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In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes. [ABSTRACT FROM AUTHOR]

New in vitro measurements from two human donors for both steady and transient hemorheology are presented that are particularly suited for testing thixotropic and viscoelastic models for human blood and are made available to the community along with the relevant blood physiology. This more complete data set is analyzed within the context of recent thixo-elasto-visco-plastic models, and we improve upon the Horner-Armstrong-Wagner-Beris (HAWB) model to better model transient hemorheology. The improved model features an additional viscoelastic equation for the red blood cell rouleaux within blood, along with simplifications to the structure kinetics equation. The resulting model is fit to additional experimental data on human whole blood for a step shear change and steady shear experiments, and the corresponding parameter values are used to predict oscillatory shear moduli, transient large amplitude oscillatory shear, and unidirectional large amplitude oscillatory shear data. The modified HAWB model shows significant improvement in fitting and predicting the experimental data. Specifically, a significant overshoot is captured in step shear changes from a low shear rate to a moderate shear rate, and a plateau for the storage modulus is observed at low frequencies. Highly nonlinear behavior is observed for the third harmonic in unidirectional large amplitude oscillatory shear in the form of multiple extremum separated widely in frequency, which can be identified with the two dominant mechanisms for generating viscoelasticity in human blood, namely, rouleaux structuring and red blood cell deformation. We also discuss the potential applications and difficulties associated with the constitutive modeling of transient blood rheology and provide insight into microstructural sources of the stress contributions to the bulk flow behavior. [ABSTRACT FROM AUTHOR]

The mechanics of understanding a new application of the bracket theory of Non-Equilibrium Thermodynamics that allows for the incorporation of microstructural inertia effects within conformation tensor-based constitutive models of macroscopic material behavior is presented. Introducing inertia effects generally requires the replacement of a first order in time evolution equation for the conformation tensor by a second order one. Through the analysis of a simple damped oscillator we bring forward here the close connection to the structural dissipation brackets present in the two cases, with the weights being inverted as one transitions from the inertialess to the inertial description. Moreover, one may also describe inertial effects in material flow in certain situations through a simple modification of the first order evolution equation for the conformation tensor, which consists of adding a new non-affine term that couples the conformation and the vorticity tensors, as detailed in a recent publication (P. M. Mwasame, N. J. Wagner and A. N. Beris, Phys. Fluids, 30 (2018), 030704). As shown there, when applied to the low particle Reynolds flow of dilute emulsions, this reduced inertial flow model provides predictions consistent with literature-available microscopically based asymptotic results. [ABSTRACT FROM AUTHOR]

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

The flow behavior of mixtures of micron-sized cubic particles suspended in a concentrated colloidal dispersion is investigated across a broad range of cubic particle concentrations. In the semi-dilute regime, the qualitative shape of the dynamic moduli and flow curves reflect those of the underlying colloidal dispersion medium. These curves are superimposed with the underlying colloidal dispersion using shift factors that are found to be larger than those obtained in a recent study of suspensions of non-colloidal spherical particles in the same colloidal dispersion medium. At higher concentrations of cubic particles, deviations from this shifting procedure are apparent. Scaling calculations suggest depletion interactions are responsible for the increase in the low shear viscosity and confinement of the underlying colloidal dispersion can be expected to enhance the shear thickening behavior at high shear stresses. The results of this study provide guidance for formulating suspensions through control of particle shape and mixture concentration. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1091-1101, 2017 [ABSTRACT FROM AUTHOR]

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

We study the medium amplitude oscillatory shear (MAOS) of a semi-dilute, hard-sphere colloidal dispersion. Through solution of the Smoluchowski equation governing the statistical distribution of suspended particles in the semi-dilute limit, we calculate the linear viscoelasticity and the normal stress differences that arise from oscillatory shear as an expansion in terms of small rates of deformation. The effects of hydrodynamic versus conservative interactions are studied via the excluded-annulus model for the hard-sphere interactions. This treats the hardsphere interactions as a steric barrier that resides beyond the hydrodynamic radius of the particles and allows for continuous variation of the strength of hydrodynamic interactions. We see remarkable distinctions between suspensions that are freely draining and those for which hydrodynamic lubrication among the particles dominate their motion. In oscillatory shear flow of a freely draining suspension at high-frequency, the normal stress differences are generated by hard-sphere stresses. In contrast, for a hydrodynamically interacting suspension at highfrequency, the first normal stress difference derives from Brownian stresses while the second normal stress difference is dominated by hydrodynamic stresses. When the first normal stress difference is plotted parametrically against the oscillatory rate of strain, the resulting Lissajous- Bowditch curves for freely draining suspensions and those with full hydrodynamic interactions take on distinct and disparate shapes. Additionally, we use an asymptotic analysis to predict that the third harmonic of the suspension stress for hard spheres is dominated by the hydrodynamic lubrication in the limit of high frequency oscillation. Our calculations demonstrate that under MAOS, hydrodynamic interactions play a central and qualitative role in the stress response of a semi-dilute colloidal dispersion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Dispersions of multiarm star polymers in an athermal solvent are studied as a model system to explore the effects of soft colloidal interactions on the dynamics of colloidal glasses. Linear viscoelastic measurements in the glassy state are congruent with Mode Coupling Theory predictions for hard sphere glasses at moderate frequencies, indicating similarities in the relaxation processes of hard and soft colloidal glasses near equilibrium. On the other hand, distinct features of the star relaxation (related to arm disengagement) are observed to affect the nonlinear behavior associated with shear melting of the glass, which exhibits transitions previously unreported for hard sphere systems. Whereas a single maximum in G″(γ) is evident under large amplitude oscillatory shear at frequencies near the beta relaxation, secondary transitions between yielding and the onset of macroscopic flow are observed at higher and lower frequencies. The latter are annealed out upon complete fluidization of the star polymer suspension. The overall nonlinear behavior of the soft glassy suspension is interpreted in terms of two primary mechanisms: (i) deformation and yielding of the cage-like glassy microstructure, as in the hard sphere case, and (ii) local stretching and disengagement of interpenetrating arms of the colloidal star polymers. [ABSTRACT FROM AUTHOR]

The topology of self-assembled surfactant solutions includes varying degrees of micellar branching, ranging from linear wormlike micelles to a micellar network. Micellar branching acts as an effective attraction between micelles such that network condensation can lead to phase separation. Unlike chemical branching in polymers, micellar branches are labile. Movement of branches along a micelle contour has therefore been proposed as a mechanism of stress relaxation that leads to a reduction in the structural relaxation time and thus, the zero-shear viscosity. Branching is also thought to suppress flow alignment, and for lower levels of branching, may also suppress instabilities such as shear banding. The suppression of shear banding can lead to a lesser degree of shear-thinning in the apparent viscosity at higher shear rates, as well as a reduction in extensional thickening. However, for higher levels of branching, shear can induce branching for samples in proximity to such a phase transition, which can result in shear banding due to shear-induced phase separation. Recent modeling and simulations of the energetics of branching, as well as experiments on model systems, show that the reduction in zero-shear viscosity is due to micelle branching. Current research includes efforts to develop a more mechanistic, quantitative understanding of micellar branching and more generally, its effects on micellar solution rheology. [ABSTRACT FROM AUTHOR]

Abstract: We present a systematic study of the self-assembly of wormlike micelles (WLMs) comprised of cetyltrimethylammonium bromide (CTAB) and sodium nitrate (NaNO3) in aqueous solution as a function of CTAB concentration, NaNO3 concentration, and temperature throughout the dilute and semi-dilute regions of the phase diagram where linear micelles are observed. Combining measurements using isothermal titration calorimetry, rheometry, flow-birefringence, cryo-transmission electron microscopy (cryo-TEM), and small angle neutron scattering (SANS) enables complete characterization of the structure, thermodynamics, and rheology of CTAB/NaNO3 micelles. The addition of NaNO3 is found to increase the micellization enthalpy as well as the micellar scission energy, resulting in the elongation and growth of WLMs. We find quantitative agreement between the scission energy determined from rheology and the enthalpy of micellization determined from ITC, as well as for contour lengths extracted from rheology and SANS. At fixed molar ratio of NaNO3 and CTAB, the solution rheology exhibits scaling consistent with dilute, semi-dilute overlapping, and semi-dilute entangled regimes typically found in polymer solutions, as confirmed by cryo-TEM and SANS. The transition between these scaling regimes coincides with the structural transitions identified by SANS. The results validate the relationship between structural parameters and rheological behavior underlying theories for ionic WLMs. [Copyright &y& Elsevier]