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Rheology plays a pivotal role in understanding the flow behavior of fluids by discovering governing equations that relate deformation and stress, known as constitutive equations. Despite the importance of these equations, current methods for deriving them lack a systematic methodology, often relying on sense of physics and incurring substantial costs. To overcome this problem, we propose a novel method named Rheo-SINDy, which employs the sparse identification of nonlinear dynamics (SINDy) algorithm for discovering constitutive models from rheological data. Rheo-SINDy was applied to five distinct scenarios, four with well-established constitutive equations, and one without predefined equations. Our results demonstrate that Rheo-SINDy successfully identified accurate models for the known constitutive equations and derived physically plausible approximate models for the scenario without established equations. Notably, the identified approximate models can accurately reproduce nonlinear shear rheological properties, especially at steady state, including shear thinning. These findings validate the availability of Rheo-SINDy in handling data complexities and underscore its potential for advancing the development of data-driven approaches in rheology. Nevertheless, further refinement of learning strategies is essential for enhancing robustness to fully account for the complexities of real-world rheological data. [ABSTRACT FROM AUTHOR]

The rheological characterization of complex liquids is of great importance in many applications. Among the properties that can be measured, the relaxation time has great relevance, as it provides a measure of fluid elasticity. In this work, we propose a novel method to estimate the longest relaxation time of viscoelastic fluids by applying machine learning to microfluidics. Specifically, we train a long-short term memory (LSTM) neural network to identify the Weissenberg number that characterizes the dynamics of trains of rigid particles suspended in a viscoelastic liquid flowing in a cylindrical microchannel. We first study the effect of the Weissenberg number on the evolution of the microstructure through numerical simulations. An in silico dataset consisting of the distributions of the interparticle distances at different channel sections is built and used to train the network. The performance of the LSTM model is tested on both classification and regression problems. The proposed method is nonintrusive, requires a simple setup, and can in principle be used to measure other properties of the fluid. [ABSTRACT FROM AUTHOR]

Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson's® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids. [ABSTRACT FROM AUTHOR]

Coalescence event in pendant and sessile droplets is distinguished by the formation and evolution of the liquid bridge created upon singular contact. For Newtonian droplets, the bridge radius, R , is known to evolve as R ∼ t b , with universal values of the power-law exponent, b , signifying the dominant governing forces. However, recent works on different subclasses of rheologically complex fluids comprising of macromolecules have highlighted the effects of additional forces on coalescence. In this work, we experimentally explore the phenomenon in distinct subclasses of rheologically complex fluids, namely, colloidal and noncolloidal suspensions, that have particle hydrodynamic interactions as the origin of viscoelasticity. Our observations suggest that such fluids have flow-dependent thinning responses with finite elasticity in shear rheology but negligible elasticity in extensional rheology. Based on these, the study extends the Newtonian universality of b = 0.5 to these thinning fluids. Further, we fortify these observations through a theoretical model developed by employing Ostwald–de Waele's constitutive law. Finally, we utilize this theoretical model to inspect the existence of arrested coalescence in generalized Newtonian fluids. [ABSTRACT FROM AUTHOR]

Equibiaxial elongational deformations are omnipresent in polymer processing technologies. The challenge of generating well-controlled equibiaxial elongational deformations in the laboratory has, however, severely inhibited progress on understanding the rheology of polymeric liquids and other complex fluids in this flow. More recently, a novel technique known as continuous lubricated squeezing flow has been developed that allows for rheological measurements in equibiaxial elongational deformations. In the present study, we examine the rheological behavior of two entangled polyisobutylene (PIB) melts with different molecular weight distributions in constant strain rate equibiaxial elongation flows. These new data are compared with predictions from two molecular models for entangled polymer melts inspired by the idea that entanglements dominate the relaxation dynamics. One model is the discrete slip-link model (DSM), and the other is known as the Rolie Double Poly (RDP) model. For the PIB with a relatively narrow molecular weight distribution, the predictions of both models are in good agreement with experiments and the DSM gives nearly quantitative agreement. For the broad molecular weight distribution PIB, both the DSM and RDP model predict strain hardening, which is not observed in the experiments. [ABSTRACT FROM AUTHOR]

Understanding the yielding of complex fluids is an important rheological challenge that affects our ability to engineer and process materials for a wide variety of applications. Common theoretical understandings of yield stress fluids follow the Oldroyd–Prager formalism in which the material behavior below the yield stress is treated as solidlike, and above the yield stress as liquidlike, with an instantaneous transition between the two states. This formalism was built on a quasi-static approach to the yield stress, while most applications, ranging from material processing to end user applications, involve a transient approach to yielding over a finite timescale. Using stress-controlled oscillatory shear experiments, we show that yield stress fluids flow below their yield stresses. This is quantified through measuring the strain shift, which is the value about which the strain oscillates during a stress-controlled test and is a function of only the unrecoverable strain. Measurements of the strain shift are, therefore, measurements of flow having taken place. These experimental results are compared to the Herschel–Bulkley form of the Saramito model, which utilizes the Oldroyd–Prager formalism, and the recently published Kamani–Donley–Rogers (KDR) model, in which one constitutive equation represents the entire range of material responses. Scaling relationships are derived, which allow us to show why yield stress fluids will flow across all stresses, above and below their yield stress. Finally, derivations are presented that show strain shift can be used to determine average metrics previously attainable only through recovery rheology, and these are experimentally verified. [ABSTRACT FROM AUTHOR]

Surfactants at gas-liquid and liquid-liquid interfaces have profound effects on interfacial stresses that strongly influence flow in bulk phases in contact with the interface. These effects include changes in interfacial tension and the development of extra stresses that arise when the interface is deformed. Surfactants are important in nature, biological function, and numerous technologies. Understanding interfacial rheology is critical to the development of improved surfactants for these important applications. Here, we propose a novel and noninvasive technique for the investigation of interfacial rheological behavior in shear deformations. In recent years, several techniques for such measurements have been developed and utilized to study a wide range of surfactant systems. However, existing techniques may inherently be invasive making it difficult to isolate the intrinsic interfacial rheological behavior from disturbances to the interface caused by the measurement itself. The proposed technique is indirect in that it does not require the introduction of a probe to deform the interface making it noninvasive. The viability of the technique is demonstrated through comprehensive fluid dynamics modeling of the flow involving a gas-liquid interface with different rheological behaviors. [ABSTRACT FROM AUTHOR]

The formation and evolution of a heterogeneous flow and flow reversal are examined in highly elastic, gel-like wormlike micelles (WLMs) formed from an amphiphilic triblock poloxamer P234 in 2M NaCl. A combination of linear viscoelastic, steady shear, and creep rheology demonstrate that these WLMs have a yield stress and exhibit viscoelastic aging, similar to some soft glassy materials. Nonlinear shear rheology and rheoparticle tracking velocimetry reveal that these poloxamer WLMs undergo a period of strong elastic recoil and flow reversal after the onset of shear startup. As flow reversal subsides, a fluidized high shear rate region and a nearly immobile low shear rate region of fluid form, accompanied by wall slip and elastic instabilities. The features of this flow heterogeneity are reminiscent of those for aging yield stress fluids, where the heterogeneous flow forms during the initial stress overshoot and is sensitive to the inherent stress gradient of the flow geometry. Additionally, macroscopic bands that form transiently above a critical shear rate become "trapped" due to viscoelastic aging in the nearly immobile region. This early onset of the heterogeneous flow during the rapidly decreasing portion of the stress overshoot differs from that typically observed in shear banding WLMs and is proposed to be necessary for observing significant flow reversal. Exploring the early-time, transient behavior of this WLM gel with rheology similar to both WLM solutions and soft glassy materials provides new insights into spatially heterogeneous flows in both of these complex fluids. [ABSTRACT FROM AUTHOR]

Rheological characterization of complex fluids subjected to cyclic shear-rate sweep often exhibits hysteresis. Since both viscoelastic and thixotropic materials show hysteresis loops, it is important to understand distinguishing features (if any) in the same shown by either. Lately, there has been substantial work that attempts to relate the area enclosed by the hysteresis loop with the manner in which shear rate is varied in the cycle, in order to infer thixotropic parameters of a material. In this work, we use the nonlinear Giesekus model to study its response to the application of cyclic shear-rate sweep. We find that this model produces each type of qualitatively similar hysteresis loop that has hitherto been ascribed to thixotropic materials. We also show that the area of the hysteresis loop for a viscoelastic material as a function of sweep rate shows bell-shaped/bi-modal curves as has been observed for thixotropic materials. This study illustrates that caution needs to be exercised while attributing hysteresis loops and associated features observed in a material exclusively to thixotropy. Another feature related to the hysteresis loop is the occurrence of shear banding instability. We find that viscoelastic hysteresis may not have any connection to shear banding instability. [ABSTRACT FROM AUTHOR]

Oscillatory rheology, at both small and large (LAOS) amplitudes, was performed to measure the dynamic response of a soft solid, formed on dispersing colloids into a thermotropic nematic liquid crystal at volume fractions of ϕ > 18 %. Due to weak homeotropic anchoring of nematogens at colloid surfaces, a Saturn-ring defect line, known as a "disclination," encircles each particle and entangles with neighboring Saturn-ring disclinations [Wood et al., Science 334, 79–83 (2011)]. We present the first experimental investigation of the yielding behavior of the resulting gel to reveal the underpinning physics. Results reveal that the frequency response of the composite is independent of volume fraction ϕ , an indication that the dispersed phase simply increases the density of disclinations spanning the composite without further effect. Beyond the linear viscoelastic regime (LVR), LAOS experiments indicate the composite is an elastoplastic fluid exhibiting both strain-hardening and shear-thinning behaviors with Chebyshev coefficients e 3 > 0 and ν 3 < 0 , respectively. We deduce that the disclination number density nd is constant until the strain amplitude is sufficient to break disclinations leading to shear-thinning behavior beyond the LVR. A simple theory is introduced revealing that the Ericksen number E r determines the onset of flow, when E r > 1 , generating a strain-hardening response since Frank elasticity resists reorientation of molecular alignment within confined nematic domains. Above a critical frequency ω c , the loss modulus G ″ increases slowly due to enhanced viscosity within confined nematic domains, G ″ ∝ ω 1 / 2 [Larson, R. G., The Structure and Rheology of Complex Fluids (Oxford University, 1999), p. 463]. Observation of this behavior in a small-molecule nematic solvent provides insights into the physics of flow behavior in other, more complex, defect-mediated liquid crystalline structures exhibiting similar properties [Colby, Europhys. Lett. 54, 269–274 (2001); Sahoo and Dhara, Liq. Cryst. 44, 1582–1591 (2017); and Romo-Uribe, Polym. Adv. Technol. 32, 651–662 (2021)]. [ABSTRACT FROM AUTHOR]

In single-particle microrheology, the viscoelastic properties of a complex fluid can be extracted using the generalized Stokes–Einstein (GSE) relation by embedding a micrometer-sized particle and tracking its motion through the fluid. Applying the same analysis to molecular dynamics simulations can result in overestimated G ∗ values because of the hydrodynamic interaction between the probe bead and its periodic images. We derive a simple correction to the GSE equation by implementing an analytical solution for Stokes drag on a periodic array of spheres, which allows smaller box sizes to be simulated while still retaining accuracy. Fluid and particle inertia are neglected, although the approach used here might be generalized to include them. The correction is applied to molecular dynamics simulations of a coarse-grained polymer melt. For several bead-to-box-size ratios R / L and two probe sizes, we measure the mean squared displacement and calculate G ∗ using both the original GSE and the corrected hydrodynamic Stokes–Einstein (HSE) equations. These results are compared to small amplitude oscillatory non-equilibrium molecular dynamics (NEMD) simulations, which show that the HSE analysis correctly predicts the G ∗ values at low frequencies but breaks down when either fluid inertia is important or the bead size is too small to "see" a continuum. For small R / L , the GSE and HSE results are similar, although a small correction is still required for the finite box size and computational cost is significantly larger. The HSE equation allows the use of smaller box sizes, reducing computational costs by more than an order of magnitude. [ABSTRACT FROM AUTHOR]

A new pressure sensor array, positioned on the bottom plate of a standard torsional rheometer, is presented. It is built from a unique piezo-capacitive polymeric foam and consists of 25 capacitive pressure sensors (of surface 4.5 × 4.5 mm 2 each) built together in a 5 × 5 regular array. The sensor array is used to obtain a mapping of the normal stresses in complex fluids, which dramatically extends the capability of the rheometer. We demonstrate this with three examples. First, a pressure profile is reconstructed in a polymer solution, which enables the simultaneous measurement of the first and the second normal stress differences N 1 and N 2 , with a precision of 2 Pa. In a second part, we show that negative pressures can also be measured. Finally, we focus on the normal stress fluctuations that extend both spatially and temporally in a shear-thickening suspension of cornstarch particles. We evidence the presence of a unique heterogeneity rotating very regularly. In addition to their low cost and high versatility, the sensors show here their potential to finely characterize the normal stresses in viscosimetric flows. [ABSTRACT FROM AUTHOR]

In this work, we introduce a comprehensive machine-learning algorithm, namely, a multifidelity neural network (MFNN) architecture for data-driven constitutive metamodeling of complex fluids. The physics-based neural networks developed here are informed by the underlying rheological constitutive models through the synthetic generation of low-fidelity model-based data points. The performance of these rheologically informed algorithms is thoroughly investigated and compared against classical deep neural networks (DNNs). The MFNNs are found to recover the experimentally observed rheology of a multicomponent complex fluid consisting of several different colloidal particles, wormlike micelles, and other oil and aromatic particles. Moreover, the data-driven model is capable of successfully predicting the steady state shear viscosity of this fluid under a wide range of applied shear rates based on its constituting components. Building upon the demonstrated framework, we present the rheological predictions of a series of multicomponent complex fluids made by DNN and MFNN. We show that by incorporating the appropriate physical intuition into the neural network, the MFNN algorithms capture the role of experiment temperature, the salt concentration added to the mixture, as well as aging within and outside the range of training data parameters. This is made possible by leveraging an abundance of synthetic low-fidelity data that adhere to specific rheological models. In contrast, a purely data-driven DNN is consistently found to predict erroneous rheological behavior. [ABSTRACT FROM AUTHOR]

An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies, revealing a rich dataset consisting of up to 19 measurements of the third-order complex modulus at distinct three-frequency coordinates. We discuss how the choice of input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and reducing variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting dataset is indeed large and feature-rich, while still acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represent measurements of an intrinsic material function by studying its internal consistency, compatibility with low-frequency predictions for Coleman–Noll simple fluids, and agreement with data obtained via MAOS amplitude sweeps. Finally, the data are compared to predictions from the corotational Maxwell model to demonstrate the power of MAPS rheology in determining whether a constitutive model is consistent with a material's time-dependent response. [ABSTRACT FROM AUTHOR]

We explore theoretically the interplay between shear banding and edge fracture in complex fluids by performing a detailed simulation study within two constitutive models: the Johnson–Segalman model and the Giesekus model. We consider separately parameter regimes in which the underlying constitutive curve is monotonic and nonmonotonic, such that the bulk flow (in the absence of any edge effects) is, respectively, homogeneous and shear banded. Phase diagrams of the levels of edge disturbance and of bulk (or quasibulk) shear banding are mapped as a function of the surface tension of the fluid–air interface, the wetting angle where this interface meets the walls of the flow cell, and the imposed shear rate. In particular, we explore in more detail the basic result recently announced by Hemingway and Fielding [Phys. Rev. Lett. 120, 138002 (2018)]: that precursors to edge fracture can induce quasibulk shear banding. We also appraise analytical predictions that shear banding can induce edge fracture [S. Skorski and P. D. Olmsted, J. Rheol., 55, 1219 (2011)]. Although a study of remarkable early insight, Skorski and Olmsted [J. Rheol., 55, 1219 (2011)] made some strong assumptions about the nature of the "base state," which we examine using direct numerical simulation. The basic prediction that shear banding can cause edge fracture remains valid but with qualitatively modified phase boundaries. [ABSTRACT FROM AUTHOR]

A new electrorheological cell for the capillary breakup extensional rheometer (HaakeTM CaBER 1TM, Thermo Scientific) allowing the analysis of the rheological properties of complex fluids under the simultaneous application of an extensional flow and an electric field has been developed and tested. In this study, the add-on is described in full detail and different cornstarch suspensions in olive oil are characterized under different stretching conditions with and without an electric field. The results show that, under extensional flow and no electric field, the sample behaves as a Newtonian-like fluid, showing a linear relationship between time and filament minimum diameter. However, when the external electric field is imposed, the filament thinning process delays increasing the breakup time. If the external electric field is further increased, then the filament may even not break, depending on the imposed voltage, the Hencky strain, and the concentration of particles in the fluid sample. [ABSTRACT FROM AUTHOR]

We perform a detailed theoretical study of the edge fracture instability, which commonly destabilizes the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means of direct nonlinear simulations, we map out phase diagrams showing the degree of edge fracture in the plane of the surface tension of the fluid-air interface and the imposed shear rate, within the Giesekus and Johnson–Segalman models, for different values of the nonlinear constitutive parameters that determine the dependencies on the shear rate of the shear and normal stresses. The threshold for the onset of edge fracture is shown to be relatively robust against variations in the wetting angle where the fluid-air interface meets the hard walls of the flow cell, whereas the nonlinear dynamics depend strongly on the wetting angle. We perform a linear stability calculation to derive an exact analytical expression for the onset of edge fracture, expressed in terms of the shear-rate derivative of the second normal stress difference, the shear-rate derivative of the shear stress (sometimes called the tangent viscosity), the jump in the shear stress across the interface between the fluid and the outside air, the surface tension of that interface, and the rheometer gap size. (The shear stress to which we refer is σ x y with x ^ being the flow direction and y ^ being the flow-gradient direction. The interface normal is in the vorticity direction z ^ .) Full agreement between our analytical calculation and nonlinear simulations is demonstrated. We also elucidate in detail the mechanism of edge fracture and finally suggest a new way in which it might be mitigated in experimental practice. We also suggest that, by containing the second normal stress difference, our criterion for the onset of edge fracture may be used as a means to determine that quantity experimentally. Some of the results in this paper were first announced in an earlier letter [E. J. Hemingway, H. Kusumaatmaja, and S. M. Fielding, Phys. Rev. Lett. 119, 028006 (2017)]. The present paper provides additional simulation results, calculational details of the linear stability analysis, and more detailed discussion of the significance and limitations of our findings. [ABSTRACT FROM AUTHOR]

We have progressively developed an ultrasonic spinning rheometry (USR) that has the potential to visualize complex details of rheology, such as time-dependence, coexistence of gel and sol, effective viscosity of multiphase fluids, and other particulars. This rheometry makes it possible to overcome the main issues in conventional rheometry, originating from nonideal velocity profiles in the complex fluids. The most notable advantage of USR is the ability to perform "local" rheological evaluations from only the velocity information for a short-time period by solving the equation of motion. This benefit is provided while avoiding noise augmentations by introducing a linear viscoelastic analysis in the frequency domain. Solving the equation of motion with a rheological model equation in the frequency domain, multiple rheological parameters are quantified by minimizing the cost function. In this paper, the analysis presented by USR is verified by comparative experiments using a rheometer with the typical geometry of parallel disks. As a complementary technique for conventional rheometers, the USR efficacies are shown through rheological assessments for Newtonian, shear-thinning, and thixotropic fluids. Additionally, USR can provide instantaneous flow curves O(1 s) that lead to understanding the rheology in complex fluids with time-dependency. [ABSTRACT FROM AUTHOR]

Carbon black suspensions exhibit complex, shear-dependent macroscopic properties that are a consequence of the state of the suspension microstructure. In this work, the shear-induced microstructure of a model, reversible suspension of conductive carbon black in propylene carbonate is measured using simultaneous steady shear rheology and small angle neutron scattering. These experiments provide microstructural evidence for a bifurcation in the rheological properties. We show that the demarcation line for this bifurcation is the inverse Bingham number, Bi−1, which relates the magnitude of the stress response to an applied shear rate to the yield stress of the presheared suspension. At high shear rates where Bi−1 > 1, the suspension flows homogeneously and exhibits a thixotropic response that arises due to the self-similar breakdown of agglomerates with increasing shear rate. Conversely, at low shear rates where Bi−1 < 1, the applied shear drives the densification and growth of these agglomerates. This densification process leads to a gravitationally driven instability resulting in an inhomogeneous volume fraction distribution along the height of the geometry that is a function of both time under shear and shear rate. Under these shear conditions, the suspension exhibits apparent rheopexy, or antithixotropy, where a significant decline in the viscosity is observed with a step down in shear rate. The unique microstructural measurements presented here reconcile many observations in the literature regarding carbon black suspensions, including an apparent shear-thickening behavior, tunability of both the yield stress and elasticity through shear history, and transient macroscopic properties. [ABSTRACT FROM AUTHOR]

Edge instabilities are believed to be one of the possible causes of shear banding in entangled polymeric fluids. Here, we investigate the effect of edge disturbance on the shear-induced dynamics of well-entangled DNA solutions. Using a custom high-aspect-ratio planar-Couette cell, we systematically measure the velocity profiles of sheared DNA samples at different distances away from the edge of the shear cell. Under a weak oscillatory shear with the corresponding Weissenberg number (Wi) smaller than 1, where DNA solutions exhibit linear velocity profiles with strong wall slip, the penetration depth of the edge disturbance is on the order of the gap thickness of the shear cell, consistent with the behavior of Newtonian fluids. However, under a strong oscillatory shear with Wi > 1 that produces shear-banding flows, the penetration depth is an order of magnitude larger than the gap thickness and becomes spatially anisotropic. Moreover, we find that the shear-banding flows persist deep inside the sheared sample, where the effect of edge disturbance diminishes. Hence, our experiments demonstrate an abnormally long penetration depth of edge disturbance and illustrate the bulk nature of shear-banding flows of entangled polymeric fluids under time-dependent oscillatory shear. [ABSTRACT FROM AUTHOR]

We propose a rheometry using ultrasonic velocity profiling (UVP) that visualizes and evaluates quantitatively opaque complex fluids in a cylindrical open vessel performing unsteady rotation. The methodology termed "ultrasonic spinning rheometry (USR)" is expected to provide details of various rheological properties. In our study of USR applications, an enhancement in measuring some rheological properties was achieved for three different non-Newtonian fluids. For quantitative evaluations, we focused on momentum propagation in unsteady shear flows from an oscillating cylindrical container. In such flows, this propagation is represented in the radial profiles of the phase lag of velocity fluctuations. The phase lag information is obtained by a discrete Fourier transform of the spatio-temporal velocity distributions measured using UVP and indicates that the phase lag changes substantially as rheological properties change in a test fluid. As the primary rheological property, a local effective viscosity that is representative of the Newtonian viscosity in the bulk of a measurement volume is determined using UVP. In addition, the shear stress distribution, yield stress, spatial viscosity profile, and shear modulus are obtained as secondary rheological properties. [ABSTRACT FROM AUTHOR]

The soft glassy rheology (SGR) model has successfully described the time dependent simple shear rheology of a broad class of complex fluids including foams, concentrated emulsions, colloidal glasses, and solvent-free nanoparticle-organic hybrid materials (NOHMs). The model considers a distribution of mesoscopic fluid elements that hop from trap to trap at a rate which is enhanced by the work done to strain the fluid element. While an SGR fluid has a broad exponential distribution of trap energies, the rheology of NOHMs is better described by a narrower energy distribution and we consider both types of trap energy distributions in this study. We introduce a tensorial version of these models with a hopping rate that depends on the orientation of the element relative to the mean stress field, allowing a range of relative strengths of the extensional and simple shear responses of the fluid. As an application of these models we consider the flow of a soft glassy material through a dilute fixed bed of fibers. The dilute fixed bed exhibits a range of local linear flows which alternate in a chaotic manner with time in a Lagrangian reference frame. It is amenable to an analytical treatment and has been used to characterize the strong flow response of many complex fluids including fiber suspensions, dilute polymer solutions and emulsions. We show that the accumulated strain in the fluid elements has an abrupt nonlinear growth at a Deborah number of order one in a manner similar to that observed for polymer solutions. The exponential dependence of the hopping rate on strain leads to a fluid element deformation that grows logarithmically with Deborah number at high Deborah numbers. SGR fluids having a broad range of trap energies flowing through fixed beds can exhibit a range of rheological behaviors at small Deborah numbers ranging from a yield stress, to a power law response and finally to Newtonian behavior. [ABSTRACT FROM AUTHOR]

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag-Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to show how predictions of nonlinear viscometric properties, such as shear-thinning in the viscosity and in the first normal stress coefficient, can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and suitably modify it for power-law materials exhibiting Mittag-Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox-Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel- Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule, which is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shear-thinning Cross-type or Carreau-type flow curves. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters. [ABSTRACT FROM AUTHOR]

Large amplitude oscillatory shear (LAOS) fingerprinting of the nonlinear response of polymers and other complex soft matter has proven an excellent tool in the characterization of such materials. The major methods of quantitative characterization of nonlinearity using LAOS are the use of Lissajous-Bowditch (LB) curves and Fourier transform rheology (FTR). Another LAOS-based tool, mechanical spectral hole burning (MSHB), has been developed in our labs to investigate the heterogeneous dynamics of polymer melts and solutions and offers the possibility of a complementary method to the LB and FTR analyses for the fingerprinting of the nonlinear response of polymers and other complex fluids. Here, we present results from an investigation of the MSHB, LB loop, and FTR behaviors of polybutadiene and polystyrene solutions. The goal of the study was to examine similarities and differences in how these methods "fingerprint" the nonlinear response of the different polymer solutions. We find that the vertical holes in the MSHB experiments vary in intensity with the square of the sine wave pump magnitude. This is also true for the third harmonics obtained in the FTR, but the origins are possibly different for the two signatures. We have analyzed the fingerprinting categories as a function of strain amplitude and frequency from the LB loops and higher harmonics of FTR and add an additional feature to the fingerprints that are related to MSHB signatures, which are found to complement the other two methods and add new information to the fingerprinting diagrams. [ABSTRACT FROM AUTHOR]

Oscillatory shear is a widely used characterization technique for complex fluids but the microstructural changes that produce the material response are not well understood. We apply a recent micromechanical model to soft particle glasses subjected to oscillatory flow. We use particle scale simulations at small, intermediate and large strain amplitudes to determine their microstructure, particle scale mobility, and macroscopic rheology. The macroscopic properties computed from simulations quantitatively agree with experimental measurements on well-characterized microgel suspensions, which validate the model. At the mesoscopic scale, the evolution of the particle pair distribution during a cycle reveals the physical mechanisms responsible for yielding and flow and also leads to quantitative prediction of shear stress. At the local scale, the particles remain trapped inside their surrounding cage below the yield strain and yielding is associated with the onset of large scale rearrangements and shear-induced diffusion. This multiscale analysis thus highlights the distinct microscopic events that make these glasses exhibit a combination of solid-like and liquid-like behavior. [ABSTRACT FROM AUTHOR]

We characterize the linear viscoelastic properties of complex fluids using a new technique, based on the measurement of surface fluctuations: surface fluctuation specular reflection (SFSR) spectroscopy. The thermally excited waves propagating on a free surface are measured through the deflection of a laser beam specularly reflected from that surface. Elastic and loss moduli of the complex fluids are inferred from the measured power spectrum density of thermal noise, with the implicit use of Kramers-Kronig relations. The technique, besides being noninvasive, provides rheological data in a large frequency range and at vanishing strains. It is therefore especially well suited for the rheological characterization of complex fluids. We present measurements of the viscoelastic modulus of supramolecular polymer solutions in a frequency range extending up to six decades. We compare the SFSR measurements with rheometric data at low and high frequencies, and show that they are in good agreement. Using supramolecular polymer solutions of different natures, exhibiting or not surface viscoelasticity, we furthermore show that SFSR provides a characterization of the bulk properties of the fluids. In addition, we discuss the accuracy of the measurements. [ABSTRACT FROM AUTHOR]

The behavior of materials under tension is a rich area of both fluid and solid mechanics. For simple fluids, the breakup of a liquid as it is pulled apart generally exhibits an instability driven, pinch-off type behavior. In contrast, solid materials typically exhibit various forms of fracture under tension. The interaction of these two distinct failure modes is of particular interest for complex fluids, such as foams, pastes, slurries, etc. The rheological properties of complex fluids are well-known to combine features of solid and fluid behaviors, and it is unclear how this translates to their failure under tension. In this paper, we present experimental results for a model complex fluid, a bubble raft. As expected, the system exhibits both pinch-off and fracture when subjected to elongation under constant velocity. We report on the critical velocity vc below which pinch-off occurs and above which fracture occurs as a function of initial system width W, length L, bubble size R, and fluid viscosity for both monodisperse and polydisperse systems. Though both exhibit a transition from pinch-off to fracture, the behavior as a function of L/W is qualitatively different for the two systems. For the polydisperse systems, the results for the critical velocity are consistent with a simple scaling law vcτ/R∼L/W, where the fluid viscosity sets the typical time for bubble rearrangements τ. We show that this scaling can be understood in terms of the dynamics of local bubble rearrangements (T1 events). For the monodisperse systems, we observe a critical value for L/W below which the system only exhibits fracture. [ABSTRACT FROM AUTHOR]

In this study, we use microparticle image velocimetry (μ-PIV) and adapt a commercial birefringence microscopy system for making full-field, quantitative measurements of flow-induced birefringence (FIB) for the purpose of microfluidic, optical rheometry of two wormlike micellar solutions. In combination with conventional rheometric techniques, we use our microfluidic rheometer to study the properties of a shear-banding solution of cetylpyridinium chloride (CPyCl) with sodium salicylate (NaSal) and a nominally shear-thinning system of cetyltrimethylammonium bromide (CTAB) with NaSal across many orders of magnitude of deformation rates (10-2≤γ≤104s-1). We use μ-PIV to quantify the local kinematics and use the birefringence microscopy system in order to obtain high-resolution measurements of the changes in molecular orientation in the wormlike fluids under strong deformations in a microchannel. The FIB measurements reveal that the CPyCl system exhibits regions of localized, high optical anisotropy indicative of shear bands near the channel walls, whereas the birefringence in the shear-thinning CTAB system varies more smoothly across the width of the channel as the volumetric flow rate is increased. We compare the experimental results to the predictions of a simple constitutive model, and we document the breakdown in the stress-optical rule as the characteristic rate of deformation is increased. [ABSTRACT FROM AUTHOR]

We investigate the response of a well-characterized colloidal star glass to large-amplitude oscillatory stress and strain fields. By combining these measurements with dynamic time sweeps we demonstrate the importance of probing both strain- and stress-induced nonlinear rheology of such complex fluids in order to elucidate the yielding and fluidization behavior. We also show that, due to the strong time dependence, it is essential to perform dynamic time sweeps at different strain and stress amplitudes, which result in different departures of the glass cage from its quiescent quasiequilibrium structure. This allows for steady-state responses to be reached and for nonlinear oscillatory responses to be treated properly while also suggesting that yielding is a gradual process. Further, we use a recently published framework for analyzing nonlinear responses to large-amplitude oscillatory shear [Rogers et al., J. Rheol. 55, 435 (2011)], based on the analysis of the whole stress waveforms as a sequence of physical processes, in order to measure the points of static and dynamic yielding. By doing so, we show that the stress-amplitude dependence of the dynamic yield stress can be linked to the strain-rate-amplitude dependence via the form of the steady-state flow curve. [ABSTRACT FROM AUTHOR]

Room temperature ionic liquids (ILs) are a class of complex fluids with valuable physical properties. Therefore, the investigation of dynamics of IL is vital for the fundamental understanding of their physical nature as well as for the successful engineering design in their applications. We succeeded in performing the first in-depth rheological studies of two ionic liquids of different nature in a wide frequency and temperature range (up to the glass transition and beyond), utilizing advanced techniques with an oversampling procedure and with adjustment of the instrument compliance. The important physical parameters of IL, such as Vogel temperatures, fragility, fractional free volume at the glass transition temperature, and volume expansion coefficient, were determined by rheology. Deviation from the Vogel-Fulcher-Tammann behavior is detected in the vicinity of the glass transition. The master curves of dynamic moduli for both IL show systematic deviations from Maxwell behavior in the low and high frequency domains. The calculated spectra exhibit a broad relaxation time distribution, which can be approximated by two non-Maxwellian modes. We attribute the fast mode to the motion of single ions, while the slow mode might reflect the cooperative motion of ions. Our results are supported by recent dielectric and optical studies, theoretical models, and simulations, which reported dynamical heterogeneities in IL. [ABSTRACT FROM AUTHOR]

We develop a systematic method for the derivation of closed-form and thermodynamically consistent constitutive equations of complex fluids from microscopic models. The method builds upon our recent work [Ilg et al., Phys. Rev. E 79, 011802 (2009)] on thermodynamically guided simulations within a consistent coarse-graining scheme. These simulations are powerful at low to intermediate flow rates and have the considerable advantage that they do not require flow-adapted boundary conditions, i.e., operate at arbitrary homogeneous flows. The new method for deriving constitutive equations is illustrated for low-molecular polymer melts subjected to imposed, homogeneous flow fields. The differential constitutive equation we obtain for this model system is a simple, nonlinear equation of change for the conformation tensor, from which the stress tensor is readily obtained. The proposed constitutive model shows shear thinning (shear viscosity exhibiting fractional power laws in the range -0.40 to -0.86, the corresponding range for the first viscometric function is -1.20 to -1.43), stress overshoots, normal stress coefficients, and elongational viscosities in agreement with reference results. The constitutive equation can be interpreted as a molecularly derived, modified Giesekus model with conformation-dependent coefficients. [ABSTRACT FROM AUTHOR]

The present work investigates nonlinear behavior in large amplitude oscillatory shear (LAOS) of four different polymeric materials using simultaneous conventional rheometric measurements and particle-tracking velocimetric observations. In contrast to most studies in the literature that treat nonlinearity in LAOS in steady state, we emphasize by the present four examples that nonlinearity in LAOS often arise in complex fluids due to time-dependent rearrangement of their microstructures in response to LAOS. Consequently, no correlation is obvious between strain dependence of the steady-state stress response and the time-dependent characteristics of the steady-state response. For instance, a highly viscoelastic material made of nano-sized polybutadiene particles exhibits homogeneous deformation and an approximate sinusoidal wave despite strong strain softening. In a second example, a well-entangled polybutadiene solution becomes inhomogeneous over time, and the corresponding nonlinearity (i.e., strain softening) took a finite time to develop to its fullest. In the example of wall slip of a monodisperse entangled polyisoprene melt, contrary to the literature claim that even harmonics would emerge, we show that the stress response only involves odd harmonics in the absence of any edge fracture. Last, a polydisperse poly(dimethyl siloxane) melt experiences homogeneous LAOS without displaying significant higher harmonics in the absence of any edge failure. In contrast, the Fourier transform analysis shows that meniscus failure is responsible for the emergence of higher harmonics including some even ones. [ABSTRACT FROM AUTHOR]

Transient structure development at a specific distance from the channel wall in a pressure-driven flow is obtained from a set of real-time measurements that integrate contributions throughout the thickness of a rectangular channel. This “depth sectioning method” retains the advantages of pressure-driven flow while revealing flow-induced structures as a function of stress. The method is illustrated by applying it to isothermal shear-induced crystallization of an isotactic polypropylene using both synchrotron x-ray scattering and optical retardance. Real-time, depth-resolved information about the development of oriented precursors reveals features that cannot be extracted from ex-situ observation of the final morphology and that are obscured in the depth-averaged in-situ measurements. For example, at 137 °C and at the highest shear stress examined (65 kPa), oriented thread-like nuclei formed rapidly, saturated within the first 7 s of flow, developed significant crystalline overgrowth during flow and did not relax after cessation of shear. At lower stresses, threads formed later and increased at a slower rate. The depth sectioning method can be applied to the flow-induced structure development in diverse complex fluids, including block copolymers, colloidal systems, and liquid-crystalline polymers. [ABSTRACT FROM AUTHOR]

Diffusing wave spectroscopy’s (DWS) sensitivity to local shear rate has been used to investigate the nonlinear rheology of (1) a doped shear thinning, semidilute polymer solution measured in the cone-plate and parallel-plate geometries and of (2) doped shear banding wormlike micelles solutions measured in the cylindrical-Couette geometry. DWS measurements of the semidilute polymer solution in the cone-plate geometry under stress controlled conditions were used to construct a flow curve for the material, the expected radial dependence of the local shear rate being demonstrated in the parallel-plate geometry. The method is shown to be sensitive to shear banding in semidilute wormlike micelles in the cylindrical-Couette geometry under strain controlled conditions, and DWS correlation functions were quantitatively interpreted using a heterogeneous shear flow model. Flow curves and shear rate profiles were inferred from these measurements. [ABSTRACT FROM AUTHOR]

We describe the design and construction of a new microrheometer designed to facilitate the viscometric study of complex fluids with very small sample volumes (1–10 μl) 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 200 μm. 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 video microscope. This configuration then allows us to determine the microgap-dependent flow behavior of complex fluids over 5 decades of shear rate. We demonstrate the capability of the FMR by characterizing the complex stress and gap-dependent flow behavior of a typical microstructured food product (mayonnaise) over the range of gaps from 8 to 100 μm and stresses from 10 to 1500 Pa. We correlate the gap-dependent rheological response to the microstructure of the emulsion and changes induced in the material by prolonged shearing. [ABSTRACT FROM AUTHOR]

A new microrheology set-up which allows us to quantitatively measure the transient rheological properties of solvent-responsive complex fluids was constructed by integrating particle tracking microrheology and microfluidics. The dialysis cell consists of a reservoir, porous dialysis membrane, and sample chamber. Solvent molecules can freely diffuse between the reservoir and the sample chamber while macromolecular sample components are trapped in the sample chamber with a rigid semipermeable dialysis membrane. The design enables manipulation of the solvent composition in the sample chamber by simply switching the fluid composition in the reservoir. Validation experiments for solvent diffusion in the dialysis cell showed good agreement with numerical solutions of the transport equations and confirmed that the solvent composition in a sample can be changed in a controlled and predictable fashion within a few minutes due to the small device dimensions. For aqueous solutions of sodium alginate and sodium polystyrene sulfonate, transient rheological properties were measured in response to changes in salt concentration. The results showed that the dialysis cell is a useful and versatile tool to study the response of complex fluids to reversible changes in solvent composition. [ABSTRACT FROM AUTHOR]