Filling the gap between transient and steady shear rheology of aqueous graphene oxide dispersions

Even though the rheological behavior of aqueous graphene oxide (G-O) dispersions has been shown to be strongly time-dependent, only few transient measurements have been reported in the literature. In this work, we attempt to fill the gap between transient and steady shear rheological characterizations of aqueous G-O dispersions in the concentration range of 0.004 < ? <?3.5 wt%, by conducting comprehensive rheological measurements, including oscillatory shear flow, transient shear flow, and steady shear flow. Steady shear measurements have been performed after the evaluation of transient properties of the G-O dispersions, to assure steady-state conditions. We identify the critical concentration ? _c =?0.08 wt% (where G-O sheets start to interact) from oscillatory shear experiments. We find that the rheology of G-O dispersions strongly depends on the G-O concentration ?. Transient measurements of shear viscosity and first normal stress difference suggest that G-O dispersions behave like nematic polymeric liquid crystals at ?/? _c =?25, in agreement with other work reported in the literature. G-O dispersions also display a transition from negative to positive values of the first normal stress difference with increasing shear rates. Experimental findings of aqueous graphene oxide dispersions are compared and discussed with models and experiments reported for nematic polymeric liquid crystals, laponite, and organoclay dispersions.     

Rheology of molecular liquids and concentrated suspensions by microscopic dynamical simulations

The rheology and the associated changes that arise in sheared molecular and colloidal liquids are investigated by Molecular and Brownian Dynamics Computer Simulation. Significant shear thinning and normal pressure effects occur in all liquids when the shear rate approximately equals an inverse characteristic relaxation time for the material. The shear and bulk moduli, and self-diffusion coefficients increase with shear rate for all liquids and stable dispersions. The importance for rheology of hydrodynamic coupling between macromolecule trajectories at high packing fractions is demonstrated. The infinite frequency moduli depend on the packing fraction to a power which is effectively the same for all materials, i.e. ca. 3.5, above a percolation transition at a packing fraction 0.25. The suspending fluid enhances the degree of shear thinning above that of the corresponding single component fluid consisting of pure macroparticles.     

Viscoelastic melt rheology and time–temperature superposition of polycarbonate–multi-walled carbon nanotube nanocomposites

This work investigates the linear and non-linear viscoelastic melt rheology of four grades of polycarbonate melt compounded with 3 wt% Nanocyl NC7000 multi-walled carbon nanotubes and of the matching matrix polymers. Amplitude sweeps reveal an earlier onset of non-linearity and a strain overshoot in the nanocomposites. Mastercurves are constructed from isothermal frequency sweeps using vertical and horizontal shifting. Although all nanocomposites exhibit a second plateau at ～10⁵ Pa, the relaxation times estimated from the peak in loss tangent are not statistically different from those of pure melts estimated from cross-over frequencies: all relaxation timescales scale with molar mass in the same way, evidence that the relaxation of the polymer network is the dominant mechanism in both filled and unfilled materials. Non-linear rheology is also measured in large amplitude oscillatory shear. A comparison of the responses from frequency and amplitude sweep experiments reveals the importance of strain and temperature history on the response of such nanocomposites.     

Viscosity and dynamics of nanorod (carbon nanotubes, cellulose whiskers, stiff polymers and polymer fibers) suspensions

The zero shear viscosity and the dynamic behaviors of different nanorod dispersions (carbon nanotubes (CNTs), cellulose whiskers, polymer nanofibers, crosslinked polymer nanofibers, and stiff polymers such as poly(γ-benzyl-α-l-glutamate) (PBLG)) were compared and discussed from literature data. Their Brownian dynamic behaviors have always been discussed in the frame of the Doi–Edwards theory. In agreement with this theory, the straight rigid rods (CNTs, cellulose whisker, polymer nanofibers) obey a master curve in the reduced viscosity (or rotary diffusivity) c power laws on viscosity (η ₀ ∝ φ ³) and diffusivity (D _r ∝ ? ^?2). On the contrary, stiff polymer chains and crosslinked polymer fibers at temperature above T _g exhibit different and two distinct dynamic behaviors. Despite their deviation from the ideal rigidity, surprisingly it can be noted that stiff polymers such as PBLG have been extremely used in the literature to verify the Doi–Edwards theory. Finally, flexible crosslinked chains at T > T _g , do not obey the Doi–Edwards theory, and their dynamics are close to the physics of polymer solutions in terms of power laws.     

Transient shear rheology of carbon nanofiber/polystyrene melt composites

We characterize the transient shear rheology of polystyrene/carbon nanofiber composites. Our experimental measurements of the composites show increasing stress overshoot responses to transient shear as the carbon nanofiber concentration increases. We also find the steady state viscosity reached at long times during application of a constant shear rate increases with increasing carbon nanofiber concentration. Flow reversal experiments show the effects of nanofiber orientation and structural evolution on the composite's rheological response.We present a microstructurally based constitutive model where all but two parameters are determined by rheological characterization of the pure polymer and the shape and concentration of the nanoparticles. The Folgar-Tucker constant, C_I, is treated as a fitting parameter, while several definitions for the shape factors A, B, C and F are evaluated. We make note of the effects each parameter has on the model's predictions. We find that the constitutive model is in agreement with our experimentally measured transient shear rheology of the PS/CNF melt composites for the CNF concentrations and shear rates presented.     

Dynamic properties of shear thickening colloidal suspensions

The transient shear rheology (i.e., frequency and strain dependence) is compared to the steady rheology for a model colloidal dispersion through the shear thickening transition. Reversible shear thickening is observed and the transition stress compares well to theoretical predictions. Steady and transient shear thickening are observed to occur at the same value of the average stress. The critical strain for shear thickening is found to depend inversely on the frequency at fixed applied stress for low frequencies (high strains), but is limited to an apparent minimum critical strain at higher frequencies. This minimum critical strain is shown to be an artifact of slip. Lissajous plots illustrate the transition in material properties through the shear thickening transition, and the energy dissipated by a shear thickening suspension is analyzed as a function of strain amplitude.     

Localised dynamics of laminar pulsatile flow in a rectangular channel

The exploitation of flow pulsation in low-Reynolds number micro/minichannel flows is a potentially useful technique for enhancing cooling of high power photonics and electronics devices. Although the mechanical and thermal problems are inextricably linked, decoupling of the local instantaneous parameters provides insight into underlying mechanisms. The current study performs complementary experimental and analytical analyses to verify novel representations of the pulsating channel flow solutions, which conveniently decompose hydrodynamic parameters into amplitude and phase values relative to a prescribed flow rate, for sinusoidally-pulsating flows of Womersley numbers 1.4 ≤ Wo ≤ 7.0 and a fixed ratio of oscillating flow rate amplitude to steady flow rate equal to 0.9. To the best of the authors’ knowledge, the velocity measurements – taken using particle image velocimetry – constitute the first experimental verification of theory over two dimensions of a rectangular channel. Furthermore, the wall shear stress measurements add to the very limited number of studies that exist for any vessel geometry. The amplification of the modulation component of wall shear stress relative to a steady flow (with flow rate equal to the amplitude of the oscillating flow rate) is an important thermal indicator that may be coupled with future heat transfer measurements. The positive half-cycle time- and space-averaged value is found to increase with frequency owing to growing phase delays and higher amplitudes in the near-wall region of the velocity profiles. Furthermore, the local time-dependent amplification varies depending on the regime of unsteadiness: (i) For quasi-steady flows, the local values are similar during acceleration and deceleration though amplification is greater near the corners over the interval 0 – 0.5π. (ii) At intermediate frequencies, local behaviour begins to differ during accelerating and decelerating periods and the interval of greater wall shear stress near the corners lengthens. (iii) Plug-like flows experience universally high amplifications, with wall shear stress greater near the corners for the majority of the positive half-cycle. The overall fluid mechanical performance of pulsating flow, measured by the ratio of bulk mean wall shear stress and pressure gradient amplifications, is found to reduce from an initial value of 0.97 at Wo = 1.4 to 0.28 at Wo = 7.0, demonstrating the increasing work input required to overcome inertia.     

The interlayer shear effect on graphene multilayer resonators

Graphene nanostrips with single or few layers can be used as bending resonators with extremely high sensitivity to environmental changes. In this paper we report molecular dynamics (MD) simulation results on the fundamental and secondary resonant frequencies f of cantilever graphene nanostrips with different layer number n and different nanostrip length L. The results deviate significantly from the prediction of not only the Euler-Bernoulli beam theory (f∝nL⁻²), but also the Timoshenko's model. Since graphene nanostrips have extremely high intralayer Young's modulus and ultralow interlayer shear modulus, we propose a multibeam shear model (MBSM) that neglects the intralayer stretch but accounts for the interlayer shear. The MBSM prediction of the fundamental and secondary resonant frequencies f can be well expressed in the form f−f_mono∝[(n-1)/n]^bL^−2(1−b), where f_mono denotes the corresponding resonant frequency as the layer number is 1, with b=0.61 and 0.77 for the fundamental and secondary resonant modes. Without any additional parameters fitting, the prediction from MBSM agrees excellently with the MD simulation results. The model is thus of importance for designing multilayer graphene nanostrips based applications, such as resonators, sensors and actuators, where interlayer shear has apparent impacts on the mechanical deformation, vibration and energy dissipation processes therein.     

A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. II. Shear flows

The results from numerical calculations for steady shear, the start-up and cessation of steady shear, and the stress relaxation after a step shear stain are discussed in detail for a bead-spring chain model with consistently averaged hydrodynamic interaction between the beads and consistently averaged finite extensible springs. Calculations are made for a large range of spring stiffnesses 10 ⩽ b ⩽ ∞ and a hydrodynamic interaction strength h^* = 0.15 a value which has been estimated from experimental results. This model is found to satisfy the Hassager-Bird and the Lodge-Meissner relations.     

Reological behaviour of concentrated monodisperse suspensions as a function of preshear conditions and temperature: an experimental study

 The influence of preshearing on the rheological behaviour of model suspensions was investigated with a stress-controlled cone-and-plate rheometer. The used matrix fluids showed Newtonian behaviour over the whole range of applied shear stresses. Highly monodisperse spherical glass spheres with various particle diameters were used as fillers. By applying steady preshearing at a low preshear stress, where a diffusion of particles can be expected, it was found for all model suspensions investigated at volume fractions ranging from 0.20 to 0.35 that the time-temperature superposition in the steady shear and in the dynamic mode holds within the chosen temperature range. Furthermore, all presheared model suspensions displayed a high and a low frequency range which are either separated by a shoulder or by a plateau value of G′ at intermediate frequencies. It could clearly be demonstrated that the low frequency range strongly depends on the preshear conditions. Hence, the features observed in the low frequency range can be attributed to a structure formation of a particulate network. In the high frequency range a frequency-dependent behaviour was observed which obeys the classical behaviour of Newtonian fluids (G′∝ω², G′′∝ω). The resulting temperature shift factors from the dynamic and the steady shear mode are identical and independent of the volume fraction and the particle size of the filler. Received: 29 November 2000 Accepted: 12 July 2001     

Large amplitude oscillatory shear rheology of three different shear-thickening particle dispersions

We present a large amplitude oscillatory shear rheology (LAOS) investigation of three different shear-thickening particle dispersions - fumed silica in polyethylene oxide (FLOC), fumed silica in polypropylene glycol (HydroC), and cornstarch in water (JAM). These systems shear-thicken by three different mechanisms - shear-induced formation of particle clusters flocculated by polymer bridging, hydrocluster formation, and jamming. The viscoelastic non-linearities of the three fluids were studied as a function of strain and strain-rate space through the use of Lissajous-Bowditch curves and local nonlinear viscoelastic moduli of an oscillatory shear cycle. The nonlinear behaviors of the three fluids were compared and contrasted to understand the nonlinear shear-thickening mechanism of each. Both HydroC and JAM dispersions were found to exhibit strong strain stiffening of the elastic moduli and strain thickening of the loss moduli behavior associated with possible hydrocluster formation and particle jamming. However, the FLOC dispersion, in contrast, showed strong strain softening and strain thinning behavior at large strain amplitudes associated with yielding of the microstructure. The expected thickening of the loss modulus of FLOC in LAOS with increasing strain was not observed even though viscosity of FLOC was found to shear-thicken in steady-shear measurements. This disagreement is likely due to very large strain amplitudes required for shear-thickening to occur by shear-induced polymer bridging mechanism. The hypothesis was confirmed through stress growth experiments. Conversely, the HydroC and JAM dispersions required relatively small applied strains for shear-thickening to occur by hydrocluster and jamming mechanism. The comparison of local intra-cycle nonlinearity through Lissajous-Bowditch plots and nonlinear viscoelastic parameters indicated that the elastic nonlinearities of all three systems are primarily driven by a strong dependence on the magnitude of the applied strain-rates within an oscillatory cycle rather than the amplitude of the applied strain. A close inspection of the LAOS data reveals strong differences in the viscoelastic nonlinearities of these three different shear-thickening dispersions which can be used to create a nonlinear rheological fingerprint for each and offers valuable new insights into the nonlinear dynamics associated with each of the shear-thickening mechanisms.     

Linear viscoelastic behavior of copper phthalocyanine dispersions used in printing inks

In this paper we describe the linear viscoelastic properties of copper phthalocyanine (CuPCN) dispersions that are used in the manufacturing of offset lithographic printing inks. Transmission electron microscopy shows that the primary pigment particles are rod-like and have sizes in the range of 10 to 300 nm. Steady shear measurements show that the dispersions are Newtonian at a pigment volume fraction of 0.073 and become increasingly shear thinning as the pigment volume fraction is increased. The strong shear-thinning nature of these dispersions can be attributed to the highly flocculated nature of the dispersions, which is due to interparticle attractions. The structural complexity of the dispersions also results in an unexpected linear viscoelastic response. While at low frequencies (0.1 and 1.0 Hz) the ex tent of the linear region decreases with increasing pigment concentration, at a higher frequency (10 Hz) the extent of the linear region increases with increasing pigment concentration. This increase in the linear region with increasing pigment concentration suggests that at higher frequencies the dispersion is less brittle, and that the rheological behavior is dominated by intra-aggregate associations. In addition, frequency sweeps show that the dispersions behave like a viscoelastic liquid at low pigment concentrations. However, at higher pigment concentrations (yet significantly lower than the maximum packing fraction) the dispersions behave like a cross-linking polymer at its gel point.     

LES and DES Investigations of Turbulent Flow over a Sphere at Re = 10,000

Large Eddy Simulation (LES) using a dynamic Smagorinsky type subgridstress (SGS) model and Detached Eddy Simulation (DES) are applied toprediction and investigation of the flow around a sphere at a Reynoldsnumber of 10⁴ in the subcritical regime. In this regime the boundarylayers at separation are laminar, and transition to turbulence occursfarther downstream in the separated shear layers via Kelvin–Helmholtz(K–H) instabilities. The dynamic eddy viscosity model of Germano et al.(Physics of Fluids 3 (1991) 1760–1765) is used in the LES, while the current implementation of the DESemploys a formulation based on the Spalart–Allmaras (S–A) model. DES isa hybrid approach in which the closure is a modification to theproduction/destruction term of the original Reynolds-AveragedNavier–Stokes (RANS) model, reducing to RANS in the attached regions,and to LES away from the wall. In the present work where we simulate theflow over a sphere in the subcritical regime in which the boundarylayers at separation are laminar, DES can be viewed as LES with adifferent SGS model. Effects of the discretization scheme used toapproximate the convective terms are considered, along with sensitivityof predictions to changes in the additional model coefficient, C _DES, in the DES formulation. DES and LES yield similar predictions of the wakestructure, large-scale vortex shedding and the Strouhal numberassociated with the low frequency mode in the wake. Predictions ofquantities such as the drag coefficient, wake frequencies, position oflaminar separation on the sphere, and the mean pressure andskin-friction distributions along the sphere are in good agreement withthe measurements of Achenbach (Journal of Fluid Mechanics 54 (1972) 565–575). Predictions of the primaryReynolds shear stress, turbulent kinetic energy, eddy viscosity, andturbulent dissipation for the two models are also similar. In addition,both models successfully resolve the formation of the vortex tubes inthe detached shear layers along with the value of the Strouhal numberassociated with the high frequency instability mode, provided that thelevel of numerical dissipation introduced by the discretization schemeremains sufficiently low. Flow physics investigations are focused onunderstanding the wake structure in the subcritical regime.     

E-FiRST: Electric field responsive shear thickening fluids

A novel electrorheological (ER) effect is presented where the application of an electric field, orthogonal to the vorticity-flow plane, increases the critical hydrodynamic stress required to shear thicken concentrated, colloidal dispersions (the E-FiRST effect). The shear thickening behavior of a Brownian charge stabilized dispersion (226 nm silica in 4-methylcyclohexanol at 53, 50. and 41 vol.%) is studied in the presence of an electric field as a function of the field strength and coupling parameter ( ß) where the latter is a function of a.c. field frequency due to diffusion limitations on the polarization of the particles' double layer. A mechanism is proposed whereby the applied electric field suppresses the formation of the self-organized hydrocluster microstructure responsible for shear thickening, thus delaying the onset of shear thickening to higher applied shear stresses. A Mason-number type scaling law is found to scale the effect, which supports the proposed mechanism.     

From linear viscoelasticity to the architecture of highly branched polyethylene

In this work, the linear viscoelastic behavior of some low-density polyethylene in the melt is used to obtain their architecture. In this way, the number of branches per molecule and long chain branching (LCB) content is determined. For this purpose, a method based on the molecular dynamics of simple star-shaped molecules is presented. It allows one to infer the topology of an average molecule through a set of 2N _c parameters {C ⁿ _i , the number concentration of a level i} and {M _bi , the mass of a segment of level i} representing an irregular Cayley tree with N _c levels. The inverse problem uses the complex shear modulus as a function of the frequency data along with a minimization algorithm. Results from the present method are compared with NMR and SEC measurements of the level of branching. It appears that SEC and rheology leads to similar results on the determination of LCB while NMR overestimate the number of branch points per molecule. Moreover, rheology allows one to go further than the basic evaluation of LCB content and shows a picture of the structure of the molecules that is in agreement with the kinetics of free radical polymerization of polyethylene.     

High-frequency viscoelasticity of crosslinked actin filament networks measured by diffusing wave spectroscopy

We study the short-time relaxation dynamics of crosslinked and uncrosslinked networks of semi-flexible polymers using diffusing wave spectroscopy (DWS). The networks consist of concentrated solutions of actin filaments, crosslinked with increasing amounts of α-actinin. Actin filaments (F-actin) are long semi-flexible polymers with a contour length 1–100μm and a persistence length of 5–15μm; α-actinin is a small 200kDa homodimer with two actin-binding sites. Using the large bandwidth of DWS, we measure the mean-square-displacement of 0.96μm diameter microspheres imbedded in the polymer network, from which we extract the frequency-dependent viscoelastic moduli via a generalized Langevin equation. DWS measurements yield, in a single measurement, viscoelastic moduli at frequencies up to 10⁵Hz, almost three decades higher in frequency than probed by conventional mechanical rheology. Our measurements show that the magnitude of the small-frequency plateau modulus of F-actin is greatly enhanced in the presence of α-actinin, and that the frequency dependence of the viscoelastic moduli is much stronger at intermediate frequencies. However, the frequency-dependence of loss and storage moduli become similar for both crosslinked and uncrosslinked networks at large frequencies, G′(ω)∝G′′(ω)∝ω^0.75±0.08. This high-frequency behavior is due to the small-amplitude, large-frequency lateral fluctuations of actin filaments between entanglements. Received: 20 January 1998 Accepted: 12 February 1998     

Extrudate swell of Boger fluids

Boger fluids are dilute polymer solutions exhibiting high elasticity at low apparent shear rates, which leads to high extrudate swell. Numerical simulations have been undertaken for the flow of three Boger fluids (including benchmark Fluid M1), obeying an integral constitutive equation of the K-BKZ type, capable of describing the behavior of dilute polymer solutions. Their rheology is well captured by the integral model. The flow simulations are performed for planar and axisymmetric geometries without or with gravity. The results provide the extrudate swell and the excess pressure losses (exit correction), as well as the shape and extent of the free surface. All these quantities increase rapidly and monotonically with increasing elasticity level measured by the stress ratio, S_R. It was found that the main reason for the high extrudate swelling is high normal stresses exhibited in shear flow (namely, the first normal-stress difference, N₁). Surprisingly, the elongational parameter of the model or a second normal-stress difference N₂ do not affect the results appreciably. Gravity serves to lower the swelling considerably, and makes the simulations easier and in overall agreement with previous experiments.     

Transient shear flow behavior of concentrated long glass fiber suspensions in a sliding plate rheometer

In order to eventually predict the behavior of long fiber suspensions in complex flows commonly found in processing operations, it is necessary to understand their rheology and its connection to the evolution of fiber orientation and configuration in well defined flows. In this paper we report the transient behavior at the startup of shear flow of a polymer melt containing long glass fibers with a length (L) >1 mm, using a sliding plate rheometer (SPR). The operation of the SPR was confirmed by comparing the transient shear viscosity (η⁺) for a polymer melt and a melt containing short glass fibers (L < 1 mm) with measurements obtained from a cone-and-plate device, using a modified sample geometry that was designed to avoid wall effects. For the long fiber systems, measurements could only be obtained in the SPR because these systems would not stay within the gap of the rotational rheometer. Transient stress growth behavior of the long fiber systems was obtained as a function of shear rate and fiber concentration for samples prepared with three different initial orientations. Results showed that, unlike short fiber systems (with a random planar initial orientation) that usually exhibit a single overshoot peak followed by a steady state, η⁺ of the long fiber suspensions often passed through multiple transient regions, depending on the fiber concentration and applied shear rate. Additionally, η⁺ of the long fiber suspensions was found to be highly dependent on the initial orientation of the sheared samples. Finally, the initial and final fiber orientations of the long glass fiber samples were measured and used to initiate an explanation of the viscosity behavior. The results obtained in this research will be useful for future assessment of a quantitative correlation between transient rheology and the evolution of fiber orientation.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.