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The nonlinear viscoelasticity of a dilute suspension of Brownian spheroids subject to an oscillatory shear deformation is calculated numerically. This is achieved by determining the suspension microstructure, parameterized via the orientation distribution function. Specifically, the long-time periodic orientation distribution function is obtained via a numerical solution to the Fokker–Planck equation by combining a finite-difference approximation in space with a Fourier series in time. From an ensemble average of the particle stresslet, weighted by the orientation distribution function, the entire stress tensor and relevant birefringence parameters, namely, the average orientation angle and linear dichroism, are calculated; this is done over a range of the Weissenberg number (W i) and the Deborah number (D e), or dimensionless strain-rate amplitude and oscillation frequency, respectively. Detailed calculations are presented for prolate spheroids of aspect ratio r = 20 ; however, our methodology is general and can be applied to spheroids of arbitrary aspect ratio. We provide results in four viscoelastic regimes: linear viscoelastic (W i ≪ 1), quasilinear viscoelastic (W i > 1 and W i / D e ≪ 1), quasisteady viscoelastic (D e → 0), and finally, the nonlinear viscoelastic regime (W i ≳ 1 and W i / D e ≳ 1), which is our main emphasis. In this last regime, where the nonlinear and unsteady viscoelasticity of the material is probed, multiple overshoots are observed in the shear stress and first normal stress difference. The mechanistic origin of these overshoots can be understood from the periodic orientation dynamics (i.e., Jeffery orbits) of a particle under steady shear in the absence of Brownian rotation (W i → ∞). This is achieved by simultaneously analyzing the microstructure, shear stress, first normal stress difference, and birefringence parameters specifically at W i = 20 and D e = 1. For these values of W i , D e , and r , the period of a Jeffery orbit is comparable to the period of an oscillation cycle, allowing sufficient time for a single Jeffery orbit (and subsequent overshoot) to occur during an oscillation cycle. We contrast this behavior to recent work by Khair [J. Fluid. Mech. 791, R5 (2016)] on nearly spherical particles, for which many more overshoots are observed during an oscillation cycle, due to the shorter period of the Jeffery orbit. We briefly provide results for oblate spheroids of aspect ratio r = 0.05 and compare to the results for r = 20. Finally, we comment on the relevance of the present micro-mechanical analysis to the nonlinear viscoelasticity of other complex fluid materials. [ABSTRACT FROM AUTHOR]

We present new dynamic rheological tests of human blood that motivate an improved model for the thixotropic shear rheology of human blood. Unidirectional large amplitude oscillatory shear (UD-LAOS) is proposed as a dynamic test relevant for understanding in vivo arterial pulsatile blood flow, and data are presented for two healthy donors studied previously using more traditional steady and step-rate experiments. The model analyzes the overall extra stress of the system in two components. A thixotropic component is represented by a structure-kinetics model coupled with a stress expression containing both viscoelastic and thixotropic elements to account for the presence of linear aggregates of red blood cells, known as rouleaux, which form at low shear rates. Another component is viscoelastic, described through an extend White–Metzner approach. It corresponds to the stresses that arise due to the isolated red blood cells, which deform at high shear rates. The combined model is fit to experimental steady shear and UD-LAOS data for two healthy donors and is subsequently used to predict the stress response of the blood sample to UD-LAOS experiments over a broad range of strain amplitudes and frequencies. Comparison to the previous models for transient blood rheology shows a significantly improved fit over a range of physiologically relevant flow conditions. In addition, this analysis demonstrates the usefulness of UD-LAOS tests with regards to understanding the microstructural evolution in blood under transient flow. [ABSTRACT FROM AUTHOR]

The nonlinear stress and microstructural response of a colloidal hard sphere suspension undergoing medium and large amplitude oscillatory simple shear have been studied using Accelerated Stokesian dynamics. The goal is to understand how nonlinearity arises and to link the structural effects to the resulting suspension stress. The imposed shear is given by the time-dependent rate γṀ(t) = γṀ0eiαt. Most results are shown for a hard-sphere suspension at a particle volume fraction ϕ = 0:4. These are freely flowing conditions far from either glassy or jammed conditions, but the concept of the particle cage from glass dynamics is used. The cage is defined here in a statistical manner as the surface of elevated nearest neighbor probability, a sphere at contact for equilibrium. The cage concept is used in interpreting the microstructural deformation: For sufficiently small strain amplitude γ0, the cage deforms negligibly due to flow and the suspension remains in the linear response regime, but this is found to require γ0 < 0:01 at ϕ = 0:4, as shown by a spectral decomposition of the microstructure in time, which discriminates rigorously between linear and nonlinear deformation. At larger γ0, termed medium amplitude and large amplitude in other studies, the material response is nonlinear. To preface the large amplitude oscillatory shear analysis, we use linear viscoelasticity theory to compare stress fluctuations at equilibrium to results obtained at finite Péclet number Pe and small γ0, as well as available experimental data and theoretical predictions; Pe = 6πηγṀ0a3/kT is the ratio of hydrodynamic to Brownian forces, where η is the viscosity of the suspending liquid, γṀ0 is the shear rate amplitude, a is the particle radius, k is the Boltzmann constant, and T is the absolute temperature. The shear stress σxy and the normal stress differences N1 and N2 are analyzed under oscillatory shear at amplitudes 0:01 ⩽ γ0 ⩽ 3:6 forarange of Pe. (The frequency α is related to Pe through α Ṁ0 = α α0 and the nondimensional frequency is given by the Deborah number De =Pe/α0 = 6πηγṀ0a3/kT .) Pipkin diagrams are shown for σxy, N1 and N2. When hydrodynamic forces dominate the flow of the suspension, the complex viscosity /η*/ has a nonmonotonic dependence on α 0, and Fourier-transform rheology shows the nonlinearity of the stress response to be maximized at an intermediate strain amplitude that depends on Pe. The elastic and viscous behavior of the suspension, as determined by a Chebyshev polynomial decomposition, is distinctly different for small and large Pe. The influence of the microstructure on the normal stress differences is discussed, noting that N1 is significant only when angular distortion of the microstructure is present, whereas N2 is formed with an accumulation of pair correlation at contact even at low oscillation amplitude. [ABSTRACT FROM AUTHOR]

The correlation between interfacial interparticle forces, microstructure, and rheology of particle laden interfaces is characterized for a system of polystyrene particles at an air/water interface by using both aqueous salt concentration and particle surface concentration as control parameters. Characterizing linear, interfacial shear viscoelastic moduli and microstructure simultaneously using a custom imaging system attached to a double wall ring interfacial rheometer allows the relationship between these properties to be evaluated. Interfacial viscoelastic moduli magnitude is found to be determined locally by the degree of restricted particle motion, which is dictated to both by interparticle attraction due to capillarity and severity of caging caused by local microstructure. However, macroscale rheological behaviors, such as elasticity and yield, are tied to the mesostructural organization of local microstructure. Large domains of aligned hexagonal packed particles create elastic interfaces; when these domains begin to breakup, and smaller domains can flow on the interface, a transition to viscous like behavior is observed. [ABSTRACT FROM AUTHOR]

The rheology and shear-induced structures of a series of self-assembled surfactant wormlike micelles (WLMs) with varying levels of branching are measured using rheo- and flow-small angle neutron scattering (SANS). The degree of branching in the mixed cationic/anionic surfactant (cetyltrimethylammonium tosylate/sodium dodecyl benzene sulfonate) WLMs is controlled via the addition of the hydrotropic salt sodium tosylate and verified by cryo-transmission electron microscopy. The linear viscoelasticity of the low salt (linear) micellar solutions is well described as an extended Maxwell (Oldroyd-B) fluid, and samples exhibit shear banding under steady-shear flow. The linear viscoelasticity of more highly branched solutions deviates from Maxwellian behavior, where the plateau in G' gradually increases in slope with increasing salt content. The higher salt solutions exhibit a shear thinning regime, followed by a shear thickening regime at high shear rates. Micelle segmental alignment in the flow-gradient plane is a nonmonotonic function of salt level and radial position. Spatially resolved measurements of the segmental alignment corroborate shear banding in the linear WLMs, and the absence of shear banding with branching. Rheo-SANS measurements show that the onset of shear thickening at high rates corresponds to a structural transition. The results of this study link micellar microstructure and topology to the measured shear rheology of WLM solutions. [ABSTRACT FROM AUTHOR]

We present a novel approach for using large-amplitude oscillatory shear flow experiments (LAOS) to determine--in a simple, direct, and robust manner--the mechanical behavior of materials that possess a microstructure and may exhibit solidlike, liquidlike, viscoelastic, viscoplastic, and/or thixotropic behavior. As the stress amplitude and frequency are independently varied, two classes of motion are observed: (i) structure-changing motions, characterized by a nonsinusoidal response, when the stress amplitude is large enough to cause microstructural changes and the frequency is of the order of the reciprocal of the time scale of microstructural changes; and (ii) constant-structure motions, characterized by a sinusoidal response, when either the stress amplitude is not large enough to cause microstructural changes or the stress amplitude is large enough to cause microstructural changes but the frequency is much larger than the reciprocal of the time scale of microstructural changes. For a commercial hair gel, we confirm experimentally the existence of these two classes of motions, which was theoretically predicted by de Souza Mendes and Thompson [Rheol. Acta 52(7), 673-694 (2013)]. In contrast to the presently available LAOS analyses, which focus on the structure-changing motions, our methodology--quasilinear LAOS or QL-LAOS--relies for the most part on data obtained from constant-structure motions. This fact simplifies dramatically the experiments and the analysis and provides material functions the physical meanings of which are quite evident. [ABSTRACT FROM AUTHOR]

Nonlinear oscillation shear has become an important method to study the complex fluids. However, choosing the suitable material functions is not as simple as that in linear viscoelasticity. A framework is suggested in this work to account for the stress-strain and stress-strain rate relationship based on the concept of mean stress and mean strain (rate) in the Lissajous curves. The applications of such framework in an imposed oscillatory shear strain and an imposed oscillatory shear stress are clearly demonstrated. The intracycle nonlinear modulus and viscosity are defined from the slope of the stress-strain curve and the stress-strain rate curve, respectively. The intercycle nonlinear behaviors are obtained from the strain (rate) amplitude dependence of the zero mean strain (rate) modulus or viscosity. We justify the strain-hardening/softening and shear-thickening/thinning behaviors of nonlinear moduli and viscosities by using typical constitutive models like Bingham model and the Maxwell model. It is found that the modulus (viscosity) defined from the stress-mean strain (rate) curves is the most physical reasonable quantity. In addition, we apply the new analysis method to two yield stress fluids, which reveals critical balance between aging and shear rejuvenation. [ABSTRACT FROM AUTHOR]

The interrelations between microstructure and rheology of melt compounded poly(ethylene-co-octene) (EOC) based nanocomposites containing low amounts of silica (SiO2) nanoparticles were studied. In the presence of a maleated EOC compatibilizer, hydrogen bonds are established between the silanol groups located on the surface of the particles and the succinic anhydride functionality of the compatibilizer, resulting in improved filler dispersion during compounding and the formation of a bound layer of polymer surrounding the particles. This layer alters the interface between the bulk polymeric matrix and the particles, influencing the linear viscoelastic (LVE) response. The compatibilized composites exhibited a more stable response in time sweeps and a higher critical strain for the onset of nonlinearity, compared to their noncompatibilized counterparts. Superposition of small angle oscillatory shear and creep/creep recovery experiments revealed enhancements in the LVE functions in the absence of a compatibilizer, which are attributed to the increased hydrodynamic effect due to increased propensity for particle aggregation, and to the direct interactions between the polymer chains and the surface of the filler. On the contrary these effects were moderated in the case of the compatibilized composites, due to the presence of the bound layer of polymer surrounding the particles. [ABSTRACT FROM AUTHOR]

Two tube-based molecular models, the hierarchical 3.0 model and the branch-on-branch model were evaluated for their abilities to predict the behavior of a series of polydisperse, H-shaped, 1,4-polybutadienes. The samples had been synthesized using a novel technique designed to suppress the generation of high molar mass by-products. While size exclusion chromatography data indicated that the samples were monodisperse, low molar mass by-products were later revealed by temperature gradient interaction chromatography. Viscoelastic data were obtained at temperatures ranging from -75 °C to 25 °C, and the samples were found to be thermorheologically simple. Sensitivity and uncertainty analyses revealed that among the model parameters, the value of plateau modulus has the strongest effect on model predictions. As molecular models improve, it will become ever more essential to evaluate them using accurate data on materials whose microstructures have been reliably established. This is especially important for materials that are structurally polydisperse. [ABSTRACT FROM AUTHOR]

A series of controlled microstructure poly(lactide) (PLA) samples were synthesized using a novel chiral dinuclear indium catalyst capable of living polymerization of lactide. PLAs with different ratios of L- to D- monomer ratios of 100:0, 90:10, 75:25, 50:50, and 0:100 were investigated. The relationship between intrinsic viscosity and the absolute molar mass distribution of the samples obtained by light scattering gel permeation chromatography in tetrahydrofuran gives [η] = 0.014 + 0.75 Mw, a scaling law of typical coil dimensions of linear macromolecules in good solvent. The melt rheological study includes determination of zero-shear viscosity and its relationship with the molecular weight, the relaxation spectrum, and its relation with molecular weight characteristics, as well as plateau modulus and other important rheological parameters that are helpful in predicting the linear viscoelasticity of PLA. Emphasis is placed on the uniaxial melt behavior of these polymers. At low temperatures, significant strain hardening is observed, which gradually disappears with an increase in temperature and decrease of Hencky strain rate. The K-BKZ constitutive equation is used to model the experimental data. It is concluded that in spite of their linear structure, PLAs exhibit strain hardening which is not due to strain-induced crystallization, and it is solely due to the dynamics of molecular relaxation. [ABSTRACT FROM AUTHOR]

This paper analyzes the effect of flow history on the linear viscoelastic properties of suspensions of multiwalled carbon nanotubes in an epoxy as well as the evolution of the suspension microstructure under small deformations for different concentrations and temperatures. The effect of the flow history on the microstructure is interpreted in the light of the variation of the rheological percolation threshold, which is shown to increase with the pre-shear rate. After cessation of the shear flow, the storage modulus increased with time revealing the build-up of the structure. By decreasing the pre-shear rate, the resulting storage modulus increased and the relative increase of the storage modulus with respect to the pre-shear rate was more pronounced at lower concentrations. The rate of increase in the storage modulus drastically increased with the concentration and temperature, while its variation with respect to the pre-shear rate depended on the concentration. In dilute suspensions, it decreased dramatically by increasing the rate of pre-shear, revealing a slower structure build-up while it remained almost intact in more concentrated suspensions. The increase in kinetics of structure build-up with temperature suggests the importance of Brownian forces in the absence of flow regardless of concentration or applied pre-shear rate. [ABSTRACT FROM AUTHOR]

A two-phase microstructural constitutive relation is combined with the thin-shell model for the simulation of blown film extrusion. This combination includes equations for momentum conservation, flow-enhanced crystallization, viscoelasticity, and bubble-tube cooling. Consistent with typical blown film operation, the simulations set the bubble air mass and take-up ratio as constants, while treating the machine tension and inflation pressure as dependent variables. In all the simulations performed, the high degree of crystallization, and subsequent system stiffening, located the freeze-line naturally. Bubble geometry, temperature, and crystallinity were fitted to experimental data using material and kinetic parameters mostly obtained by a simpler quasi-cylindrical model. The thin-shell microstructural model was compared to a modified quasi-cylindrical model. The models predict similar responses to operational changes, including axial locked-in stresses at the freeze-line, but have significant differences in the locked-in stresses in the transverse direction, which were attributable to the use of different momentum equations. Either model can be used for data fitting, parameter estimation, and prediction of most process responses to upsets. [ABSTRACT FROM AUTHOR]

We study the motion of a Brownian probe particle subjected to a small amplitude oscillatory external force and immersed in a colloidal dispersion, as a theoretical benchmark for particle-tracking microrheology experiments. The application of an external force on the probe drives the microstructure of the dispersion out of equilibrium; opposing this is the Brownian diffusion of the probe and colloidal “bath” particles. The degree to which the microstructure is driven away from equilibrium is given by the nondimensional external force on the probe, or Péclet number, Pe. The nonequilibrium microstructure of the dispersion is calculated for small departures from equilibrium, i.e., to first order in Pe, and to leading order in the bath particle volume fraction, accounting for excluded volume and hydrodynamic interactions between particles. The nonequilibrium microstructure is used to calculate the average velocity of the probe, from which one may infer the complex microviscosity (or modulus) of the dispersion via application of Stokes drag law. The microviscosity is computed over the entire range of oscillation frequencies, thereby determining the linear viscoelastic response of the dispersion. After appropriate scaling, our results are in qualitative agreement with traditional (macro-) rheology studies, suggesting that oscillatory-probe microrheology can be a useful tool to examine the viscoelasticity of hard-sphere colloidal dispersions and perhaps other complex fluids. [ABSTRACT FROM AUTHOR]