Large Amplitude Oscillatory Shear Flow Research Articles

Normal Stress Differences of Human Blood in Unidirectional Large-Amplitude Oscillatory Shear Flow

Abstract This work analyzes normal stress difference responses in blood tested in unidirectional large-amplitude oscillatory shear flow (udLAOS), a novel rheological test, designed for human blood. udLAOS mimics the pulsatile flow in veins and arteries, in the sense that it never reverses, and yet also nearly stops once per heartbeat. As for our continuum fluid model, we choose the Oldroyd 8-constant framework for its rich diversity of popular constitutive equations, including the corotational Jeffreys fluid. This work arrives at exact solutions for normal stress differences from the corotational Jeffreys fluid in udLAOS. We discover fractional harmonics comprising the transient part of the normal stress difference responses, and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. More generally, predictions from the Oldroyd 8-constant framework are explored by means of the finite difference method. Finally, the generalized versions of both the Oldroyd 8-constant framework and the corotational Jeffreys fluid are employed to predict the nonlinear normal stress responses for the model parameters fitted to udLAOS measurements from three very different donors, all healthy. From our predictions, we are led to expect less variation in normal stress differences in udLAOS from healthy donor to donor, than for the corresponding measured shear stress responses.

Delay of re-entanglement kinetics by shear-induced nucleation precursors in isotactic polypropylene melt

Rheological measurements were carried out to in-situ monitor the re-entanglement process of large amplitude oscillatory shear flow (LAOS) modified partially disentangled isotactic polypropylene (i-PP) melt. The characteristic entanglement recovery time (τent) was essentially longer than the average reptation time (τD) of fully entangled melt. At temperatures above 200 °C, the Arrhenius temperature dependence of τent and τD are the same, displaying a normal chain diffusion-controlled mechanism with flow activation energy of 41.4 kJ/mol. However, when the temperature is lower than 200 °C, τent is unexpectedly longer than expectation extrapolated from high temperatures, and a much higher activation energy of 98.6 kJ/mol is observed for the re-entanglement process. Based on our understanding, the re-entanglement process of shear-induced disentanglements in i-PP melt was postponed by the existence of quasi-ordered clusters created by shear at relatively low temperatures and their dissipation turns to be the rate-determining step for the whole recovery. Moreover, morphological study under polarized optical microscope showing much higher nucleation density which originates from the flow-induced precursors corroborates our hypothesis. Meanwhile, the surviving time of LAOS-generated nucleation precursors is comparable to the recovery time of disentangled chains, suggesting that the delay effect of nucleation precursors on chain diffusion may last over the entire re-entanglement process. Notwithstanding the obstruction of “extra” physical entanglements for chain diffusion, the molecular weight (Mw) dependence of entanglement recovery still follows the reptation model-based power law: τent=(a+b)Mw3.4, where a and b is the contribution of chain diffusion and dissipation of precursors, respectively.

A methodology for adding thixotropy to Oldroyd-8 family of viscoelastic models for characterization of human blood

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, a yield stress, and thixotropy. After decades of modeling only the steady state blood data, steady state models, such as the Casson, Carreau–Yasuda, and Herschel–Bulkley models, have been developed. The advancement and evolution of blood modeling to transient flow conditions now has renewed interest. Using recently collected human blood rheological data from a strain-controlled rheometer, we show and compare a new modeling effort using the Oldroyd-8 viscoelastic framework as a foundation. This foundation is enhanced with the application of a recent thixotropic framework recently published to model elastic and viscoelastic contributions from the microstructure to three Oldroyd-8 families of models: the corotational Jeffreys model, the convected Maxwell model, and the Oldroyd 4-constant model. The elastic and viscoelastic stress contributions from the microstructure are then linearly superimposed with the viscoelastic backbone solution for stress given by the Oldroyd-8 family of models. Demonstrated here is a parametric analysis, model comparison, and a comparison of the new approaches made using the ability to predict large amplitude oscillatory shear and uni-directional large amplitude oscillatory shear flow. The new family of models can solve components of the full stress tensor, making them ideal for use with a future conformation tensor to evolve, model, and better understand the effects of the microstructure of human blood. In addition, there is now a methodology to model the normal forces of blood.

Direct simulation of fiber suspensions under smalland large amplitude oscillatory shear flow

Experimentally, oscillatory shear flow is used to investigate polymeric viscoelastic properties. However, the knowledge of the microstructure’s orientation evolution (kinematics) with time is essential in order to predict those properties, and is difficult experimentally. Therefore it is often required to conduct numerical simulations to get insight on the kinematics evolution of fiber suspensions. The main aim of the current work is to use direct numerical simulations to investigate the time evolution of the orientation and kinematics of fiber suspensions under small and large amplitude oscillatory shear flow. Keywords: fiber suspensions; direct numerical simulation; oscillatory shear flow; fiber-fiber interactions;

Large-amplitude oscillatory shear flow loops for long-chain branching from general rigid bead-rod theory

General rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60, 4001–4008 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of this theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric branched macromolecules. In this work, we explore how adding long-chain branching to polymers affects the shapes of large-amplitude oscillatory shear (LAOS) flow loops. By loops, we mean plots of the alternant part of the shear stress response vs the cosinusoidal shear rate. We choose LAOS for its ability to amplify subtle differences in small-amplitude oscillatory shear flow at a high Weissenberg number. When non-dimensionalized with the product of the zero-shear viscosity and the shear rate amplitude, the loop shapes depend on the sole dimensionless architectural parameter, the macromolecular lopsidedness of the long-chain branched macromolecule. In this work, in this way, we compare and contrast the loop shapes of macromolecular chains that are straight with those branched. Specifically, we explore symmetric branch multiplicity, branch functionality, branch length, branch position, branch distribution, and multiple branch asymmetry. We find that adding branching collapses and distorts the loops. We then find that so long as branch length, branch position, and branch distribution are held constant and so long as the branching is symmetric about the center of mass, the peak shear stress increases with branch multiplicity. We also find that branch functionality hardly affects the loops. The structural details explored in this paper have yet to be explored in the laboratory.

Pattern method for higher harmonics of first normal stress difference from molecular orientation in oscillatory shear flow

This study examines the simplest relevant molecular model of a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow: rigid dumbbells suspended in a Newtonian solvent. For such suspensions, the viscoelastic response of the polymeric liquid depends exclusively on the dynamics of dumbbell orientation. Previously, the explicit analytical expressions of the zeroth, second, and fourth harmonics of the alternating first normal stress difference response in LAOS have been derived. In this paper, we correct and extend these expressions by seeking an understanding of the next higher harmonic. Specifically, this paper continues a series of studies that shed light on molecular theory as a useful approach in investigating the response of polymeric liquids to oscillatory shear. Following the general method of Bird and Armstrong [“Time-dependent flows of dilute solutions of rodlike macromolecules,” J. Chem. Phys. 56, 3680 (1972)], we derive the expression of the first normal stress coefficient up to and including the sixth harmonic. Our analysis relies on the extension of the orientation distribution function to the sixth power of the shear rate. Our expression is the only one to have been derived from a molecular theory for a sixth harmonic and thus provides the first glimpse of the molecular origins of a first normal stress difference higher than the fourth.

Series expansion for normal stress differences in large-amplitude oscillatory shear flow from Oldroyd 8-constant framework

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we focus on the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. The normal stress difference responses for the Oldroyd 8-constant framework has recently yielded to the exact analytical solution. However, in its closed form, Bessel functions appear 24 times, each within summations to infinity. In this paper, to simplify the exact solution, we expand it in a Taylor series. We truncate the series after its 17th power of the shear rate amplitude. Our main result reduces to the well-known expression for the special cases of the corotational Jeffreys and corotational Maxwell fluids. Whereas these special cases yielded to the Goddard integral expansion (GIE), the more general Oldroyd 8-constant framework does not. We use Ewoldt grids to show our main result to be highly accurate for the corotational Jeffreys and corotational Maxwell fluids. For these two special cases, our solutions agree closely with the exact solutions as long as Wi/De<3310. We compare our main result, for the special case of the Johnson–Segalman fluid, with measurements on dissolved polyisobutylene in the isobutylene oligomer. For this, we use the Spriggs relations to generalize our main result to multimode, which then agrees closely with the measurements.

The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region.

We carry out a numerical study to investigate the dynamics of non-Brownian hard-sphere suspensions near the liquid and crystal coexistence region in small to large amplitude oscillatory shear flow. The first normal stress difference (N1) and related rheological functions are carefully analyzed, focusing on the strain stiffening phenomenon, which occurs in the large strain amplitude region. Under oscillatory shear, we observe several unique behaviors of N1. A negative nonzero mean value of N1 (N1,0) is observed for the applied strain amplitudes. The change of the sign, from negative to positive, at the maximum value of N1 (N1,max) is observed at a specific point, which is not consistent with the critical strain amplitude (γ0,c) at which the modulus begins to deviate from linear viscoelasticity. The behavior of N1 in the oscillatory shear flow is different from that of N1 in steady shear flow, that is, the characteristics of N1 in strain stiffening and shear thickening are quite distinguished from each other. We also perform structural analysis to confirm the relationship between the rheological properties and microstructure of the suspension. A strong correlation is observed between the global bond order parameter (Ψ6) and the distortions in both nonlinear shear and normal stresses. The most noticeable characteristic is captured through the maximum of the global bond order parameter (Ψ6,max). The strain amplitude at the slope change of Ψ6,max corresponds to the point where a unique behavior of N1 is observed, i.e. the change of the sign in N1,max, but a strong correlation is not captured at γ0,c. This demonstrates that the normal stress responds to particle ordering more sensitively than other rheological functions based on shear stress like dynamic moduli. As far as we are concerned, the behavior of N1 has rarely been fully explored and related with the strain stiffening of non-Brownian suspensions so far. Therefore, this study has significance as the first report to strictly analyze strain stiffening along with the first normal stress difference N1.

Anomalous behavior of a wormlike micellar solution in large-amplitude oscillatory shear flow in a parallel disk flow cell

Anomalous behavior of a wormlike micellar solution in large-amplitude oscillatory shear flow in a parallel disk flow cell

Pattern method for higher harmonics from macromolecular orientation in oscillatory shear flow

For a suspension of rigid dumbbells, in any simple shear flow, we must first solve the diffusion equation for the orientation distribution function by a power series expansion in the shear rate. Our recent work has uncovered the pattern in the coefficients of this power series [L. M. Jbara and A. J. Giacomin, “Orientation distribution function pattern for rigid dumbbell suspensions in any simple shear flow,” Macromol. Theory Simul. 28, 1800046-1–1800046-16 (2019)]. Specifically, we have here used this pattern on large-amplitude oscillatory shear (LAOS) flow, for which we have extended the orientation distribution function to the 6th power of the shear rate. In this letter, we embed this extension into the Giesekus expression for the extra stress tensor to arrive at the alternant shear stress response, up to and including the seventh harmonic. We thus demonstrate that the pattern method for macromolecular orientation now allows our harmonic analysis to penetrate the shear stress response to oscillatory shear flow far more deeply than ever.

Deformation of Chemically Heterogeneous Interfacial Layers of Polymer Nanocomposites.

Dynamics of entangled interfacial polymer layers around nanoparticles determine the linear rheological properties of polymer nanocomposites. In this study, the nonlinear elastic properties of nanocomposites are examined under large-amplitude oscillatory shear (LAOS) flow to reveal the effect of interfacial chemical heterogeneity on the deformation mechanism of polymer-grafted and polymer-adsorbed nanoparticle composites. Adsorbed-poly(methyl methacrylate) (PMMA) layers presented stronger interfacial stiffening and reinforcement than PMMA-grafted layers. Chemical heterogeneities of interfacial layers, provided by polymer-adsorbed and low graft density particles, deformed at smaller strains than the poly(ethylene oxide) (PEO) matrix. Interfaces of loosely bound PMMA and PEO exhibited stiffening at low strains due to the enhanced chain mixing and entanglements. These results demonstrate that chemical and dynamic heterogeneities in interfacial layers have significant importance in designing adaptive polymer nanocomposites for large shear deformation.

Viscoelasticity of olive oil/water Pickering emulsions stabilized with starch nanocrystals

The olive oil-in-water Pickering emulsions stabilized with starch nanocrystal (SNC) were prepared for the morphological and rheological studies. Different kinds of shear flows were applied and the viscoelastic responses of emulsions were detected in terms of SNC concentrations (0.2–2.0 wt%) and surface acetylation levels (0.11-0.41° of substitution). The results show that the emulsifying capacity of SNC is improved evidently after surface acetylation due to decreased surface hydrophilicity of SNC and to enhanced electrostatic repulsive effect during emulsification, which is evidenced by the gelation behavior in small amplitude oscillatory shear (SAOS) flow. The modulus and viscosity of the emulsion with acetylated SNC increase by about two orders of magnitude as compared to those of the emulsion with pristine one. The former even shows weak overshoot behavior during large amplitude oscillatory shear (LAOS) flow. This work provides valuable information on motivating development of the Pickering emulsions using SNC as particle emulsifier.

Unidirectional large-amplitude oscillatory shear flow of human blood

Blood is a non-Newtonian suspension of red and white cells, platelets, fibrinogen, and cholesterols in Newtonian plasma. To assess its non-Newtonian behaviors, this work considers a newly proposed blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS). In the laboratory, we generate this experiment by superposing LAOS onto steady shear flow in such a way that the shear rate never changes sign. It is thus intended to best represent the unidirectional pulsatile flow in veins and arteries. To model human blood, we consider the simplest model that can predict infinite-shear viscosity, the corotational Jeffreys fluid. We arrive at an exact analytical expression for the shear stress response of this model fluid. We discover fractional harmonics comprising the transient part of the shear stress response and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. We generalize the corotational Jeffreys fluid to multimode to best represent three blood samples from three healthy but different donors. To further improve our model predictions, we consider the multimode Oldroyd 8-constant framework, which contains the corotational Jeffreys fluid as a special case. In other words, by advancing from the multimode corotational Jeffreys fluid to the multimode Oldroyd 8-constant framework, five more model parameters are added, yielding better predictions. We find that the multimode corotational Jeffreys fluid adequately describes the steady shear viscosity functions measured for three different healthy donors. We further find that adding two more specific nonlinear constants to the multimode corotational Jeffreys fluid also adequately describes the behaviors of these same bloods in udLAOS. This new Oldroyd 5-constant model may find usefulness in monitoring health through udLAOS.

Evolution of chain entanglements under large amplitude oscillatory shear flow and its effect on crystallization of isotactic polypropylene

The effect of large amplitude oscillatory shear (LAOS) flow on isotactic polypropylene (i-PP) chain entanglement-disentanglement transition and on the subsequent crystallization behavior was studied by dynamic rheology and polarized optical microscope (POM). i-PP with reduced entanglement density was generated through the application of LAOS flow at 180 °C. The re-entanglement process of disentangled chains was in-situ monitored by time-sweep rheological measurements. Interestingly, the re-entanglement kinetics was substantially slower than expectations based on the linear viscoelastic relaxation time of the fully entangled melt. Moreover, with the adjustment of shear conditions (strain amplitude, frequency and temperature), the entanglement density could be effectively modified. Disentangled chains exhibiting less topological constraints played a distinct role in the subsequent crystallization process. The nucleation density and growth rate of spherulites increased with reducing the entanglement density, resulting in a faster overall crystallization kinetics, compared to that in the fully entangled melt. It is worth to note that LAOS flow could produce a less disentangled melt state, and has a correspondingly weaker influence on the subsequent crystallization behavior, with respect to steady shear flow.

Recovery rheology via rheo‐SANS: Application to step strains under out‐of‐equilibrium conditions

AbstractStress relaxation from a step strain test provides important information about constituent dynamics, but if a material has experienced a complex shear history, the underlying physics is not straightforward to access. We use recovery rheology and rheo‐small‐angle neutron scattering to probe the nonlinear dynamics of an entangled wormlike micelle solution by applying step strains after complex shear histories enforced by large‐amplitude oscillatory shear (LAOS) flow. We show that a universal relaxation modulus can be obtained from step strain tests with complex shear histories, as long as the modulus is defined in terms of the recoverable strain. The shear and normal stresses, as well as the alignment of micellar Kuhn segments, are shown to be positively correlated with the recoverable strain. We identify re‐entanglement of polymeric chains after cessation of LAOS and show that this process occurs over the same timescales as linear‐regime stress relaxation. This work, therefore, lays the foundation of how to accurately probe out‐of‐equilibrium rheology in a consistent manner.

Hydrodynamic interaction for rigid dumbbell suspensions in steady shear flow

From kinetic molecular theory, we can attribute the rheological behaviors of polymeric liquids to macromolecular orientation. The simplest model to capture the orientation of macromolecules is the rigid dumbbell. For a suspension of rigid dumbbells, subject to any shear flow, for instance, we must first solve the diffusion equation for the orientation distribution function. From this distribution, we then calculate the first and second normal stress differences. To get reasonable results for the normal stress differences in steady shear flow, one must account for hydrodynamic interaction between the dumbbell beads. However, for the power series expansions for these normal stress differences, three series arise. The coefficients for two of these series, (ck, dk), are not known, not even approximately, beyond the second power of the shear rate. Analytical work on many viscoelastic material functions in shear flow must be checked for consistency, in their steady shear flow limits, against these normal stress difference power series expansions. For instance, for large-amplitude oscillatory shear flow, we must recover the power series expansions in the limits of low frequency. In this work, for (ck, dk), we arrive at the exact expressions for the first 18 of these coefficients.

Large-amplitude oscillatory shear flow simulation for a FENE fluid

In this work, the FENE dumbbell model under small- and large-amplitude oscillatory shear flows using a micro-macro approach is presented. This approach involves the evolution of an ensemble of Brownian Configuration Fields which describes the polymer dynamics of the microscopic scale and the momentum equation describes the macroscopic scale. The Lissajous curves for the shear stress and the first normal stress difference versus the instantaneous strain or strain rate for the elastic or viscous projection are shown. The influences of the solvent/polymer viscosity ratio, the maximum extension length, and the relation between strain rate and frequency are analyzed. An important finding is the self-intersection of the Lissajous curves, which forms secondary loops for short extension lengths and high Weissenberg/Deborah dimensionless numbers ratio.

Rheology of the sesame oil-in-water emulsions stabilized by cellulose nanofibers

The sesame oil-in-water Pickering emulsions using cellulose nanofibers (CNF) as the emulsifier were prepared for the rheological study, aiming at establishing relationship between emulsion viscoelasticity and morphology. A droplet cluster structure forms in those systems due to multicomponent properties of sesame oil and fibrillar structure of CNF. Its deformation and relaxations result in weak strain overshoot behavior in large amplitude oscillatory shear (LAOS) flow, but not affect the scaling behavior of small amplitude oscillatory shear (SAOS) responses. The relaxation time scales can be evaluated by creep of emulsions. This structure can evolve during ramp shear flow, rearranged and oriented at the higher flow rates, which has evident influence on the thixotropic behavior of emulsions. The mechanisms of evolution and relaxations of droplet cluster structure are traced through rheo-optical way. This work presents some interesting results and paves a possible way to control morphology and viscoelasticity of edible Pickering emulsions.

A simple method to analyze materials under quasilinear large amplitude oscillatory shear flow (QL-LAOS)

A new method to analyze materials exploring the quasilinear oscillatory regime has been described. One of its advantages is a significant reduction of the number of rheological tests needed, as compared to the originally proposed quasilinear large-amplitude oscillatory shear flow method. Furthermore, the authors improved the data analysis to a great extent, rendering it quite straightforward and physically sound. To validate the new method, we used two materials of qualitatively different rheological behavior, namely, a commercial hair gel and a solution of polyacrylamide in water/glycerol. The data obtained are presented in two distinct forms. The first one uses either the traditional Kelvin–Voigt analysis—which yields as material functions the storage and loss moduli G ′ and G ″, respectively—or the traditional Maxwell analysis, which yields as material functions the storage and loss compliances J ′ and J ″, respectively. The second form originates from a Jeffreys analysis, which gives as output two material functions, namely, the relaxation time θ 1 and the retardation time θ 2. The results of the different analyses are compared and discussed.A new method to analyze materials exploring the quasilinear oscillatory regime has been described. One of its advantages is a significant reduction of the number of rheological tests needed, as compared to the originally proposed quasilinear large-amplitude oscillatory shear flow method. Furthermore, the authors improved the data analysis to a great extent, rendering it quite straightforward and physically sound. To validate the new method, we used two materials of qualitatively different rheological behavior, namely, a commercial hair gel and a solution of polyacrylamide in water/glycerol. The data obtained are presented in two distinct forms. The first one uses either the traditional Kelvin–Voigt analysis—which yields as material functions the storage and loss moduli G ′ and G ″, respectively—or the traditional Maxwell analysis, which yields as material functions the storage and loss compliances J ′ and J ″, respectively. The second form originates from a Jeffreys analysis, which gives as ou...

Power series for normal stress differences of polymeric liquids in large-amplitude oscillatory shear flow

Exact solutions for normal stress differences in polymeric liquids subjected to large-amplitude oscillatory shear flow (LAOS) contain many Bessel functions, each appearing in infinite sums. For the simplest relevant model of a polymeric liquid, the corotational Maxwell fluid, Bessel functions appear 38 times in the exact solution. By relevant, we mean that higher harmonics are predicted in LAOS. By contrast, approximate analytical solutions for normal stress differences in LAOS often take the form of the first few terms of a power series in the shear rate amplitude, and without any Bessel functions at all. Perhaps the best example of this, from continuum theory, is the Goddard integral expansion (GIE) that is arrived at laboriously. There is thus practical interest in extending the GIE to an arbitrary number of terms. However, each term in the GIE requires much more work than its predecessor. For the corotational Maxwell fluid, for instance, the GIE for the normal stress differences has yet to be taken beyond the fifth power of the shear rate amplitude. In this paper, we begin with the exact solution for normal stress difference responses in corotational Maxwell fluids, then perform an expansion by symbolic computation to confirm up to the fifth power, and then to continue the GIE. In this paper, for example, we continue the GIE to the 41st power of the shear rate amplitude. We use Ewoldt grids to show that our main result is highly accurate. We also show that, except in its zero-frequency limit, the radius of convergence of the GIE is infinite. We derive the pattern for the common denominators of the GIE coefficients and also for every numerator for the zeroth harmonic coefficients. We also find that the numerators of the other harmonics appear to be patternless.