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We report the first-ever complete measurement of MAOStress material functions, which reveal that stress can be more fundamental than strain or strain rate for understanding linearity limits as a function of Deborah number. The material used is a canonical viscoelastic liquid with a single dominant relaxation time: Polyvinyl alcohol (PVA) polymer solution crosslinked with tetrahydroborate (Borax) solution. We outline experimental limit lines and their dependence on geometry and test conditions. These MAOStress measurements enable us to observe the frequency dependence of the weakly nonlinear deviation as a function of stress amplitude. The observed features of MAOStress material functions are distinctly simpler than MAOStrain, where the frequency dependence is much more dramatic. The strain-stiffening transient network model (SSTNM) was used to derive a model-informed normalization of the nonlinear material functions that accounts for their scaling with the linear material properties. Moreover, we compare the frequency-dependence of the critical stress, strain, and strain-rate for the linearity limit, which are rigorously computed from the MAOStress and MAOStrain material functions. While critical strain and strain-rate change by orders of magnitude throughout the Deborah number range, the critical stress changes by a factor of about two, showing that stress is a more fundamental measure of nonlinearity strength. This work extends the experimental accessibility of the weakly nonlinear regime to stress-controlled instruments and deformations, which reveal material physics beyond linear viscoelasticity but at conditions that are accessible to theory and detailed simulation.

Extensibility is beyond the paradigm of classical soft glassy materials, and more broadly, yield-stress fluids. Recently, model yield-stress fluids with significant extensibility have been designed by adding polymeric phases to classically viscoplastic dispersions [1, 2, 3]. However, fundamental questions remain about the design of and coupling between the shear and extensional rheology of such systems. In this work, we propose a model material, a mixture of soft glassy microgels and solutions of high molecular weight linear polymers. We establish systematic criteria for the design and thorough rheological characterization of such systems, both in shear and in extension. Using our material, we show that it is possible to dramatically change the behavior in extension with minimal change in the shear yield stress and elastic modulus, thus enabling applications that exploit orthogonal modulation of shear and extensional material properties., Comment: 23 pages, 13 figures, Supplementary Information included (6 pages)

Thixotropy, anti-thixotropy, and viscoelasticity are three types of time-dependent dynamics that involve fundamentally different underlying physical processes. Yet distinguishing them can be very challenging, which hinders the understanding of structure-property relations. Here we show that hysteresis is a promising technique to contrast the three dynamics by exploring signatures of the most basic thixotropic, anti-thixotropic, and nonlinear viscoelastic models. From these signatures, using shear-rate controlled ramps that begin and end at high shear rates, we identify two distinguishing features in hysteresis loops. The first is the direction of the hysteresis loops: clockwise for thixotropy, but counterclockwise for viscoelasticity and anti-thixotropy. A second feature is achieved at high ramping rates where all responses lose hysteresis: the viscoelastic response shows a stress plateau at low shear rates (lack of stress relaxation), whereas the thixotropic and anti-thixotropic responses are purely viscous with minimal shear thinning or thickening. The features are observed independent of the model details. We establish further evidence for these signatures by experimentally measuring the hysteresis of thixotropic Laponite suspensions, anti-thixotropic carbon black suspensions, and viscoelastic poly (ethylene oxide) solutions. The protocols explored here can be used to distinguish thixotropy, anti-thixotropy, and viscoelasticity, which helps reveal the underlying microstructural physics of complex fluids.

We report a detailed experimental study of peculiar thixotropic dynamics of carbon black (CB, Vulcan XC-72) suspensions in mineral oil, specifically the observation of sequential stress increase then decrease at a fixed shear rate in a step-down test. We verify that such dynamics, though peculiar, come from a true material response rather than experimental artifacts. We also reveal how this long-time stress decay is associated with anti-thixotropy, rather than viscoelasticity, by using orthogonal superposition (OSP) rheometry to probe viscoelastic moduli during the step-down tests. The orthogonal storage and loss modulus are present, showing this two-timescale recovery then decay response, which demonstrates that this response is anti-thixotropic, and it involves shear-induced structuring. We further show a mechanical anisotropy in the CB suspension under shear using OSP. Based on the rheological results, a microstructural schematic is proposed, considering qualitatively thixotropic structure build-up, anti-thixotropic densification, and anisotropic structure evolution. Our observation for these CB suspensions is outside the standard paradigm of thixotropic structure-parameter models, and the elastic response provides us with new insight into the transient dynamics of CB suspensions.

Uncertainty propagates through calculations, down to molecular scales to infer microstructural features, and up to macroscopic scales with predictive flow simulations. Here we study uncertainty quantification for sequential (two-step) versus simultaneous (all at once) fitting methods with linear and weakly-nonlinear rheological data. Using an example of a combined dataset on small-amplitude oscillatory shear (SAOS) and medium-amplitude oscillatory shear (MAOS) for a linear entangled polymer melt (cis-1,4-polyisoprene), we demonstrate with a multi-mode Giesekus model how the fit parameter uncertainties are significantly under-estimated with the sequential fit because of the neglect of model parameter correlations. These results are surprising because weakly-nonlinear data is only an asymptotic step away from the linear data, yet it has significant impact on calibrating the linear model parameters. Similarly, the nonlinear parameter estimates and uncertainties are impacted by considering the linear data in a simultaneous fit. To compare multi-mode spectra of nonlinear parameters (mobility parameters {\alpha_i} from the Giesekus model), we derive new average measures based on moments of the spectra related to the high-frequency MAOS limit. The spectral averages are also sensitive to sequential versus simultaneous fitting. Our results reveal the importance of using simultaneous fitting for honest uncertainty quantification, even with weakly-nonlinear data., Comment: 46 pages, 12 figures; includes Supplementary Information

There is no universal model for thixotropy, and comparing thixotropic effects between different fluids is a subtle yet challenging problem. We introduce a generalized (model-insensitive) framework for comparing thixotropic properties based on thixotropic spectra. A superposition of exponential stress modes distributed over thixotropic timescales is used to quantify buildup and breakdown times and mode strengths in response to step-change input. This mathematical framework is tested with several experimental step-shear rate data on colloidal suspensions. Low-dimensional metrics based on moments of the distribution reveal characteristic average thixotropic properties which are visualized on Ashby-style diagrams. This method outlines a framework for describing thixotropy across a diverse range of microstructures, supporting scientific studies as well as material selection for engineering design applications., Comment: 27 pages, 7 figures, Supplementary Information included in ancillary files as SI.pdf

We show that Hertzian particle contacts are the underlying cause of the as-yet-unexplained noninteger power laws in weakly nonlinear rheology. In the medium amplitude oscillatory shear (MAOS) region, the cubic scaling of the leading order nonlinear shear stress ($\sigma_\mathrm{3} \sim \gamma_\mathrm{0}^{m_\mathrm{3}}$, $m_\mathrm{3}=3$) is the standard expectation. Expanding on the work by Natalia et al. [J. Rheol. 64 625-635 (2020)], we report an extensive data set of noncubical, noninteger power law scalings $m_\mathrm{3}$ for particle suspensions in two immiscible fluids with a capillary attractive interaction, known as capillary suspensions. Here, we show that distinct power law exponents are found for the storage and loss moduli and these noninteger scalings occur at every secondary fluid concentration for two different contact angles. These compelling results indicate that the noninteger scalings are related to the underlying microstructure of capillary suspensions. We show that the magnitude of the third harmonic elastic stress scaling $m_\mathrm{3,elastic}$ originates from Hertzian-like contacts in combination with the attractive capillary force. The related third harmonic viscous stress scaling $m_\mathrm{3,viscous}$ is, found to be associated with adhesive-controlled friction. These observations, conducted for a wide range of compositions, can help explain previous reports of noninteger scaling for materials involving particle contacts and offers a new opportunity using the variable power law exponent of MAOS rheology to reveal the physics of particle bonds and friction in the rheological response under low deformation instead of at very high shear rates.

This is an integrated experimental and theoretical study of the dynamics and rheology of self-crosslinked, slightly charged, temperature responsive soft Poly(N-isopropylacrylamide) (pNIPAM) microgels over a wide range of concentration and temperature spanning the sharp change in particle size and intermolecular interactions across the lower critical solution temperature (LCST). Dramatic, non-monotonic changes in viscoelasticity are observed with temperature, with distinctive concentration dependences in the dense fluid, glassy, and soft-jammed states. Motivated by our experimental observations, we formulate a minimalistic model for the size dependence of a single microgel particle and the change of interparticle interaction from purely repulsive to attractive upon heating. Using microscopic equilibrium and time-dependent statistical mechanical theories, theoretical predictions are quantitatively compared with experimental measurements of the shear modulus. Good agreement is found for the nonmonotonic temperature behavior that originates as a consequence of the competition between reduced microgel packing fraction and increasing interpar-ticle attractions. Testable predictions are made for nonlinear rheological properties such as the yield stress and strain. To the best of our knowledge, this is the first attempt to quantitatively understand in a unified manner the viscoelasticity of dense, temperature-responsive microgel suspensions spanning a wide range of temperatures and concentrations., Comment: additional supplementary information provided

We use high-speed imaging to study the effect of thixotropic aging in drop impact of yield-stress fluids on pre-coated substrates. Our results reveal that drop splashing is suppressed for "aged" compared to "unaged" samples, indicating that thixotropic breakdown timescales during impact are long enough to affect the dynamics. We propose and test several hypotheses for modifying the dimensionless group ${\rm IF}(D/t)$ [1,2] to account for thixotropic aging. The main challenge is that the steady flow properties (Herschel-Bulkley model parameters) used in the current dimensionless group cannot be defined or measured for thixotropically aged samples, because any deformation inherently rejuvenates and breaks down the microstructure. We find the most suitable hypothesis is to only increase the yield stress ($\sigma_{\rm y}$, plastic component) based on the storage modulus of aged samples, while keeping the viscous parameters ($K$ or $\eta_{\infty}$) constant. The work reveals fundamental insight into rarely studied short-timescale flow conditions with thixotropic effects. These results are important for applications such as fire suppression or spray coating that involve complex fluids of varying degrees of thixotropic aging.

We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS (Martinetti & Ewoldt Phys. Fl. (2019)). The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.

We report viscous flow properties of a redox-active organic molecule, N-(2-(2-methoxyethoxy)ethyl)phenothiazine (MEEPT), a candidate for non-aqueous redox flow batteries, and two of its radical cation salts. A microfluidic viscometer enabled the use of small sample volumes in determining viscosity as a function of shear rate and concentration in the non-aqueous solvent, acetonitrile, both with and without supporting salts. All solutions tested show Newtonian behavior over shear rates of up to 30,000 1/s, which is rationalized by scaling arguments for the diffusion-based relaxation time of a single MEEPT molecule without aggregation. Neat MEEPT is flowable but with a large viscosity (412 mPa s) at room temperature), which is approximately 1,000 times larger than acetonitrile. When dissolved in acetonitrile, MEEPT solutions have low viscosities; at concentrations up to 0.5 M, the viscosity increases by less than a factor of two. From concentration-dependent viscosity measurements, molecular information is inferred from intrinsic viscosity (hydrodynamic diameter) and the Huggins coefficient (interactions). Model fit credibility is assessed using the Bayesian Information Criterion (BIC). It is found that the MEEPT and its charged cation are "flowable" and do not flocculate at concentrations up to 0.5 M. MEEPT has a hydrodynamic diameter of around 0.85 nm, which is largely insensitive to supporting salt and state of charge. This size is comparable to molecular dimensions of single molecules obtained from optimized structures using density function theory calculations. The results suggest that MEEPT is a promising candidate for redox flow batteries in terms of its viscous flow properties., Comment: 22 pages, 11 figures in manuscript; 8 pages, 5 figures in supporting information

We report temperature-responsive soft composites of semiflexible biopolymer networks (fibrin) containing dispersed microgel colloidal particles of poly(N-isopropylacrylamide) (pNIPAM) that undergo a thermodynamically driven de-swelling transition above a Lower Critical Solution Temperature (LCST). Unlike standard polymer-particle composites, decreasing the inclusion volume of the particles (by increasing temperature)is concomitant with a striking increase of the overall elastic stiffness of the composite. We observe such a behavior over a wide composition space. The composite elastic shear modulus reversibly stiffens by up to 10-fold over a small change in temperature from 25-35{\deg}C. In isolation, the fibrin network and microgel suspension both soften with increased temperature, making the stiffening of the composites particularly significant. We hypothesize that stiffening is caused by contracting microgel particles adsorbing on the fibrin filaments and modifying the structure of the semiflexible network. We develop two phenomenological models that quantify this hypothesis in physically distinct manners, and the derived predictions are qualitatively consistent with our experimental data, Comment: 35 pages, 14 figures

We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, neutral, repulsive pNIPAM microgel suspensions over concentration (c) range spanning the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G'~$c^{5.64}$, followed by a sharp crossover to a nearly linear growth at high concentrations. We formulate a theoretical approach to address all three regimes within a single conceptual Brownian dynamics framework. A minimalist single particle description is constructed that allows microgel size to vary with concentration due to steric de-swelling effects. Using a Hertzian repulsion interparticle potential and a suite of statistical mechanical theories, quantitative predictions under quiescent conditions of microgel collective structure, dynamic localization length, elastic modulus, and the structural relaxation time are made. Based on a constant inter-particle repulsion strength parameter which is determined by requiring the theory to reproduce the linear elastic shear modulus over the entire concentration regime, we demonstrate good agreement between theory and experiment. Theoretical predictions of how quiescent structural relaxation time changes under deformation, and how the yield stress and strain change as a function of concentration has been made. Reasonable agreement with our observations is obtained. To the best of our knowledge, this is the first attempt to quantitatively understand structure, quiescent relaxation and shear elasticity, and nonlinear yielding of dense microgel suspensions using microscopic force based theoretical methods that include activated hopping processes. We expect our approach will be useful for other soft polymeric particle suspensions in the core-shell family.

Hagfish slime is a unique predator defense material containing a network of long fibrous threads each ~ 10 cm in length. Hagfish release the threads in a condensed coiled state known as thread cells, or skeins (~ 100 microns), which must unravel within a fraction of a second to thwart a predator attack. Here we consider the hypothesis that viscous hydrodynamics can be responsible for this rapid unraveling, as opposed to chemical reaction kinetics alone. Our main conclusion is that, under reasonable physiological conditions, unraveling due to viscous drag can occur within a few hundred milliseconds, and is accelerated if the skein is pinned at a surface such as the mouth of a predator. We model a single thread cell unspooling as the fiber peels away due to viscous drag. We capture essential features by considering one-dimensional scenarios where the fiber is aligned with streamlines in either uniform flow or uniaxial extensional flow. The peeling resistance is modeled with a power-law dependence on peeling velocity. A dimensionless ratio of viscous drag to peeling resistance appears in the dynamical equations and determines the unraveling timescale. Our modeling approach is general and can be refined with future experimental measurements of peel strength for skein unraveling. It provides key insights into the unraveling process, offers potential answers to lingering questions about slime formation from threads and mucous vesicles, and will aid the growing interest in engineering similar bioinspired material systems., Comment: 30 pages, 11 figures, RevTeX 4-1 style

This is an entry to the Gallery of Fluid Motion at the 66th annual meeting of the APS-DFD, held November 2013 in Pittsburgh, PA. In this fluid dynamics video we demonstrate distinct features of yield-stress fluid droplets impacting pre-coated surfaces., Comment: Video included, 2:57 in length (high-quality mpeg-4, small size version mpeg-1)

We introduce a comprehensive scheme to physically quantify both viscous and elastic rheological nonlinearities simultaneously, using an imposed large amplitude oscillatory shear (LAOS) strain. The new framework naturally lends a physical interpretation to commonly reported Fourier coefficients of the nonlinear stress response. Additionally, we address the ambiguities inherent in the standard definitions of viscoelastic moduli when extended into the nonlinear regime, and define new measures which reveal behavior that is obscured by conventional techniques., Comment: 10 pages, 3 figures, full-page double-space preprint format