Index of content:
Volume 56, Issue 5, September 2012

Yield stress in magnetorheological suspensions near the limit of maximumpacking fraction
View Description Hide DescriptionThis work deals with the magnetic fieldinduced static yield stress of magnetorheological (MR)suspensions with concentration near the limit of maximumpacking fraction. With this aim, homogeneous suspensions of iron microparticles with 50 vol.% concentration were prepared, and their yield stress measured as a function of the applied magnetic field. In view of the failure of existing models to predict, on the basis of realistic hypotheses, the values of the yield stress of highly concentrated MRsuspensions, we developed a new model. Our model considers that field application induces bodycentered tetragonal structures. Upon shearing, these structuresdeform in such a way that interparticle gaps appear between neighboring particles of the same chain, whereas the approach of particles of parallel chains ensures the mechanical stability of the whole multichain structure. Based on this hypothesis, and using finite element method simulations of interparticle magnetic interactions, our model is able to quantitatively predict the yield stress of highly concentrated MRsuspensions. Furthermore, estimations show that the main contribution to the fielddependent part of the yield stress comes from the change in the permeability of the structures as interparticle gaps are enlarged by the shear.

Extensional rheometry at interfaces: Analysis of the Cambridge Interfacial Tensiometer
View Description Hide DescriptionWhereas devices for measuring the interfacial shear and dilatational rheology are readily available, extensional rheometry at interfaces remains essentially unexplored. However, a setup mimicking a 2D filament stretching rheometer, the Cambridge Interfacial Tensiometer, was proposed for this very purpose [Jones and Middelberg, Chem. Eng. Sci. 57, 1711–1722 (2002)]. In the present work, a framework is presented for analyzing the interfacial flow field in such device for Newtonian interfaces in the presence of Marangoni flows. Based on the dimensionless numbers that govern the interfacial flow field, different dominant flow types can be identified and the sensitivity of the device for measuring the extensional interfacialviscosity is determined. For the flow field to be dominated by extensional deformations, either the Marangoni number or the ratio of dilatational viscosity to shear viscosity should be at least an order of magnitude higher than the Trouton ratio. Using an analysis for Newtonian materials, the contribution to the overall force by the extensional stress can be determined. It should be noted that obtaining these viscosities from the Cambridge Interfacial Tensiometer also requires knowledge of the interfacial shear and dilatational rheology together with the surface pressure isotherm. To test the technique and evaluate the model, experiments on a dipalmitoylphosphatidylcholine monolayer at an airwater interface have been performed and analyzed.

Slow flow of Boger fluids through model fibrous porous media
View Description Hide DescriptionThe flow of viscoelastic fluids through square arrays of parallel cylinders was investigated experimentally by measuring the pressure drop and flow rate and by mapping the velocity field using particle image velocimetry. The arrays had solid volume fractions of 2½%, 5%, and 10% and the fluids were Boger fluids—specifically, two solutions of polyisobutylene in polybutene. With Reynolds numbers less than 0.1, viscosity and elasticity were the only relevant fluid properties.Measurements were made first with a glycerol/water mixture to establish an inelastic baseline. For the three arrays and two viscoelastic fluids, elastic effects started consistently at a Deborah number (De) of 0.5. For De up to 4, the flow resistance due to elasticity was up to several times that due to viscosity, which is comparable to previous findings with much higher volume fractions. But, unlike prior flows, the present ones were steady. Particle image velocimetrymeasurements revealed unitcell velocity profiles, which became progressively asymmetrical as De increased. Also, flow structures related to elasticity were found in the wake regions; they were spaced periodically in the spanwise direction and offset from column to column to create a honeycomblike pattern. Stress analyses indicate that the flow resistance due to elasticity was likely caused more by the normal stresses of N_{1} than by extensional stresses.

Constant force elongational flow of polymer melts: Experiment and modelling
View Description Hide DescriptionCharacterizing elongational behavior of polymer melts in constant elongation rate or constant tensile stress experiments is hampered by the onset of “necking” instabilities according to the Considère criterion: For an elastic filament, homogeneous uniaxial extension is not guaranteed for strains larger than the strain at which a maximum occurs in the force versus extension curve. Although simulations and experiments seem to indicate that in viscoelastic fluids viscosity effects delay the onset of necking to higher strains, integral measurements of elongational viscosities in Meissner or Münstedttype elongational rheometers are often affected by inhomogeneous deformations. A simple means of avoiding the consequences of the Considère criterion consists in operating at constant tensile force, but little attention has been paid so far to constant force elongational rheometry since the pioneering work of Raible et al. [J. NonNewtonian Fluid Mech. 11, 239 (1982)]. Constant force elongation is also of great industrial relevance, since it is the correct analog of steady fiber spinning, as, e.g., exemplified by the socalled Rheotens test. We present experimental data for two longchain branched polyethylene melts obtained in constant elongation rate and constant tensile force modes by use of a Sentmanat extensional rheometer in combination with an Anton Paar MCR301 rotational rheometer. The accessible experimental window and experimental limitations are discussed. Constant force elongation can be subdivided into three distinct deformation regimes: At small deformations (regime 1), constant force elongation is equivalent to creep at constant tensile stress. This is followed by regime 2, which is characterized by a steep increase in tensile stress at roughly constant strain rate, while regime 3 corresponds to elongation of a viscous powerlaw fluid. All three regimes can be modelled quantitatively by a single integral constitutive equation, and a constitutive analysis reveals substantial underestimation of the effective strainhardening effect observed in constant strainrate elongation in comparison to constant tensile force extension, which may be indicative of the effect of necking under constant elongationrate conditions.

The rheology of binary mixtures of highly concentrated emulsions: Effect of droplet size ratio
View Description Hide DescriptionBinary mixtures of highly concentrated emulsions (HCE) with three droplet size ratios and different compositions were prepared. It was found that by the proper selection of droplet size ratio and composition of binary mixtures, the shear modulus,viscosity,yield stress, and yield strain can be dropped lower than mixing rules and even primary HCE. This effect is similar to what is known for dispersions with volume fraction less than 0.7 but has not been described for HCE. For such formulations, the caged mechanism of droplets dynamics is not dominant due to the provided free volume that can be occupied by smaller droplets during flow. This is originated from the increase in maximum closest packing and thus more efficient spatial packing. By studying the scaling behavior of shear modulus and yield stress, the significance of interdroplet interaction was distinguished.

Exact mechanical models of fractional hereditary materials
View Description Hide DescriptionFractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order such that . In this paper, two mechanical models with stressstrain relation exactly restituting fractional operators, respectively, in ranges and are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a sheartype indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of powerlaw type, strictly related to the order of the fractional derivative. Because the critical value 1/2 separates two different behaviors with different mechanical models, we propose to distinguish such different behavior as elastoviscous case with and viscoelastic case for . The motivations for this different definitions as well as the comparison with other existing mechanical models available in the literature are presented in the paper.

Wall slip and flow of concentrated hardsphere colloidal suspensions
View Description Hide DescriptionWe present a comprehensive study of the slip and flow of concentrated colloidalsuspensions using coneplate rheometry and simultaneous confocal imaging. In the colloidalglass regime, for smooth, nonstick walls, the solid nature of the suspension causes a transition in the rheology from Herschel–Bulkley (HB) bulk flow behavior at large stress to a Binghamlike slip behavior at low stress, which is suppressed for sufficient colloidwall attraction or colloidscale wall roughness. Visualization shows how the slipshear transition depends on gap size and the boundary conditions at both walls and that partial slip persist well above the yield stress. A phenomenological model, incorporating the Bingham slip law and HB bulk flow, fully accounts for the behavior. Microscopically, the Bingham law is related to a thin (subcolloidal) lubrication layer at the wall, giving rise to a characteristic dependence of slip parameters on particle size and concentration. We relate this to the suspension’s osmotic pressure and yield stress and also analyze the influence of van der Waals interaction. For the largest concentrations, we observe nonuniform flow around the yield stress, in line with recent work on bulk shear banding of concentrated pastes. We also describe residual slip in concentrated liquid suspensions, where the vanishing yield stress causes coexistence of (weak) slip and bulk shear flow for all measured rates.

Linear viscoelasticity of immiscible blends: The application of creep
View Description Hide DescriptionA new method to characterize the longtime linear relaxation mechanisms of immiscible blends based on creep experiment was developed. Smallamplitude oscillatory shear and incomplete creep/recovery experiments were combined to characterize immiscible blends of polypropylene with dispersed droplets of polystyrene. An experimental protocol was defined such that the full creep compliance function could be obtained while minimizing morphological changes. Dynamic experiments were performed to characterize the shorter time relaxation processes, and creep and recovery measurements were used to detect the longer time portions of the relaxation spectra. Extended retardation and relaxation spectra were constructed by combining these data. It was found that using this technique, very longtime relaxation peaks which were inaccessible with dynamic experiments alone could be detected.

Stochastic simulation of entangled polymeric liquids in fast flows: Microstructure modification
View Description Hide DescriptionWe have modified the fullchain stochastic tube (XDS) model developed by Xu et al. [J. Rheol. 50, 477–494 (2006)] to simulate the rheology of entangled melts and solutions of linear monodisperse polymers. The XDS model, which has a single adjustable parameter that is equivalent to the Rouse time, successfully describes steady and transient shear and normal stress data at low to moderate rates, but the results deviate systematically from experimental data at high rates. The algorithm for reentanglement was revised, and a configurationdependent friction coefficient (CDFC), as originally proposed by Giesekus, was incorporated to account for microstructural change of the tube away from equilibrium. The simulation results from the modified model significantly reduce the deviation from the experimental data in shear, and they also agree well with extensional data for entangled solutions, including an initial −0.5power dependence of the steady extensional viscosity on extension rate. We also applied the CDFC to the molecular model developed by Mead et al. [Macromolecules 31, 7895–7914 (1998)] and obtained improved predictive performance at high deformation rates, reinforcing the idea that there is a structural change in the tube far from equilibrium that accelerates relaxation processes. Finally, noting that molecular models make fundamentally different assumptions about the effect of the deformation on the entanglement density but give essentially equivalent rheological predictions, we explored the effect of the dynamics of the entanglement density by changing the entanglement assumptions in the stochastic model.

Boundary layer in pastes—Displacement of a long object through a yield stress fluid
View Description Hide DescriptionWhen it moves through a yield stress fluid, a solid object continuously reaches and liquefies new solid regions, so that both flow in liquid regions and deformations in solid regions occur. In the present work, we focus on the displacement of a plate through simple yield stress fluids (nonthixotropic). Through force vs velocity and particle imaging velocimetrymeasurements with a detailed analysis of the deformation history, we are able to identify the solid and liquid regions and their respective role in the flow characteristics. It is shown that the displacement of a long object through a yield stress fluid gives rise to the formation of a liquid boundary layer (BL) of uniform thickness at short distance from the leading edge, while the rest of the material remains solid. The original result is that the thickness of this boundary layer, which is of the order of 10 mm, only slightly increases with velocity and does not tend to zero when the velocity tends to zero, in contrast with usual flows of yield stress fluids along solid surfaces. Moreover, it does not change for significant variations of the rheological characteristics of the fluid in its liquid regime. We show that these specific characteristics of the liquid layer are mainly governed by the progressive transition from an elasticsolid to a liquid, starting slightly ahead of the leading edge of the plate.

Jetting behavior of polymer solutions in dropondemand inkjet printing
View Description Hide DescriptionThe jetting of dilute polymer solutions in dropondemand printing is investigated. A quantitative model is presented which predicts three different regimes of behavior depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi < ½), the polymer chains are relaxed and the fluid behaves in a Newtonian manner. In regime II (½ < Wi < L), where L is the extensibility of the polymer chain, the fluid is viscoelastic, but the chains do not reach their extensibility limit. In regime III (Wi > L), the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (13ν), (16ν), and −2ν in the three regimes, respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of monodisperse polystyrene in diethyl phthalate with molecular weights between 24 and 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model.

A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach
View Description Hide DescriptionAn entirely new way of analyzing linear and nonlinear oscillatory material responses is presented. The new quantitative sequence of physical processes (SPP) method views generic oscillatory responses within the FrenetSerret frame as sequences of planar 2D curves embedded in the 3D space defined by the strain, strain rate, and stress axes. Associated with the curve within each socalled “osculating” plane is a binormal vector that wholly determines the orientation of the plane. Physically meaningful information is obtained by calculating the angles between a modified form of the binormal vector and two reference vectors from local information at any point in a cycle. Information from a full period of oscillation is not a requirement of this technique, so that moduli can be calculated from partial or incomplete oscillations. Timedependent phase and complex modulus information, or dynamic moduli information are obtainable throughout a period for arbitrary oscillatory responses. The SPP method is applied to the Bingham plastic model, powerlaw fluids, the Herschel–Bulkley model, and the nonlinear Giesekus model to accustom readers to its function. Application of the SPP method to these nonlinear models necessitates the refinement of some common language, as well as changes to the way results from strain amplitude sweeps are displayed and discussed.

Probing structure in colloidal gels of thermoreversible rodlike virus particles: Rheology and scattering
View Description Hide DescriptionAggregated suspensions of rodlike particles are commonly encountered in soft biological materials and their solidlike response at extremely low volume fractions is also exploited technologically. Understanding the link between the physicochemical parameters such as size, aspect ratio, volume fraction, and interparticle forces with the resulting microstructure and the subsequent rheological response remains challenging. In the present work, suspensions of monodisperse rodlike virus particles, whose surface is modified by grafting with a thermoreversible polymer poly(Nisopropylacrylamide), are used as a model system. The repulsive and attractive contributions to the total interaction potential can be changed independently by varying the ionic strength and the temperature. The effects of these changes on the strength and structure of gels have been studied near the gel transition using a combination of rheological and scattering measurements. Rheological measurements of the near critical gel properties as a function of concentration and ionic strength proved to be more sensitive compared to scattering in resolving the structural differences. A percolating structure can be formed at very low volume fractions, which show a weak dependence on the ionic strength with the anisotropy of the repulsive interactions playing the main role in creating more “open” structures. The intrinsic stiffness of the rodlike particles does not affect the moduli of the gel states very strongly.

Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions
View Description Hide DescriptionIn active, nonlinear microrheology, a Brownian “probe” particle is driven through a complex fluid and its motion tracked in order to infer the mechanical properties of the embedding material. In the absence of external forcing, the probe and background particles form an equilibrium microstructure that fluctuates thermally. Probe motion through the medium distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, , compared to thermal forces, kT/b, defining a Péclet number, , where kT is the thermal energy and b is the characteristic microstructural length scale. Recent studies showed that the mean probe speed can be interpreted as the effective material viscosity, whereas fluctuations in probe velocity give rise to an anisotropic forceinduced diffusive spread of its trajectory. The viscosity and diffusivity can thus be obtained by two simple quantities—mean and meansquare displacement of the probe. The notion that diffusive flux is driven by stress gradients leads to the idea that the stress can be related directly to the microdiffusivity, and thus the anisotropy of the diffusion tensor reflects the presence of normal stress differences in nonlinear microrheology. In this study, a connection is made between diffusion and stress gradients, and a relation between the particlephase stress and the diffusivity and viscosity is derived for a probe particle moving through a colloidal dispersion. This relation is shown to agree with two standard micromechanical definitions of the stress, suggesting that the normal stresses and normal stress differences can be measured in nonlinear microrheological experiments if both the mean and meansquare motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in Pe for and vanishes as for . The expression obtained for stressinduced migration can be viewed as a generalized nonequilibrium Stokes–Einstein relation. A final connection is made between the stress and an “effective temperature” of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a “nonequilibrium equation of state.”