry during continuous extrusion at a sufficiently high volumetric throughput or pressure results in extrudate distortion that is often also known as gross melt fracture.