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In the present work, we focus on the large deformation of a viscoelastic droplet suspended in a Newtonian matrix. We use the constrained volume model as a basic theoretical framework for the description of droplet shape evolution, and we account for the viscoelasticity of the droplet phase using the single-mode Giesekus model. The velocity gradient term describing flow inside the droplet is modified by the viscoelastic stresses, and the resulting model—we herein call the non-Newtonian constrained volume model—is calibrated by matching its predictions to those of the model of Yu et al. [J. Rheol. 48, 417–438 (2004)] at small deformation and slow flow conditions. The non-Newtonian constrained volume model is then examined under conditions of large deformation and/or fast flow, and its predictions are compared against experimental results. The new model shows the growth of the droplet's width in the vorticity direction at conditions of large capillary number, moderate-to-large viscosity ratio, and small elastocapillary number.

Our recent continuum theory for stress-gradient-induced migration of polymers in confined solutions, including the depletion from the solid boundaries [Hajizadeh, E., and R. G. Larson, Soft Matter, 13, 5942–5949 (2017)], is applied to a two-dimensional rotational shearing flow in the gap between eccentric cylinders. Analytical results for the steady-state distribution of polymer dumbbells in the limit of dilute polymer solution c/c∗≪1 (c∗ is the chain overlap concentration) and in the absence of hydrodynamic interactions are obtained. The effects of eccentricity e and of three perturbation variables, namely, Weissenberg number Wi, gradient number Gd(which defines the level of polymer chain confinement), and Peclet number Pe on the polymer concentration pattern, are investigated. The stress-gradient-induced migration results in polymer migration toward the inner cylinder, while wall-depletion-induced migration results in near-zero polymer concentration close to flow boundaries, which couples to a stress-gradient-induced migration effect. In the presence of wall-depletion, we obtain first order concentration variation proportional to Wi. However, in the absence of wall-depletion, there is no first order contribution and, therefore, the lowest-order concentration variation is proportional to Wi2. An upper limit of Wi=1.6 exists, beyond which the numerical solution demands an excessive under-relaxation to converge. In addition, for a high degree of polymer chain confinement, i.e., for Gd greater than 0.5, the continuum theory fails to be accurate and mesoscopic simulations that track individual polymer molecules are needed.

The rheology of noncolloidal suspensions in superposed simple shearing and oscillatory shearing was explored. With a Newtonian matrix fluid, one would expect that G′ would be zero in an oscillatory flow, but this was not found; the action of Coulomb friction between the particles appears to cause an increment of G′ at lower frequencies. To understand this frictional effect, measurements of small and medium strain oscillatory flows, up to 10% strain magnitude, were made. The matrix fluid was 12 Pa s silicone oil, and the polystyrene spheres were on average 40.3 μm in diameter. Hysteresis during tests with varying strain amplitudes was more dominant in the storage modulus than in the loss modulus, and, at a 50% volume fraction, the effect was severe. Because of the observed tendency to hysteresis, the oscillatory flow was then combined with a parallel steady shear flow to try to control or eliminate hysteresis. The hysteresis appears to be a frictional effect, and it was reduced under superposed shearing. The effect of variable oscillatory shear stress and steady shear stress was studied, and a model was proposed for the superposed storage modulus, loss modulus, and shear viscosity responses. Frictional effects are considered in the proposed model, and one observes a generally satisfactory fit to the experimental data. From the model, the average friction coefficient is shown to be less at higher frequencies due to higher relative rubbing speeds and better lubrication between the particles. Clearly, suspension rheology is dominated by friction and is essentially a study in tribology.

By means of extensive particle dynamics simulations in a three-dimensional model, we analyze the rheology and granular texture in the steady-state of the viscoinertial granular flow. The interactions between dry particles are added by the theoretical description of the capillary cohesion forces and viscous forces due to the presence of the viscous liquid bridge. We show that the rheology of such flow characterized by the apparent friction coefficient and packing fraction can be nicely described as a function of the viscoinertial number combining the particle inertia and viscous stress of the liquid bridge by keeping the constant value of the liquid-vapor surface tension. Furthermore, the flow behavior can alternatively be described by the effective viscosities (normal and shear components) as a function of the imposed volume fraction, which is in good agreement with previous numerical simulations of particles immersed in a viscous fluid and experiments in dense suspensions. Interestingly, the granular texture characterized by the fabric and force anisotropies and the bond coordination number is also well-described by this modified inertial number. Remarkably, the stress transmission ratio reflects the intermediate relationship between microstructure and mechanical behavior of wet granular flow, expressed as a function of the viscoinertial number. We also find that shearing leads to variations of the compressive and tensile interactions between neighboring particles.

The rheological properties (viscosity, plasticity, viscoelasticity, and elasticity) of noncolloidal suspensions with varying concentrations of a solid phase (Al powder) in oligomeric polyethylene glycol have been studied in the shear mode of deformation. All typical types of rheological behavior have been observed. In the concentration range up to approximately 30%, suspensions are Newtonian liquids, while at a certain concentration, non-Newtonian and viscoelastic effects appear. With further increases in concentration, the flow curves become a power-law type, though the yield stress can be found only for suspensions with a high solid phase content. The elasticity of the suspensions can be detected at concentrations in the order of 55%. In a narrow range of concentrations, the rheological state of the suspensions can be treated as viscoplastic, wherein they preserve fluidity and become elastic. This concentration threshold, determined by the change in various rheological characteristics including the loss tangent, corresponds to the gelation or “colloid” glass transition. The most detailed experiments were devoted to the concentration range of 60–70 vol. %, which are treated as highly concentrated suspensions (HCSs). A concentration of 70% is the upper limit, because mixtures with higher concentrations do not keep their continuity and crumble. The rheological state of HCSs corresponds to the elastoplastic type of behavior. The separation of the total deformation into plastic and elastic components showed that plastic deformations (but not the flow) in the shearing of HCSs are small. Repeated shearing in the loading-unloading mode has been performed. In this case, a decrease in the elastic deformation and a remarkable growth of the shear elastic modulus was observed. This effect is presumably explained by the orientation of the particles and shear-induced anisotropy. A stress-concentration diagram of the physical states of suspensions has been proposed. The concentration range somewhat below that of the HCS state is of special interest for the powder injection molding technology, which is limited by the domain of plasticity.

We report direct measurements of spatially resolved surface stresses over the entire surface of a dense suspension during discontinuous shear thickening (DST) using boundary stress microscopy (BSM) in a parallel-plate rheometer. We find that large fluctuations in the bulk rheological response at the onset of DST are the result of localized transitions to a state with very high stress, consistent with a fully jammed solid that makes direct contact with the shearing boundaries. This jammed solidlike phase (SLP) is rapidly fractured, producing two separate SLPs that propagate in opposite directions. By comparing the speed of propagation of the SLPs with the motion of the confining plates, we deduce that one remains in contact with the bottom boundary and the other remains in contact with the top. These regions grow, bifurcate, and eventually interact and decay in a complex manner that depends on the measurement conditions (constant shear rate vs constant stress). In a constant applied stress mode, BSM directly reveals dramatic stress fluctuations that are completely missed in the standard bulk rheology.

Rheological measurements in which the applied stress or strain is oscillated are widely used to interrogate viscoelastic properties due to the independent control over the time scale and length scale afforded by changes in amplitude and frequency. Taking a nontraditional approach, we treat stress-controlled oscillatory tests as creep tests with transiently varying stress and apply an analysis typically used for steady creep and recovery experiments. Defining zero strain as the state prior to external shearing, it is shown that strain responses to small-amplitude oscillatory stressing are naturally shifted from the starting point by an amount proportional to the phase of the applied stress. The phenomenology is experimentally observed with entangled polymerlike micelles and polyethylene oxide solutions. A theory of strain shifting in the steady alternating state is provided based on recovery rheology, where differences between total strain and recoverable strains are acknowledged. User-controlled variables, such as the amplitude of the stress, the angular frequency, and the phase of the stress, as well a lone material parameter, the zero-shear viscosity, are shown to dictate the amount of shifting. A rapid and efficient approach of determining the zero-shear viscosity is, therefore, presented. We investigate the microstructural evolution via in situ small-angle neutron scattering when strain shifting appears. The microscopic orientation is shown to correlate to the recoverable strain independent of the shifting. Additional measurements are carried out on collagen, pluronic-hyaluronic acid, alginate gels, and polystyrene melts to show the generic nature of the strain shift phenomenon. In addition, we demonstrate that the strain-shift knowledge can be applied to determine the horizontal shift factor in time-temperature superposition, free of any numerical fitting procedures.

We propose to extend the well-known Doi–Edwards theory to model the viscosity divergence caused by shear-induced crystallization occurring upon startup flow experiments in segmented block copolymers ( M w ¯ = 50 kg mo l − 1 ). Unlike models such as Convective Constraint Release in which the chain relaxation is accelerated by the shear, we propose to increase the final relaxation time of the polymer within the memory function to take into consideration the progressive association of the hard-segments. To this aim, we make use of the Avrami equation in which we parametrize the crystallization rate to depend on the shear rate in a linear way. In this context and contrary to what is generally proposed for supramolecular polymers, we consider the hard-segments aggregation as an irreversible process (infinite lifetime) due to the crystalline nature and the high-functionality of the resulting topological nodes. The exponential trend of the Avrami process is then validated by stress relaxation experiments performed at different levels of strain. Moreover, the growth mode parameter, usually assigned to the geometry of the crystallites, is found to be independent of the shear rate and in excellent agreement with a previous work in which we investigated the quiescent crystallization of the same system. We finally apply our model to fit data measured at different temperatures, well-confirming the development of hard-segments’ crystallites from the very first stages of the isothermal shearing process.We propose to extend the well-known Doi–Edwards theory to model the viscosity divergence caused by shear-induced crystallization occurring upon startup flow experiments in segmented block copolymers ( M w ¯ = 50 kg mo l − 1 ). Unlike models such as Convective Constraint Release in which the chain relaxation is accelerated by the shear, we propose to increase the final relaxation time of the polymer within the memory function to take into consideration the progressive association of the hard-segments. To this aim, we make use of the Avrami equation in which we parametrize the crystallization rate to depend on the shear rate in a linear way. In this context and contrary to what is generally proposed for supramolecular polymers, we consider the hard-segments aggregation as an irreversible process (infinite lifetime) due to the crystalline nature and the high-functionality of the resulting topological nodes. The exponential trend of the Avrami process is then validated by stress relaxation experime...

This review deals with non-Brownian (noncolloidal) suspension rheology; experimental and computational works are compared where possible. The matrix fluids are non-Newtonian, and the rigid particles have an aspect ratio close to one. Volume fractions of 0.5 and below are considered. Shearing and extensional flows are discussed; the former are fairly well understood but the latter are not prominent in the literature. Unsteady and oscillatory flows are surveyed. A comparison of Newtonian and viscoelastic suspension rheology is made, and some aspects of finding constitutive models for these suspensions are discussed. While progress has been made, it appears that satisfying agreement between computation and experiment is rare. More attention to rheological and frictional modeling is needed, and improved computational methods need to be developed.

In this study, the normal stress in magnetorheological polymer gel (MRPG) under large amplitude oscillatory shear was investigated using experiments and particle-level simulations. Under large amplitude oscillatory shear, an intensely oscillating normal stress was measured with a period of exactly half the strain period. As the amplitude of the strain increased, the peak of the normal stress increased and the trough decreased. Changes in the normal stress were mainly caused by two factors: the Poynting effect, in which shear produces a normal force perpendicular to the shear direction, and magnetic-induced normal stress, which changes with the particle structure. In MRPG, both effects are related to the particle structure. The particle structure in MRPG with different strain was calculated and the simulation results show that the amplitude of the structural strain in oscillatory shearing is less than that of the applied strain. Additionally, a phase difference was observed between the structural strain and the applied strain. Based on the calculated particle structure, the change in the normal stress was obtained and found to agree well with the experimental results.

The transient structural and rheological behavior of soft glassy materials out of equilibrium is studied under small, medium, and large amplitude oscillatory shearing and interpreted via the fully quantitative sequence of physical processes (SPP) technique. We identify features of the local strain distribution that cause particular rheological responses and show that the SPP metrics accurately reflect the structural transitions. The SPP modulus is shown to reflect how much of the imposed strain is stored in the form of recoverable elastic strain, establishing it as an accurate measure of structural elasticity. We demonstrate the ability of the SPP scheme to accurately determine the amount of recoverable strain acquired in elastically dominated regimes by matching values estimated solely on the basis of the macroscopic stress to structural measures. In one case of large amplitude oscillatory shearing, the recoverable strain is shown to be around half a nondimensional strain unit by structural determination and from the SPP analysis, while the total imposed strain over the same interval is on the order of ten strain units. We therefore demonstrate the importance of separating the total and recoverable strains under strain-controlled conditions for the formation of accurate structure-property relations. We demonstrate how the alternating oscillatory state may be considered a consequence of a complex shear history. The results of this study show that the SPP scheme is a powerful tool for researchers wishing to understand the structural and rheological properties of soft glassy materials far from equilibrium.

Elastoviscoplastic materials present a transition from a gel-like to a liquidlike state induced by shearing: While the first is primarily elastic, the second is predominantly viscous. The point that characterizes this transition is usually known as the yield point, which is associated to critical quantities such as yield stress and/or yield strain. Another characteristic of elastoviscoplastic materials is the transition from linear to nonlinear viscoelasticity. In the current work, a commercial hair gel, which is an elastoviscoplastic material, was tested in two rotational rheometers in order to evaluate these two transition points. Stress oscillatory amplitude sweeps at different frequencies were performed and a Fourier-Transform analysis was applied to the results in order to determine the linear viscoelastic limit. The linear viscoelastic limit stresses and strains at different frequencies were then compared to quantities that are usually associated to the yield point: The extrapolated zero-shear-rate ...

The effect of thermal and shear history on the rheology of waxy crude oils is studied in detail. A protocol sequence is presented, which enables us to systematically extract the main thixotropic features of a model waxy oil by a series of steady state and transient experiments at different temperatures. The importance of the underlying microstructure formed by a loosely aggregated and percolated network of wax crystals is discussed and quantified through differential scanning calorimetry and rheological measurements. The microstructural morphology can be described by relevant concepts used previously in the literature for concentrated suspensions of fractal aggregates and is augmented with evolution equations to capture the transient rearrangement of the microstructure, resulting in a thermokinematic memory of the shearing history and thermal history of the sample. Finally, a complete constitutive framework is derived that is able to quantitatively describe and predict a number of rheological features of the model waxy oil, such as viscoelasticity at small deformations and plasticity at large deformations, with both the yield stress and viscosity exhibiting thermokinematic memory. Direct comparison with rheometric data is used to determine the model constants and evaluate the predictive ability of the constitutive relations. The proposed model provides a new framework that can be used to describe not only waxy crude oils, but also other materials characterized by similar microstructural components, i.e., solid non-Brownian interacting particles of arbitrary shape that form a percolated sample-spanning network and convey thixotropy as well as elasto-viscoplasticity.The effect of thermal and shear history on the rheology of waxy crude oils is studied in detail. A protocol sequence is presented, which enables us to systematically extract the main thixotropic features of a model waxy oil by a series of steady state and transient experiments at different temperatures. The importance of the underlying microstructure formed by a loosely aggregated and percolated network of wax crystals is discussed and quantified through differential scanning calorimetry and rheological measurements. The microstructural morphology can be described by relevant concepts used previously in the literature for concentrated suspensions of fractal aggregates and is augmented with evolution equations to capture the transient rearrangement of the microstructure, resulting in a thermokinematic memory of the shearing history and thermal history of the sample. Finally, a complete constitu...

Particles suspended in a less-wetting fluid can be aggregated by addition of a small quantity of an immiscible fluid that preferentially wets the particles. If the added wetting fluid is sufficiently dilute, the aggregates are composed of particles held together by pendular menisci of the wetting fluid. Such pendular aggregates can then percolate into a network which endows the suspension with a yield stress. We examine the yielding behavior of pendular networks at a particle volume fraction of 20%, with wetting fluid loadings ranging from 0.08% to 6.4%. Steady shear experiments give a dynamic yield stress that increases roughly linearly with wetting fluid loading within the pendular regime, and the shear stress vs shear rate behavior can be collapsed onto a mastercurve by simply normalizing the stress by the yield stress. Linear viscoelastic moduli are found to decrease if the suspensions are sheared at a high rate prior to the modulus measurement, but this decrease can be reversed by shearing at a low ...

An experimental and numerical study on ram extrusion of bread dough was conducted in order to develop predictive models for the pressures involved, as well as the deformation of the extruded dough. Such studies are needed as high pressures can potentially lead to significant degassing, tearing and shearing of the dough and hence poor bread quality; the latter limits the use of extrusion processes which would otherwise be a cost – effective forming process. A laboratory extrusion rig was designed, with dies of varying angles and exit radii. Rate dependent behaviour was observed from tests conducted at different extrusion speeds, and higher extrusion pressure was reported for dies with smaller exit radius or larger die angle. A simulation of extrusion was performed to predict the extrusion pressure as well as the extrudate swell, as a function of die geometry and extrusion rate. A continuum approach was taken in the constitutive model of dough which is a starch filled system in a protein matrix. A nonlinear viscoelastic model combined for the first time with the Mullins model for filled rubbers is found to capture the continuum behaviour well. A Coulomb friction law combined with a maximum shear stress limit was used to describe the contact definition between the extrusion barrel and the dough. Higher die angles and higher extrusion speeds require higher shear stress limit values for the model and the experiments to agree. A possible reason for this is that the shear stress limit depends on maximum strain as well as strain rate imposed during the extrusion process. Static zones were observed both experimentally and numerically. The onset of the static zones was predicted well but quantifying the geometry of the latter needs further studies.

The rheological properties and dynamical responses of a monodisperse polyethylene (PE) liquid, C700H1402, were examined using equilibrium molecular dynamics and nonequilibrium molecular dynamics simulations of the atomistically detailed molecules. Equilibrium structural and dynamical properties of the PE liquid, such as the disengagement time ( τd), Rouse time ( τR), entanglement time, ( τe), reptation tube diameter, number of entanglements, and the distribution of the chain end-to-end vector, each followed very closely the predictions of the Doi and Edwards theory. Under steady shear conditions, the rheological and dynamical responses exhibited starkly different behavior as functions of shear rate, which could be categorized within four distinct shear rate regions; namely, γ τe−1. In the first region, the topological properties of the liquid remained relatively unperturbed from quiescent conditions and the rheological characteristic functions remained constant th...

Blends containing 75 wt. % of an amorphous polylactide (PLA) with two different molecular weights and 25 wt. % of a poly[(butylene adipate)-co-terephthalate] (PBAT) were prepared using either a Brabender batch mixer or a twin-screw extruder. These compounds were selected because blending PLA with PBAT can overcome various drawbacks of PLA such as its brittleness and processability limitations. In this study, we investigated the effects of varying the molecular weight of the PLA matrix and of two different mixing processes on the blend morphology and, further, on droplet coalescence during shearing. The rheological properties of these blends were investigated and the interfacial properties were analyzed using the Palierne emulsion model. Droplet coalescence was investigated by applying shear flows of 0.05 and 0.20 s−1 at a fixed strain of 60. Subsequently, small amplitude oscillatory shear tests were conducted to investigate changes in the viscoelastic properties. The morphology of the blends was also exam...

Whereas mixtures of colloids and nonadsorbing polymers have been studied in great detail in the last two decades, binary colloidal mixtures have not received much attention. Yet, fragmental evidence from asymmetric mixtures of hard spheres indicates a wide-ranging, complex behavior from liquid to crystal to single glass and to double glass, and respective rich rheology. Recently, we addressed the question of softness by investigating a mixture of soft and virtually hard colloidal spheres. We found an unprecedented wealth of states including repulsive single glass (RG), liquid, arrested phase separation (APS), and double glass (DG). This is a consequence of the coupling of softness and osmotic forces due to the hard component. We now report on the rheology of the different states with emphasis on the nonlinear response during startup of stress at constant rate, its relaxation upon flow cessation, and large amplitude oscillatory shearing. Distinct features are identified, whereas comparison with single-colloid (soft or hard) glasses reveals some phenomenological universalities in yielding, residual stresses and periodic intracycle stress response. In brief, the DG exhibits much larger yield and residual stresses as compared to the RG and APS, whereas the yield strain is the same for all states. Two-step yielding is unambiguously evidenced for the APS whereas both yield stress and strain exhibit a weak dependence on Peclet number. Large amplitude oscillatory tests reveal large value of the intrinsic nonlinear parameters, reflecting the role of colloidal interactions. Moreover, RG exhibits intracycle stress overshoots, a feature that characterizes most of the soft glassy materials formed by interpenetrable particles and that vanishes as hard (nearly impenetrable) colloids are added in the mixtures. These results demonstrate the sensitivity of linear and nonlinear rheology to colloidal state transitions and, more importantly, the power of entropic mixing as a means to tailor the flow properties, hence performance and handling of soft composites.Whereas mixtures of colloids and nonadsorbing polymers have been studied in great detail in the last two decades, binary colloidal mixtures have not received much attention. Yet, fragmental evidence from asymmetric mixtures of hard spheres indicates a wide-ranging, complex behavior from liquid to crystal to single glass and to double glass, and respective rich rheology. Recently, we addressed the question of softness by investigating a mixture of soft and virtually hard colloidal spheres. We found an unprecedented wealth of states including repulsive single glass (RG), liquid, arrested phase separation (APS), and double glass (DG). This is a consequence of the coupling of softness and osmotic forces due to the hard component. We now report on the rheology of the different states with emphasis on the nonlinear response during startup of stress at constant rate, its relaxation upon flow cessation, and large amplitude oscillatory shearing. Distinct features are identified, whereas comparison with single-coll...

A shear-thickening polysaccharide extracted from the New Zealand black tree fern was characterized for its time-dependent rheology and the effects of shear-history. The material exhibited antithixotropic behavior at shear rates between 4 and 10 s−1. The parallel growth of normal stresses with time at these shear rates indicated the development of an elastic network under shear. The formation of association structures is proposed to take place via cooperative zipping of stretched chains where associative groups are exposed only on shearing. Hysteresis effects were also observed at shear rates between 4 and 10 s−1. This was probably caused by rapid structure formation at these shear rates, which cannot be easily disrupted at subsequent lower shear rates (

This paper is concerned with the rheology and processing of solvent-free core shell “polymer opals” that consist of a soft outer shell grafted to hard colloidal polymer core particles. Strong iridescent colors can be produced by shearing the material in a certain way that causes the initially disordered spheres to rearrange into ordered crystalline structures and produce colors by diffraction and interference of multiple light scattering, similar to gemstone opals. The basic linear viscoelastic rheology of a polymer opal sample was determined as a function of temperature, and the material was found to be highly viscoelastic at all tested temperatures. A Cambridge multipass rheometer was specifically modified in order to make controlled mechanical measurements of initially disordered polymer opal tapes that were sandwiched between protective polyethylene terephthalate sheets. Axial extension, simple shear, and a novel “edge shearing” geometry were all evaluated, and multiple successive experiments of the edge shearing test were carried out at different temperatures. The optical development of colloidal ordering, measured as optical opalescence, was quantified by spectroscopy using visible backscattered light. The development of opalescence was found to be sensitive to the geometry of deformation and a number of process variables suggesting a complex interaction of parameters that caused the opalescence. In order to identify aspects of the deformation mechanism of the edge shearing experiment, a separate series of in situ optical experiments were carried out and this helped indicate the extent of simple shear generated with each edge shear deformation. The results show that strong ordering can be induced by successive edge shearing deformation. The results are relevant to polymer opal rheology, processing, and mechanisms relating to ordering within complex viscoelastic fluids.

The influence of nonquiescent relaxation of isotactic polypropylene on flow-induced crystallization (FIC) is investigated by a combination of particle tracking velocimeter (PTV) with a cone-plate shearing geometry and synchrotron radiation microbeam wide-angle X-ray diffraction (SR-μWAXD), which is aimed to correlate real flow profile and distribution of crystal orientation. With PTV technique, we observed that flow remains homogeneous during shear, while postshear movement and delayed fracture take place after a step strain when large shear rates and strains were imposed. Delayed fracture slices samples into several layers which move either forward or backward after the cessation of shear imposed externally. SR-μWAXD measurements reveal that the layers moving forward keep high crystal orientations while the layers moving backward show low orientations, which gives an inhomogeneous distribution of crystal orientation across the thickness of sheared samples. The correlation between moving direction and cry...

Large amplitude oscillatory shear (LAOS) is an increasingly popular nonlinear rheological test method, and the interpretation of the measurements is still an active area of research. Here, we demonstrate a new method whereby the nonlinear parameters of a popular constitutive equation used to model polymeric and other viscoelastic systems, the Giesekus model, may be determined directly from LAOS measurements without complicated, nonlinear model fitting. We define the stress response of the sample as an expansion in deformation strain and oscillation frequency. To leading order in strain, we derive the explicit analytic expressions for the first three harmonics of the stress response during LAOS for the Giesekus constitutive model. This allows for rapid determination of the Giesekus model parameters, including the nonlinear coupling parameter, directly from plots of the response obtained from modern rheological instruments. We demonstrate the validity, utility, and limits of this new method on a well-studied wormlike micelle (WLM) surfactant solution, cetyltrimethylammonium bromide (CTAB), and water. This robust and simple approach is especially advantageous for systems where steady shearing in the nonlinear regime is problematic and can provide rapid determination of parameters in rheological constitutive equations.

Using Brownian dynamics simulations, without excluded volume and hydrodynamic interactions, on single polymer molecules represented by bead-spring models with stiff Fraenkel springs mimicking a single Kuhn step, we find multiple nonlinear regimes of deformation in shear flows that are controlled by the Peclet number (Pe), which is the shear rate times the relaxation time of a Kuhn step. We observe that, for all chain lengths investigated, the average stretch in the flow direction initially increases with increasing Pe, followed by saturation in chain stretch, as observed in previous studies. At even higher Pe, the stretch begins to decrease with increasing shear rate, in accordance with similar simulations of Sendner and Netz, Eur. Phys. J. E 30, 75–81 (2009). At these rates, the trajectories reveal “premature” recoiling of the chain before attaining a fully extended state during the phase of the “tumbling orbit” in which the chain is stretching. An increasing stretch at even higher Pe is characterized by...

The dynamics of single droplets dispersed in a second, immiscible liquid undergoing a controlled mixture of shear and elongational flow has been studied using a home made eccentric cylinder device. The model system consists of poly(dimethyl siloxane) droplets in a poly(isobutylene) matrix, both Newtonian liquids at room temperature. In continuation of previous work [Boonen et al., Rheol. Acta 48, 359–371 (2009)], the effect of changing the balance of shearing and elongational flow components and varying viscosity ratio on the deformation and orientation of the droplets has been systematically investigated under sub-critical flow conditions. The experimental results obtained from optical microscopy are compared with theoretical predictions of the phenomenological model by Maffettone and Minale [J. Non-Newtonian Fluid Mech. 78, 227–241 (1998)], obtained using the transient form of the model and incorporating a flow type parameter that accounts for the relative amount of extension in the flow. Overall, a fai...

Concentrated suspensions of soft deformable particles, e.g., polymer microgel pastes and compressed emulsions, display a generic slip behavior [Meeker et al., J. Rheol. 92, 18302 (2004a); Meeker et al., J. Rheol. 48, 1295–1320 (2004b)]. When sheared with smooth surfaces, they exhibit apparent motion due to slip at the wall. Wall-slip stops at a sliding yield stress the value of which is much lower than the bulk yield stress. The physical mechanism of slip at low stresses and the origin of the sliding yield stress have so far been unresolved issues. We propose that the paste-wall interactions control the wall-slip behavior and determine the occurrence of the sliding yield point. We present experiments performed with different shearing surfaces. Two distinct slip behaviors are identified: depending on whether the interaction between the microgel particles and the wall is attractive or repulsive, wall-slip can be either suppressed or promoted. We provide an extension to the elastohydrodynamic slip model of M...

Rheology and microstructure of plate-like particle suspensions in linear shear flows are studied through numerical simulations for a range of volume fraction ϕ up to 0.30. Particles with aspect ratio AR=3–7 are modeled as planar assemblages of spheres. Numerical methods are developed to calculate the hydrodynamic interactions based on an extension of the Stokesian dynamics method for spheres. At low ϕ, suspensions exhibit a degree of particle alignment consistent with the orientation distribution predicted by Jeffery orbits. At high ϕ, hydrodynamic interactions produce a high degree of ordering with particles aligned in horizontal layers perpendicular to the gradient direction. This allows sufficient free volume for shearing of the suspension with moderate viscosity at high ϕ. A second ordering mechanism is the formation of transient stacks of plate-like particles which move as rigid assemblies. The two mechanisms—particle alignment and particle stacking—reduce the effects of hydrodynamic interaction. Ove...

The isotropic contribution of the particle phase to the bulk stress, or the particle pressure, is studied for Brownian hard sphere suspensions in computationally simulated shear flow. The particle pressure is mechanically defined as the negative mean normal stress exerted by the particles, i.e., Π=−(1∕3)[Σ11+Σ22+Σ33] for a viscometric flow where 1, 2, and 3 refer to the flow, velocity gradient, and vorticity directions, respectively. Analysis is provided to relate the particle pressure to the equilibrium osmotic pressure and to show the relation of Π to particle migration phenomena. Utilizing existing hydrodynamic functions and simulating the flow by the Stokesian Dynamics technique, the particle pressure is evaluated for particle volume fractions in the range 0.1⩽ϕ⩽0.52 for monodisperse spherical particles. The relative strength of Brownian to shearing motion is given by the Peclet number Pe=γa2∕D0, where γ is the shear rate of a simple shear flow, a is the spherical particle radius, and D0=kT∕6πηa wit...

Single-step and three types of reversing double-step experiments were conducted on concentrated solutions of a linear and two dendritic (hyperbranched or arborescent) polyisobutylenes (PIBs). The results in reversing double-step experiments further confirm our previous findings on polyethylene melts that the K-BKZ theory provides better predictions for long chain branched polymers than linear ones. The short chain branched material looks more like the linear material in the present experiments. Isochronal derivatives of the strain potential function (W1 and W2) were calculated from torque (T) and normal force (N) responses in single-step parallel plate experiments. The damping function was extracted from W1 and W2 for both linear and branched PIBs. The damping function of the linear PIB falls between two versions of the Doi–Edwards model. The arborescent PIB with longer branches and lower branching frequency shows weak damping behavior, which is a specific behavior for long chain branched polymers. The ar...

The dynamic and steady state behavior of highly entangled polybutadiene solutions has been studied in shearing flow using high-spatial-resolution particle tracking velocimetry. In Couette geometry, the velocity profile is approximately linear upon the imposition of a step shear rate, but becomes significantly curved at later times, and attains the steady shape only after more than 100 strain units. In steady state, local shear rate varies smoothly across the gap and there is no shear banding. The constitutive relation is constructed from local stress and local shear rate extracted from velocity profiles. This procedure is not affected by the common problems of slip and edge instabilities as encountered with cone and plate geometry. The constructed constitutive curve is clearly monotonic for all tested solutions with entanglement numbers up to 47, notwithstanding a local power law index in the stress plateau as small as 0.01. The slope of the stress plateau is sensitive to both the chain polydispersity and entanglement number. Transient shear banding was observed under imposition of step shear in cone and plate geometry. This banding, however, disappears at longer times, which again confirms a monotonic steady state constitutive relation.

In this work we attempt to answer several questions concerning the flow characteristics of entangled polymer solutions in a sliding plate shearing cell. We explore (a) how the molecular weight distribution affects the velocity profile in simple shear, (b) whether the observed shear banding is consistent with a nonmonotonic constitutive model, (c) whether the flow response and velocity profiles are different in simple shear depending on the different modes of shear. Our results provide a comparison with recent reports on a polydisperse polymer sample [Tapadia and Wang, Phys. Rev. Lett. 96, 016001 (2006); Tapadia, et al., Phys. Rev. Lett. 96, 196001 (2006)] that revealed the first evidence for inhomogeneous shear during startup in cone-plate flow geometry of a rotational rheometer. Using a highly monodisperse sample, we observed the sample to partition into two fractions with different local shear rates instead of possessing a smooth spatial variation of the local shear rate as seen for the polydisperse sam...

We describe the design and construction of a new microrheometer designed to facilitate the viscometric study of complex fluids with very small sample volumes (1–10μl) and gaps of micrometer dimensions. The flexure-based microgap rheometer (FMR) is a shear-rate-controlled device capable of measuring the shear stress in a plane Couette configuration with directly controlled gaps between 1 and 200μm. White light interferometry and a three-point nanopositioning stage using piezo-stepping motors are used to control the parallelism of the upper and lower shearing surfaces, which are constructed from glass optical flats. A compound flexure system is used to hold the fluid sample testing unit between a drive spring connected to an “inchworm” motor and an independent sensor spring. Displacements in the sensing flexure are detected using an inductive proximity sensor. Ready optical access to the transparent shearing surfaces enables monitoring of the structural evolution in the gap with a long working-distance vide...

Measurements are made of the viscoelastic properties of a wormlike micellar solution undergoing steady shearing. The wormlike micellar solution has a clearly defined Maxwell response in oscillation. The features (for example, the plateau of the elastic modulus, G′, and the peak of the viscous modulus, G″) are extremely well defined, allowing the differences in elastic properties brought about by steady-shearing to be easily discerned. An important feature of the solution studied is that it displays a plateau-like region with almost constant shear stress over a range of steady shear rates. We find that as the steady shear rate is increased: (i) G′ becomes negative at low frequencies; (ii) the plateau value of G′ decreases; (iii) the frequency at which the plateau value of G′ is reached shifts to higher frequencies; (iv) the width of the G″ peak decreases; (v) the position of the G″ peak shifts to higher frequencies; and (vi) the height of the G″ peak increases then decreases. The constitutive equations of ...

This article describes a systematic investigation of a discontinuous interfacial stick-slip transition (SST) in simple shear of monodisperse entangled 1,4-polybutadiene (PBD) and polyisoprene (PIP) melts with different molecular weights and architecture, using a specially designed controlled-force shear rheometer. The magnitude of the transition is found to be determined by the level of chain entanglement. Specifically, the dependence of extrapolation length b on molecular weight as b∼Mw3.4 and of the melt viscosity as b∼η is consistent with the observations based on capillary rheometric studies [X. Yang et al., Rheol. Acta 37, 415–423 (1998)]. The interfacial nature of the flow behavior is explicitly demonstrated by a surface treatment of the shearing plates and dependence of the abrupt increase of the apparent shear rate on the gap distance as well as by particle tracking velocimetry. The critical stress for different molecular weights of PBD and PIP is about 0.2 and 0.1MPa, respectively, independent of...

Soft microgel pastes are modeled as a three-dimensional system of randomly packed elastic spheres. Simulations are performed wherein the packing is subject to isochoric uniaxial extension to compute the high- and low-frequency shear moduli for various packing fractions. The simulation results agree well with the data from experiments on crosslinked polymer microgels. The low-frequency shear modulus is found to follow the osmotic pressure (the mean normal stress) closely, especially at high packing fractions. In addition, expressions involving the radial distribution function and the pair-wise Hertzian potential have been used to reproduce the high-frequency shear modulus and the osmotic pressure. The radial distribution functions for varying packing fractions are self-similar and after suitable coordinate transformations, all the first peaks collapse onto a single curve. The shift in the first peak and the peak width are related to the packing fraction through semiempirical scaling relations. Shearing int...

A novel rheometer plate was used to measure radial pressure profiles during cone-and-plate and parallel-plate shearing flows of a concentrated colloidal dispersion of poly(methyl methacryalate) spheres suspended in dioctyl phthalate. There is a long history of using suspensions of this type as a model rheological system. The measured pressure profile can be used to calculate N1 and N2, and also provides a check on the flow field in the rheometer. At shear rates just below onset of shear thickening, our measurements show that N1 is positive as predicted by Stokesian dynamics simulations of model Brownian hard spheres, but we are unable to determine the sign of N2. After the onset of thickening, we find that in both flow geometries the pressure increases sharply with radial position. This is in striking contrast to the pressure profiles ordinarily observed for viscoelastic liquids (with the exception of certain liquid crystal polymers), for which the pressure decreases with radial position. Under these cond...

Synopsis In this paper, a dissipative particle dynamics sDPDd based approach for modeling suspensions is examined. A series of tests is applied comparing simulation results to well established theoretical predictions. The model recovers the dilute limit intrinsic viscosity prediction of Einstein and provides reasonable estimates of the Huggins coefficient for semidilute suspensions. At higher volume fractions, it was necessary to explicitly include lubrication forces into the algorithm as the usual DPD interactions are too weak to prevent overlaps of the rigid bodies and account for other related effects due to lubrication forces. Results were then compared with previous studies of dense hard sphere suspensions using the Stokesian dynamics method and experimental data. Comparison of relative viscosity values determined from strain controlled shearing versus stress controlled shearing simulations are also given. The flow of spheroidal objects is studied. The rotation of a single spheroid under shear is consistent with the predictions of Jeffery. Simulations of sheared spheroids at higher volume fractions produce an apparent nematic phase. An example is given of the application of DPD to model flow in another geometry, gravitational driven flow between parallel cylinders, which is of practical interest. © 2005 The Society of Rheology

The rheology of a liquid crystalline mesophase pitch is reported. Over the range of shear rates and temperatures investigated, the steady state shear viscosity and the first normal stress difference display region 1 and region 2 flow behavior typical of many liquid crystalline systems. A kink in the transition between regions 1 and 2 is also observed. The first normal stress difference is negative at low shear rates, but transitions to positive values in the shear rate region of the kink in the viscosity. These phenomena are explained by change in the molecular orientation of the sample. The evolution of the shear stress in transient startup and relaxation experiments is measured. There is a distinct overshoot in the startup of shearing, and a rapid decay of stress upon cessation of flow. As expected, the magnitude of the overshoot depends on the rest time between shearing. The estimated elastic constant is consistent with other work.

We characterize the configurations and concentration of λ-phage deoxyribose nucleic acid (DNA) molecules in shear flow near a glass surface in a microchannel through epifluorescence microscopy. We observe that in Poiseuille flow, over a region extending from a glass surface up to about one third of the contour length of the DNA molecule, the average stretch of a λ-phage DNA molecule is significantly lower than in the bulk, in agreement with results obtained in a steady torsional shear flow by Li et al. (2004). We also find that the concentration of DNA molecules in this same region is notably lower than in the bulk, to a degree that increases with increasing Weissenberg number. A simplified explanation is proposed for the behavior of DNA molecules near the glass surface based on wall influences on hydrodynamic interaction within the chain, motivated by the recent theoretical work of Jendrejack et al. (2003, 2004).

Concentrated suspensions of non-Brownian spheres dispersed in a Newtonian carrier liquid were placed under large amplitude oscillatory shear flow. It was found that the response wave forms consisted of a transient response after each reversal in the shearing direction, followed by purely viscous behavior. It was thought that rearrangements in the particulate microstructure could account for this transient response. Further, the characteristic strain for the microstructural rearrangement was found to be essentially independent of the oscillation frequency, and showed good agreement with the corresponding characteristic strain obtained from measurements of the transient response after shear reversal in continuous shear experiments. In addition, the fluidity in the oscillatory flow after the transient response was found to be higher than that in the steady flow case. This increase in fluidity was found to depend on the particle size dispersity, with the largest fluidity difference occurring with the monodispersed systems.

Microgel pastes and concentrated emulsions are shown to exhibit a generic slip behavior at low stresses when sheared near smooth surfaces. The magnitude of slip depends on the applied stress. Well above the yield stress, slip is negligible compared to the bulk flow. Just above the yield stress, slip becomes significant and the total deformation results from a combination of bulk flow and slip. At and below the yield stress, the bulk flow is negligible and the apparent motion is entirely due to wall slip. By directly imaging the deformation of pastes and from rheological measurements, we show that slip is characterized by universal scaling properties, which depend on solvent viscosity, bulk shear modulus, and particle size. A model based on elastohydrodynamic lubrication between the squeezed particles and the shearing surface explains these properties quantitatively.

The aim of this work is to model the flow-enhanced crystallization and the flow-induced morphological changes of semi-crystalline materials during and after shearing flow. A FENE-P dumbbell model and a rigid dumbbell model are used to describe the molecular chain conformation and the orientation evolution for the amorphous phase and the semi-crystalline phase, respectively. The effect of flow on crystallization is considered by relating excess free energy and flow-induced orientation to crystallization kinetics. The crystallization of the material couples back to influence the solidification rheology of the crystallizing system. An isotactic polypropylene is used as an example to illustrate model predictions. We predict a pronounced effect of short-term shear treatments in accelerating nucleation and changing rheological behavior. Results are compared with available experimental data.

The effect of dispersed-phase elasticity on steady-state deformation and breakup of isolated droplets for polybutadiene/poly(dimethyl siloxane) blends in simple shearing flow is investigated systematically for values of the dispersed-phase Weissenberg number (Wid) ranging up to around 3, where the Weissenberg number is defined as the ratio of the first normal stress difference to twice the shear stress at the imposed shear rate. The dependence on droplet elasticity of steady-state morphology for 10%-dispersed phase blends is also studied. The polybutadiene droplet phase is an elastic “Boger” fluid prepared by dissolving a high-molecular-weight polybutadiene into a low-molecular-weight Newtonian polybutadiene melt. To isolate the contribution of droplet elasticity, all experiments were done at a fixed viscosity ratio of around unity, achieved by adjusting the temperature appropriately for each blend. When the droplet elasticity increases, the steady-state deformation of isolated droplets decreases for fixe...

The relation between morphology and the steady state rheological behavior has been investigated for blends of immiscible polymers, i.e., polydimethylsiloxane and polyisobutylene, and this over the full composition range. Cryogenic scanning electron microscopy has been used to obtain information about the morphology during shearing. By means of relaxation experiments the stresses have been decomposed in interfacial and component contributions. From the interfacial stress components the orientation of the inclusions could be estimated. These stresses do not provide a clear indication of the location of the phase inversion as they hardly change with concentration in the midconcentration range, they even seem to develop a local minimum around the 50/50 concentration. In this region fibrils can be observed that are nearly oriented in the flow direction. The values of the interfacial stress components are consistent with such a structure. The component contributions to the viscosity can also be explained on the same basis although the normal stresses are underestimated.

Interfacial slip between high density polyethylene (HDPE) and polystyrene (PS) melts was studied. The HDPE/PS layered structure was subjected to steady shear in a Cambridge shearing system. Through thickness melt velocities of the HDPE/PS layered structure were measured in situ by a confocal microscope. Velocity profiles of both HDPE and PS layers were obtained. Velocity discontinuity was observed at the HDPE/PS interface from the velocity profiles and indicated interfacial slip. The slip velocity obtained from velocity discontinuity is in good agreement with that deduced by independent rheological measurements.

This paper describes experimental results on the way immiscible drops of a Newtonian fluid can deform and breakup when subject to oscillatory shear deformation. The paper also reports a matching three-dimensional numerical simulation of corresponding events. Using an optical shearing apparatus and a modified rheometer, experimental observations on the deformation of drops with a viscosity ratio of unity were carried out for a range of strain amplitudes and frequencies. For moderate strain deformations, it was discovered experimentally that the drop deformation oscillates between a maximum and a nonzero minimum deformation parameter and that the numerical simulation was able to capture both this and start up effects. For large strain deformations it was experimentally observed that breakup occurred only by one mechanism; namely, end pinching, and this was successfully matched by the numerical simulation. The results for oscillatory deformation and breakup are compared with those obtained in steady shear.

The role of molecular weight in shear-induced structure transitions, such as striations during shear startup and banding during relaxation, was probed through small-angle light scattering and shear microscopy. The characteristic texture relaxation time for banding, τs, is molecular weight dependent. The minimum molecular weight for these shear-induced complex texture transitions to occur is estimated from τs as 27 000 for a 37 wt % poly(n-hexyl isocyanate) in 1,1,2,2-tetrachloroethane solution at room temperature. τs is independent of applied shear rate, implying that it is a material property. Thus, both of these structure transitions appear to occur only after shearing above a threshold Deborah number, γτs|c, below which viscous forces would suppress these structure transitions. Both the strain dependence of the structure transitions during shear startup and the preshear rate dependence of the banding phenomenon exhibit little or no molecular weight dependence. Increasing molecular weight does appear t...

We have examined the transient stress response under shear flow of concentrated suspensions of non-Brownian 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.

The morphology of biopolymer droplets gelled under shear as the dispersed phase of a two-phase mixture of biopolymers in aqueous solution (or “biopolymer blend”) was investigated experimentally. The process involves shearing the liquid biopolymer blend either at a steady stress till gelation, for creation of ellipsoidal gelled particles, or a stress step-up process for creation of high aspect ratio particles. The resulting particle shapes are analyzed and compared against models for affine deformation conditions [Janssen (1997)] and steady shear conditions [Maffetone and Minale (1998)]. Although they are only strictly valid for Newtonian fluid phases, application of these models to a situation where one phase is gelling, has provided insight into the morphological changes occurring in the shear-gelation process.

Low molecular weight polystyrene melts were subjected to shearing flow which was periodically halted. Weak maxima in both the viscosity and normal stress were observed upon startup of the flow, notwithstanding the absence of entanglements. The strain associated with the viscosity maxima was independent of shear rate, and consistent with the overshoot strains for entangled polymers. The stress overshoots disappeared or were of weaker intensity when the flow was resumed after a brief interruption. For sufficiently long rest periods between flow, the original behavior was reproduced. The time scale for recovery of the maxima was about the same as that for relaxation of the stress from steady state flow. This differs from the behavior of entangled polymers.

A previously proposed reptation model is used to interpret exponential shear flow data taken on an entangled polystyrene solution. Both shear and normal stress measurements are made during exponential shear using mechanical means. The model is capable of explaining all trends seen in the data, and suggests a novel analysis of the data. This analysis demonstrates that exponential shearing flow is no more capable of stretching polymer chains than is inception of steady shear at comparable instantaneous shear rates. In fact, all exponential shear flow stresses measured are bounded quantitatively by stress measurements taken during inception of steady shear. Information taken from the model about chain stretching suggests that normal stress measurements are strong indications of stretching, whereas shear stress measurements are indicative of both chain stretching and segment orientation.