Volume 46, Issue 1, January 2002
Index of content:

Elongational flow of a liquid crystalline polymer solution under a transverse electric field
View Description Hide DescriptionThe behavior of elongation flows for a liquid crystal polymer (LCP) solution under an electric field was theoretically studied using the Doi model. The behavior and the alignment of the nematic phase were found to be strongly dependent upon the mutual interactions between external fields such as the electric and flow fields. The effects of these interactions on the alignment were thoroughly examined in this study. The orientation of the nematic phase exhibits the typical behavior of the Fréedericksz transition where an abrupt change in the orientation occurs at the applied electric field above a threshold value. The results from the normal stress difference on the LCP solution indicate that this difference is attributed to the Maxwell stress effect and varies with respect to the flow direction. A dramatic reduction in this difference was found when the director of the nematic phase is switched from a direction parallel to the flow to a direction perpendicular to the flow.

Categorization of rheological scaling models for particle gels applied to casein gels
View Description Hide DescriptionRennetinduced casein gels made from skim milk were studied rheologically. A scaling model or framework for describing the rheological behavior of gels is discussed and used for classification of the structure of casein gels. There are two main parameters in the model that describe the number of deformable links in a strand and the bendability of the links. In the model at least five types of gel structure can be distinguished. Application of the model to experimental data on rennetinduced casein gels at of 6.0–6.6 and 25 °C shows that they contain straight strands with a large number of deformable links. Analysis of the experimental data of the storage modulus, maximum linear strain and yield stress as a function of the volume fraction results in the same information about the gel structure.

A triaxial rheometer for soft compressible solids
View Description Hide DescriptionThe novel instrument measures the response to compression and shear of a class of materials we call soft compressible solids, examples of which are textile solids and foams. The sample is fixed between two parallel plates, and deformation is controlled by an x,y,z displacement on one plate while the stress is measured on the other. A key component is the triaxial stress transducer, which eliminates edge effects by only measuring the stress on an interior region of the plate. The edge effects and associated measurement errors are analyzed by simple isotropic elasticity theory, and compared to measurements done on chloroprene rubberfoam.

A Rouselike model of liquid crystalline polymer melts: Director dynamics and linear viscoelasticity
View Description Hide DescriptionWe describe the linear viscoelastic response and dynamics of director orientation in monodomains of unentangled nematic liquidcrystallinepolymers(LCPs), using a Rouselike model appropriate to polymers with a significant degree of backbone flexibility, such as segmented mainchain thermotropic LCPs and sidechain LCPs. We consider the limits of: (i) mainchain directed polymers, for which the polymer backbone is extended along the director, with no hairpins, but executes a random walk in the plane perpendicular to the director, and (ii) anisotropic Gaussian polymers, for which the backbone executes an anisotropic threedimensional random walk, as for mainchain LCPs with many hairpins and many sidechain LCPs. The analysis is based upon the assumption that, in fluids of such polymers, the distribution of nematogen orientations relaxes rapidly to a state of local equilibrium, via relatively rapid local rearrangements, which follows the slower evolution of the backbone conformation. We describe the linear response in terms of five independent dynamic moduli, which are time or frequencydependent generalizations of the Leslie viscosities. We find that directed chains generally tumble in steady shear flow, and that anistropic Gaussian chains flow align. In transient experiments, the coupling between director rotation and the relaxation of backbone conformations is found to lead to an overshoot of the director orientation following a step shear, and a phenomenon of “director recoil” in response to the temporary application of a magnetic aligning field.

Investigation of the solid–liquid transition of highly concentrated suspensions in oscillatory amplitude sweeps
View Description Hide DescriptionSuspensions of quasimonodisperse polymethylmethacrylate spheres with mean diameters of 4.7 and 3.1 μm, dispersed in a lowmolecularweight polydimethylsiloxane, were characterized using oscillatory shear amplitude sweeps. Thereby, the solid volume concentration was varied. The influence of the sample preparation, the mode of the experiment (controlled shear rate, controlled shear stress), and the parameters of the amplitude sweep such as logarithmic ramp time, measurement time, and frequency were investigated. The logarithmic ramp and the measurement time were found to be the substantial factors which especially influence the experimental results at low shear stress amplitudes. The frequency has an effect only at higher shear stress amplitudes where the material behaves linearly again. All suspensions showed a Hookean solid behavior at low shear stress amplitudes and a Newtonian fluid behavior at high shear stress amplitudes. In the transition range between the Hookean and the Newtonian behavior the analysis of the primary shear straintime signal showed that the nonlinear effects were coupled with the occurrence of higher odd harmonics.

Ratedependent plasticity models derived from potential functions
View Description Hide DescriptionIn this paper we describe a method for the derivation of the constitutive behavior of ratedependent materials from two potential functions. Once the potentials have been specified an entirely standardized procedure can be adopted to derive the response, and no additional assumptions are necessary. There is some freedom in the choice of which potential functions to specify: the first is one of four energy potentials, and the second, which specifies the dissipative behavior, is either the force or flow potential. The method allows alternative models to be quickly compared and set within an appropriate hierarchy. This work extends previous work on rateindependent materials, for which the force potentials take a special form. We illustrate the method with four examples of different viscoplastic models.

Rheological behavior of hydrophobically modified hydroxyethyl cellulose solutions: A linear viscoelastic model
View Description Hide DescriptionThe rheological behavior of hydrophobically modified hydroxyethyl cellulose (HMHEC), an associative thickener, was studied and compared with that of hydrophobically modified ethoxylated urethanes (HEURs) and nonassociative celluloses. In contrast to HEURs, a simple Maxwell model does not fit the linear viscoelastic behavior of HMHEC. Differences are attributed to the stiffness and comb structure of HMHEC. A generalized Maxwell model with a logarithmic distribution of relaxation times is proposed, and another parameter that includes Rouselike relaxation is added to fit behavior at high frequencies. Four parameters are needed to describe HMHEC viscoelasticity: a mean relaxation time, its corresponding standard deviation, σ; a plateau modulus, and a viscosity at infinite frequency, Satisfactory fitting is obtained for all concentrations and temperatures in the range of frequencies studied. The sharp increase of with concentration indicates looptobridge transitions. Temperature does not influence since the reduction in the number density of elastically effective chains caused by Brownian motion masks the direct effect of temperature. The dependence of on temperature follows the Arrhenius equation, as does the relaxation time of HEURs, but it does not change with concentration, presumably because the comb structure of HMHEC prevents the formation of long superchains.

Slip at polymer–polymer interfaces: Rheological measurements on coextruded multilayers
View Description Hide DescriptionPolypropylene (PP) and polystyrene (PS), with closely matched viscosity, were coextruded into 8, 32, and 64 alternating layers. The apparent steady shear viscosity of these multilayer samples was measured with an inline slit rheometer and with a parallelplate rheometer. In both cases the apparent viscosity decreased with the number of layers providing strong evidence for interfacial slip. The velocity difference across the interface (interfacial slip velocity) versus shear stress, was calculated from the apparent viscosity measurements. showed sigmoidal behavior: a region of very low slip at low shear stress, a strongly increasing region at followed by a linear region These data could be fit with a modified Ellis model. The same function fit the different number of layers and both slit and parallelplate data indicating is a material property of the PP/PS pair. Slip was also observed in PS/PMMA (polymethyl methacrylate) and (amorphous nylon) pairs. Addition of a premade diblock copolymer to the PP/PS pair was able to suppress the interfacial slip but only after enough time for sufficient block copolymers to diffuse to the interfaces. The in situ formed graft copolymer of maleated PP with at the interface of the pair directly suppressed the slip. Our results are in qualitative agreement with the theory of Furukawa (1989) and de Gennes (1992), which predicts fewer chain entanglements near the interface between two immiscible polymers, and thus a narrow region (∼ interfacial width) with lower viscosity. This lower viscosity is the cause of apparent interfacial slip. Goveas and Fredrickson (1998) extended these ideas to calculate the slip in a symmetric bilayer where both bulk and interface are Newtonian. Their results are in qualitative agreement with our observation but predict a stronger slip. Our results also indicate that the anomalously low viscosity reported by a number of researchers for immiscible polymer blends is due to interfacial slip. Blends of PP and PS show similar negative viscosity deviations to those reported but only at No negative deviations were found for linear viscoelastic (lowstress) measurements.

Invariantbased optimal fitting closure approximation for the numerical prediction of flowinduced fiber orientation
View Description Hide DescriptionAn invariantbased optimal fitting (IBOF) closure approximation is proposed to approximate the fourth order structural orientation tensor in terms of the second order structural orientation tensor and its invariants. IBOF adopts the most general expression of a full symmetric fourth order tensor using a symmetric second order tensor and an identity tensor. The six coefficients that appear in the expression are represented by polynomial expansions in terms of the second and third invariants of the second order orientation tensor, similar to in the natural (NAT) closure approximation. Unknown parameters in the polynomial expansions are determined by following the method introduced by an orthotropic fitted closure approximation, which is a leastsquare optimization fitting technique of various flow data generated from solutions of the probability distribution function. IBOF is a hybrid of the NAT and the orthotropic fitted approximations, which are types of eigenvaluebased optimal fitting (EBOF) closure approximations. The accuracy of IBOF is as good as EBOF, and IBOF requires less computational time to obtain a solution. Also, IBOF does not suffer from the singularity problems encountered in using the NAT approximations.

Cone angle effects, radial pressure profile, and second normal stress difference for shearthickening wormlike micelles
View Description Hide DescriptionMany dilute surfactant solutions containing long, thin, wormlike micelles undergo a shearthickening transition at which the apparent viscosity jumps to a much higher value due to the formation of shearinduced structures. However, the behavior of the normalstress differences and has not been studied at the lowshear rates and shear stresses (<0.1 Pa) at which shear thickening occurs in most of the commonly studied systems, such as aqueous solutions of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSS). For dilute equimolar solutions of CTAB/NaSS, the validity of measurements of the shear flow properties η, and via coneandplate rheometry is assessed by systematically varying the cone angle, and by measuring the pressure profile during coneandplate flows. The dependence on the cone angle of the apparent viscosity value is consistent with a stratified fluid structure, as shown to occur in Couette rheometers by Hu and coworkers [Hu, Y. T. et al., J. Rheol. 42, 1209–1226 (1998)]. However, and values show no obvious dependence on cone angle, and the occurrence of flow stratification is surprisingly difficult to detect from the pressure profile. As the shear rate is increased, the measured pressure profiles are suggestive of a gradual transition from viscometric to nonviscometric flow. By combining the results presented here with earlier results by Huang and coworkers [Huang, C.M. et al., in Proceedings of the XII International Conference on Rheology, edited by A. AitKadi et al. (Canadian Rheology Group, Quebec City, 1996)], we conclude that the same wormy micellesolution exhibits at least two flow transitions that might be described as “shear thickening.” In the shearrate range of viscometric coneandplate flows, the measured normalstress ratio for dilute solutions of CTAB/NaSS wormy micelles is similar to the value observed for moderately entangled solutions of synthetic polymers.

Molecular weight distribution from viscoelastic data: The importance of tube renewal and Rouse modes
View Description Hide DescriptionRheological models based on molecular dynamics (as opposite to empirical relationships) are now preferred to link the molecular weight distribution (MWD) of linear polymers to their rheological properties. These models incorporate the double reptation concept, which represents the relaxation modulus as an integral over the molecular weight distribution. We propose a method that incorporates a detailed modeling of all the relevant relaxation processes, including Rouse fast and longitudinal modes and glassy relaxation. In addition, we take into account the effect of polydispersity on the relaxation times for reptation, i.e., “tube renewal.” In order to demonstrate the importance of these features of our technique, we compare it with one involving the direct inversion of the double reptation integral without accounting for tube renewal and additional relaxation processes. To invert the relaxation modulus in terms of the molecular weight distribution, one must either solve the illposed problem using an efficient numerical algorithm or postulate a function to describe the MWD. The second approach is more robust and less sensitive to noisy data, but one must assume the form of the MWD a priori. We present a procedure for selecting this function and use it to compare the two approaches to inverting a model. Data for several binary blends and commercial polymers are analyzed using both approaches. We conclude that the more detailed technique is necessary when the MWD is broad or when there is a significant amount of lowmolecular weight material present.

Simple shear and small amplitude oscillatory rectilinear shear permeation flows of cholesteric liquid crystals
View Description Hide DescriptionA model of rodlike cholesteric liquid crystals subjected to slow steady simple shear and low frequency small amplitude oscillatory shear flow is formulated and applied to permeation flow, also known as Helfrich permeation flow [Helfrich (1969, 1970)], when the cholesteric helix is oriented along the velocity direction and the orientation distortions retain the original planar chiralstructure. In permeation flow the elastic forces exactly balance viscous forces. The presence of a small internal length scale (pitch of the helix) leads to boundary layer behavior in the velocity and orientation fields at any shear rate and at any driving frequency. The thickness of the boundary layer region is of the order of the pitch. The apparent viscosity is larger than typical nematic viscosities by a factor proportional to the ratio of the gap thickness to the pitch length. The effect is due to the Ericksen elastic stress. The response of cholesterics to small amplitude oscillatory shear corresponds to a purely viscous material. The outofphase stress component vanishes because the viscous force is exactly cancelled by the elastic force. In the terminal region, the loss modulus exhibits a classical frequency ω dependence but its magnitude is much greater than for other cholesteric flows by a factor proportional to the ratio of the gap thickness to the pitch length.

Laser Doppler velocimetry measurements of particle velocity fluctuations in a concentrated suspension
View Description Hide DescriptionRecent statistical constitutive models of suspensions of neutrally buoyant, noncolloidal, solid spheres in Newtonian fluids suggest that the particles migrate in response to gradients in “suspension temperature,” defined as the average kinetic energy contained in the particle velocityfluctuations. These models have not yet been compared systematically with experimental data. In addition the “temperature'’ models assume isotropic particle velocityfluctuations, since the suspension temperature is given as a scalar. However, highly anisotropicparticle velocityfluctuations have been observed experimentally, which suggests that a suspension temperature tensor is more realistic. We use laser Doppler velocimetry to measureparticle velocityfluctuations arising from interparticle collisions in a concentrated suspension under nearly homogeneous shear flow in a narrowgap concentric cylinder Couette device. We compare the relative sizes of the fluctuating velocity components and determine the variation of each component with particle volume fraction and shear rate. The data indicate that the suspension temperature is anisotropic. The flow direction component is overwhelmingly the largest at every concentration and shear rate, followed in order of magnitude by the neutraldirection and velocitygradientdirection components. Additionally, over the region of the flow accessible to measurement, each fluctuating velocity component demonstrates a distinct variation with shear rate and particle volume fraction. Finally, we explain the observed anisotropy and variation of the suspension temperature in terms of the dynamics of interparticle interactions.

Rheological properties and adhesive failure of thin viscoelastic layers
View Description Hide DescriptionMethods have been developed for measuring the linear viscoelastic properties of thin adhesive layers, and for determining the stress intensity factor characterizing the driving force for adhesive failure. Both methods involve bringing a hemispherical indenter in contact with the adhesive layer while simultaneously monitoring the load, displacement, and radius of contact between the indenter and the adhesive. Dynamic moduli for the adhesive layer are obtained by oscillating the indenter, and the adhesive properties are obtained by pulling the indenter completely out of contact with the adhesive layer. Existing theories of viscoelastic contact mechanics were extended to account for the fact that the adhesive layer thickness is not substantially larger than the contact radius, as is generally assumed. A variety of correction factors were introduced that depend on the ratio of the contact radius to the adhesive layer thickness. These methods were applied to a model adhesive based on an acrylic triblock copolymer. Determination of the timedependent creep and relaxation functions for this material was simplified by the powerlaw frequency response of the dynamic moduli. The large stress intensity factors observed were related to a Dugdale model of the cohesive zone at the contact edge.

Transient response of concentrated suspensions after shear reversal
View Description Hide DescriptionWe have examined the transient stress response under shear flow of concentrated suspensions of nonBrownian spheres. We focused on the experiment where the shearing is momentarily stopped and restarted in the opposite direction. We found that the normalized stress recovery curves for different values of the initial and subsequent shear rates could be collapsed quite well if plotted against the strain. This behavior agrees with the basic concept that the transient stress behavior is a function only of the imposed strain, as predicted by some recent constitutive models of concentrated suspensions. We also found that the transient behavior of the normal stress difference showed similar data collapse. Further, there appeared to be little qualitative difference in the behavior of particulate systems with a high degree of size monodispersity and those more polydisperse.

Nonlinear rheology of hyperbranched polyisobutylene
View Description Hide DescriptionThe nonlinear shear rheology of a hyperbranched polyisobutylene (PIB) with narrow molecular weight distribution was compared to that of a polydisperse linear PIB. After adjusting the respective measurementtemperatures to yield equal shear viscosities, the rheology was found to be quite similar for the two polymers, notwithstanding their markedly different structures. These similarities persisted in capillary extrusion experiments at moderate shear rates, on the compounds reinforced with carbon black. However, at higher shear rates, the linear PIB exhibits a greater elastic response, with consequently larger extrudate swell.

Transient normal stress response in a concentrated suspension of spherical particles
View Description Hide DescriptionThe transient normal force response in a concentrated suspension of spherical particles upon startup of shear, following a period of rest, was found to depend on the direction in which shear was restarted. When shear was restarted in the same direction, the normal force signal rapidly grew to its positive steadystate value. However, when shear was restarted in the opposite direction, the normal force signal was initially negative and decreased, within the response time of the instrument, to a negative minimum, from which it gradually increased, passing through zero, to its positive steadystate value. This is believed to be the first experimental confirmation of this phenomenon, which had been suggested by the numerical simulations of previous investigators.