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We study theoretically the steady viscoelastic flow in confined and symmetric hyperbolic channels considering slip along the walls. Under the lubrication approximation and a variety of constitutive models, a high-order perturbation solution with respect to the Deborah number is calculated. The solution for all the field variables (velocity, pressure, and extra-stress) is found analytically up to eighth order and is used along with proper acceleration techniques to achieve convergence up to order one Deborah number. We reveal that even in the presence of slip, the pressure drop decreases monotonically with increasing the fluid elasticity. We evaluate the influence of slip in terms arising from two different decompositions of the pressure drop obtained with the aid of the total force balance and the mechanical energy balance of the flow system. In contrast to the nonslip Newtonian flow, our analysis also showed that the fluid slip along the walls introduces variations in the strain rate at the midplane with the distance from the inlet. However, these are small, and an effective strain rate can be well-represented using a previously developed formula [Housiadas, K. D., and A. N. Beris, Phys. Fluids 36(2), 021702 (2024)]. We also show that when the solution for the midplane velocity is used in the general formula for the Trouton ratio, instead of the Newtonian lubrication solution, there are no appreciable changes, thus confirming the validity and accuracy of our previously reported results [Housiadas, K. D., and A. N. Beris, J. Rheol. 68(3), 327–339 (2024)]. [ABSTRACT FROM AUTHOR]

Shear-induced pair interactions between viscous drops suspended in a viscoelastic matrix are numerically investigated examining the effects of elasticity and drop deformability on their post-collision trajectory. Two different trajectory types are identified depending on the Weissenberg number Wi and capillary number Ca. Drops suspended in a Newtonian matrix (Wi = 0.0) show a passing trajectory where drops slide past each other and separate in the stream-wise direction. However, when increasing the Weissenberg number above a critical value, a tumbling/doublet trajectory is observed where two drops rotate around the midpoint of the line joining their centers, as was also seen previously for rigid particles. The tumbling trajectory is explained by investigating the flow around a single drop in shear. Elasticity generates a larger region of spiraling streamlines around a drop, which, during a pair interaction, traps the second drop giving rise to the tumbling pair. Decreasing deformability (lower Ca) and increasing viscoelasticity (higher Wi) favor a tumbling trajectory. With simulations sweeping the parameter space, we obtain a phase plot of the two different trajectories as functions of Ca and Wi. Treating the tension along the curved streamlines due to the non-zero first normal stress difference in the viscoelastic medium as an enhancement to the interfacial tension, we have developed an approximate force balance model for the zone of spiraling streamlines. It qualitatively captures the observed scaling of the critical Ca and Wi values at the phase boundary. The effects of unequal size, initial configuration, and non-unity viscosity ratio are briefly investigated. [ABSTRACT FROM AUTHOR]

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, yield stress, and thixotropy. There is renewed interest in the modeling of human blood with thixo-elasto-visco-plastic rheological models. Previous work [Armstrong and Tussing, Phys. Fluids 32, 094111 (2020)] has led to the development of the enhanced thixotropic viscoelastic model for blood (ethixo-mHAWB; called here, after a minor modification, ETV) that incorporates viscoelasticity to a thixotropic model for the stress contributed by the rouleaux aggregates, in addition to describing using a nonlinear viscoelastic model the stress contributed by the individual red blood cells deforming under the action of the flow. This model has shown superior performance in fitting human blood steady state and transient rheological data from a strain-controlled rheometer [Horner et al., J. Rheol. 62, 577–591 (2018); 63, 799–813 (2019)] as compared to other alternate models. In the present work, we first develop another variant of the ETV model, the enhanced structural stress thixotropic-viscoelastic (ESSTV) model, and the modification patterned following an elastoviscoplastic model developed recently [Varchanis et al., J. Rheol. 63, 609–639 (2019)]. We develop full tensorial stress formulations of the rouleaux stresses for both the above-mentioned models, resulting in the t-ETV and t-ESSTV models. We use steady state and step-ups, and step-downs in shear rate data to independently fit the parameters of all before-mentioned models. We compare predictions against experimental data obtained on small, large, and unidirectional large amplitude oscillatory shear conditions. We find that the full tensor stress formulations t-ETV and t-ESSTV significantly improved the predictive capability of the earlier ETV model. [ABSTRACT FROM AUTHOR]

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

From results published by Rudolf Hilfer for the similar problem involving dielectric permittivities, we derive an explicit analytic expression for the step-strain relaxation modulus implied by the Havriliak–Negami model for complex viscosities. [ABSTRACT FROM AUTHOR]

From results published by Rudolf Hilfer for the similar problem involving dielectric permittivities, we derive an explicit analytic expression for the step-strain relaxation modulus implied by the Havriliak–Negami model for complex viscosities. [ABSTRACT FROM AUTHOR]

In the finite element framework, we employ decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow and then investigate highly nonlinear behavior in 2D creeping contraction flow. In the analysis of steady solutions as a preliminary study, the results are shown to be free from frustrating mesh dependence when we incorporate the tensor-logarithmic formulation [Fattal and Kupferman, J. Non-Newtonian Fluid Mech. 123, 281-285 (2004)]. Two kinds of elastic fluid have been chosen, that is, highly shear thinning and Boger-type liquids. According to each liquid property, the transient computational modeling has revealed qualitatively distinct dynamics of instability. With pressure difference imposed slightly below the steady convergence limit, the numerical scheme demonstrates fluctuating solution without approaching steady state for the shear thinning fluid. When the pressure fairly higher than the limit is enforced, severe fluctuation of flowrate, oscillation of corner vortices, and also asymmetric irregular stress wave propagation along the downstream channel wall are expressed. In addition, flow dynamics seems quite stochastic with scanty temporal correlation. For the Boger-type fluid, under the traction higher than steady limit, the flowrate and corner vortices exhibit periodic variation with asymmetry added to the dynamics. These express elastic flow instability in this inertialess flow approximation. [ABSTRACT FROM AUTHOR]

The theory of shear-flow-induced coalescence of monodisperse Newtonian droplets in Newtonian and viscoelastic (described by the Maxwell model) matrices has been derived. Changes in flattening of droplets during coalescence are considered. Calculated dependences on the system parameters of probability, Pc, that the droplet collision is followed by their fusion for Newtonian systems agree qualitatively with the Rother-Davis theory [Phys. Fluids 13, 1178-1190, (2001)]. Values of Pc for a certain set of parameters are substantially affected by the model used to describe mobility of the interface. It has been found that increasing elasticity (relaxation time) of the matrix leads to decreasing Pc irrespective of mobility of the interface. This decrease is small for short relaxation times but pronounced for long relaxation times. The shapes of the dependences of Pc on the droplet radii and the shear rate are similar for systems with a Newtonian matrix but differ qualitatively for systems with a viscoelastic matrix. Results of the theory show that Pc for viscous and viscoelastic matrices can be semiquantitatively approximated by a product of probability for spherical droplets and probability for highly flattened droplets, calculated from Janssen's theory ['Dynamics of liquid-liquid mixing,' Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1993] for a viscous system. [ABSTRACT FROM AUTHOR]

Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β∈R such that 0≤β≤1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0≤β≤1/2 and 1/2≤β≤1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to the order of the fractional derivative. Because the critical value 1/2 separates two different behaviors with different mechanical models, we propose to distinguish such different behavior as elasto-viscous case with 0≤β≤1/2 and visco-elastic case for 1/2≤β≤1. The motivations for this different definitions as well as the comparison with other existing mechanical models available in the literature are presented in the paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the rheology of algae suspensions relevant to algae biofuel processing for a range of concentrations up to 15 vol. % using mostly a piezoaxial vibrator (PAV) rheometer as a method of measuring rheological properties. Linear viscoelastic (LVE) measurements of a Scenedesmus obliquus [culture collection of algae and protozoa (CCAP) 276/7] living algae strain were obtained and a curve for complex viscosity (η*) as a function of concentration/volume fraction derived. The PAV complex viscosity data increased exponentially with cell concentration and elasticity (G′) developed in a similar way with increasing concentration. The results indicated the presence of interaction between algae cells at all measured concentrations. For concentrations above ∼5 vol. %, steady shear data obtained using a Couette geometry showed non-Newtonian 'shear-thinning' behavior and at higher concentrations there was a divergence from the Cox-Merz rule. A difference in the LVE rheological measurements was found for cells that were either alive or dead indicating that cell motility and significant interparticle contact and interactions influenced levels of viscoelasticity. The results are of potential scientific relevance and also useful in relation to the design of algae bioprocessing for the production of biofuels. [ABSTRACT FROM AUTHOR]

This paper is concerned with the experimental ability to measure viscoelasticity of low viscosity ink jet fluids and demonstrates the capability of both a piezo axial vibrator and torsion resonator rheometer to capture high frequency rheological data for both model and commercial ink jet fluids. Results are presented for polymer and particle laden suspensions together with a commercial ink. The data demonstrate that high frequency linear viscoelastic rheology can be captured using both rheometers and that both the presence of polymer and particles can induce viscoelasticity within the fluid. It is believed that the physical origin of viscoelastic effects produced by the presence of polymer or particles is different, and this results in a different high frequency limiting slope for the G′ data. [ABSTRACT FROM AUTHOR]

We present a comprehensive rheological study of a suspension of thermosensitive particles dispersed in water. The volume fraction of these particles can be adjusted by the temperature of the system in a continuous fashion. Due to the finite polydispersity of the particles (standard deviation: 17%), crystallization is suppressed and no fluid-crystal transition intervenes. Hence, the moduli G′ and G″ in the linear viscoelastic regime as well as the flow curves (shear stress σ(γ) as function of the shear rate γ) could be measured in the fluid region up to the vicinity of the glass transition. Moreover, flow curves could be obtained over a range of shear rates of 8 orders of magnitude, while G′ and G″ could be measured spanning over 9 orders of magnitude. Special emphasis has been laid on precise measurements down to the smallest shear rates/frequencies. It is demonstrated that mode-coupling theory generalized in the integration through transients framework provides a full description of the flow curves as well as the viscoelastic behavior of concentrated suspensions with a single set of well-defined parameters. [ABSTRACT FROM AUTHOR]

Several internal parameters are studied for a 3D simple shear flow of soft polydispersed granular materials consisting of viscoelastic spheres. These internal parameters include the contact time, the multiple collision group size, and the coordination number. It is found that the contour plots of the contact time and the coordination number in the plane defined by the concentration (solid fraction) and dimensionless stiffness are similar. These contours are qualitatively the same as the regime chart/flowmap proposed in earlier studies. The resulting constitutive relation shows different rate dependency at different concentrations and shear rates. Based on a simple dimensional analysis and a power law formulation, the rate dependency may be expressed by an index. The two extreme values of this index, 0 and 1, correspond to solidlike and gaslike granular materials, respectively. The contour map of this rate index (the power of the dimensionless shear rate in the constitutive relation) resembles those of the λ-shaped curve typical of a phase diagram for ordinary materials. [ABSTRACT FROM AUTHOR]

We have investigated the intentional temporary degradation and the subsequent recovery of the drag-reducing properties of surfactant solutions. Degradation was achieved by exposing the fluid to mechanical stresses after which it showed significantly reduced drag reduction capability. The recovery time varies from a fraction of second to several minutes, depending on the surfactant concentration, the counter-ion concentration and the temperature. The recovery process generally showed a linear increase of the drag reduction level with time, with the rate of recovery being essentially independent of the flow velocity and the initial level of degradation, though the recovery at rest is considerably slower than the recovery under turbulent flow conditions. The recovery time decreases sharply with increasing concentration and temperature, and with increasing counter-ion concentration for the cationic surfactant. The mechanical degradation apparently affects not only the shear-induced structure but also the rod-like micelles themselves. [ABSTRACT FROM AUTHOR]

A filament stretching extensional rheometer and capillary breakup extensional rheometer are used to measure the extensional rheology of a series of wormlike micelle solutions experiencing a uniaxial elongational flow. The experiments are performed using a series of wormlike micelle solutions of both cetylpyridinium chloride and sodium salicylate (NaSal) in an aqueous sodium chloride solution and cetyltrimethylammonium bromide and NaSal in de-ionized water. The linear viscoelasticity of all the wormlike micelle solutions is well described by a Maxwell model with just one or two relaxation times while the steady shear measurements all demonstrate characteristics of shear banding at large shear rates. In transient homogeneous uniaxial extension imposed by a filament stretching rheometer, each of the wormlike micelle solutions demonstrate significant strain hardening. At large extension rates, the wormlike micelle solution filaments are all found to fail through a dramatic rupture near the axial midplane at a constant stress independent of imposed extension rate. The result is an extensional viscosity that decays linearly with increasing extension rate. This filament failure likely stems from the local scission of individual wormlike micelle chains. For the more concentrated solutions, as the imposed extension rate is reduced, a critical extension rate is found below which the filament does not rupture, but instead elastocapillary pinch off is recovered and the elastic tensile stresses achieved in the fluid filament grow far beyond the value observed at rupture. This dramatic upturn in the elastic tensile stress and the extensional viscosity at low extension rates is not intuitively expected and is most likely a result of structural changes to the entangled wormlike micelle solution. Strain hardening is also observed in capillary breakup rheometry experiments, however, when the results of filament stretching and capillary breakup rheometry measurements at nominally the same extension rate are superimposed, the results do not agree; the extensional viscosity measurements from filament stretching are in some instances more than an order of magnitude larger. This result calls into question the use of capillary breakup rheometry for quantitatively measuring the extensional viscosity of wormlike micelle solutions. [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 coalescence in air of two polymeric drops into a single drop (also referred to as sintering) was investigated for two thermotropic liquid crystalline polymers. Initial coalescence via elastic contact was ruled out based on the magnitude of the equilibrium compliance values and the process was, therefore, believed to be driven by surface tension and resisted by means of viscous flow. Remarkably the viscous coalescence model developed for Newtonian fluids (an extension of the Frenkel and Eshelby approach) agreed well under some conditions of temperature with coalescence data (i.e., observation of neck growth under a microscope). On the other hand, the extension of the Newtonian model to the viscoelastic case by incorporating the upper convected Maxwell model (UCM) assuming steady state stresses always underpredicted the rate of coalescence. The viscous neck growth model using the UCM constitutive equation was extended to the transient stress case in order to incorporate the slow growth of viscosity at the startup of flow. The unsteady state UCM approach represented a qualitative improvement over the Newtonian and steady state UCM formulations because it predicted accelerated coalescence, relative to the Newtonian model, by increasing the relaxation time. However, the model was unable to quantitatively predict the experimental coalescence rates, as it overpredicted the acceleration of coalescence. [ABSTRACT FROM AUTHOR]

We have developed a sensitive method to detect very low levels of long chain branching in sparsely branched polymers and applied it to high-density polyethylene samples with broad molar mass distribution obtained by Ziegler–Natta, Phillips, and metallocene catalysis. We compare experimental dynamic moduli with predicted values. The predicted moduli, which are only valid for truly linear chains, are computed from a known molar mass distribution by the application of a modified time-dependent diffusion reptation model described in [van Ruymbeke et al., Macromolecules 35, 2689 (2002)]. Discrepancies between experimental and predicted moduli are observed at branching levels below the usual detection limit of 13C nuclear magnetic resonance (about 1 branch per 10000 carbon atoms). Our method is easier to implement and the results more clearcut than those obtained by the zero-shear viscosity method. The sensitivity is comparable with the activation energy spectrum method described in [Wood-Adams et al., Macromolecules 33, 7489 (2000)]. The use of our method is however not restricted to thermorheologically complex polymers. The interest of polymer fractionation is also demonstrated for the detection of extremely low levels of long chain branching. [ABSTRACT FROM AUTHOR]

We study the motion of a Brownian probe particle subjected to a small amplitude oscillatory external force and immersed in a colloidal dispersion, as a theoretical benchmark for particle-tracking microrheology experiments. The application of an external force on the probe drives the microstructure of the dispersion out of equilibrium; opposing this is the Brownian diffusion of the probe and colloidal “bath” particles. The degree to which the microstructure is driven away from equilibrium is given by the nondimensional external force on the probe, or Péclet number, Pe. The nonequilibrium microstructure of the dispersion is calculated for small departures from equilibrium, i.e., to first order in Pe, and to leading order in the bath particle volume fraction, accounting for excluded volume and hydrodynamic interactions between particles. The nonequilibrium microstructure is used to calculate the average velocity of the probe, from which one may infer the complex microviscosity (or modulus) of the dispersion via application of Stokes drag law. The microviscosity is computed over the entire range of oscillation frequencies, thereby determining the linear viscoelastic response of the dispersion. After appropriate scaling, our results are in qualitative agreement with traditional (macro-) rheology studies, suggesting that oscillatory-probe microrheology can be a useful tool to examine the viscoelasticity of hard-sphere colloidal dispersions and perhaps other complex fluids. [ABSTRACT FROM AUTHOR]

We investigate active particle-tracking microrheology in a colloidal dispersion by Brownian dynamics simulations. A probe particle is dragged through the dispersion with an externally imposed force in order to access the nonlinear viscoelastic response of the medium. The probe’s motion is governed by a balance between the external force and the entropic “reactive” force of the dispersion resulting from the microstructural deformation. A “microviscosity” is defined by appealing to the Stokes drag on the probe and serves as a measure of the viscoelastic response. This microviscosity is a function of the Péclet number (Pe=Fa/kT)—the ratio of “driven” (F) to diffusive (kT/a) transport—as well as of the volume fraction of the force-free bath particles making up the colloidal dispersion. At low Pe—in the passive microrheology regime—the microviscosity can be directly related to the long-time self-diffusivity of the probe. As Pe increases, the microviscosity “force-thins” until another Newtonian plateau is reached at large Pe. Microviscosities for all Péclet numbers and volume fractions can be collapsed onto a single curve through a simple volume fraction scaling and equate well to predictions from dilute microrheology theory. The microviscosity is shown to compare well with traditional macrorheology results (theory and simulations). [ABSTRACT FROM AUTHOR]