Strain-thickening transition in ferric-oxide suspensions under oscillatory shear

Shear-strain-thickening transition under oscillatory flow was observed in flocculated ferric-oxide suspensions in mineral oil. The value of the dynamic modulus of the suspensions that was measured at small strain amplitude after cessation of shear also became higher when the strain amplitude of the applied shear had been within or above the transition region.The ferric-oxide powders used were an acicular submicron maghemite (magnetic) and the hematite (non-magnetic) that was converted from the maghemite by heat treatment. The powders were treated with a dispersing agent and the suspensions were prepared in 33% by particle weight. The strain-thickening transition was observed in both the magnetic and the non-magnetic suspensions. However, the onset of the strain-thickening in the magnetic suspension was found at about one decade larger strain amplitude than that in the non-magnetic analog suspension, indicating particle interactions affect to the appearance of the phenomenon.A qualitative interpretation was made in view of site percolation for the enhancement of modulus at rest after the application of the large-amplitude oscillatory shear, where the process of the strain-thickening transition under shear and the development of the modulus after stopping the shear was described with a floc model in which the flocculation phase dilates as a result of the reduction of the particle linkages under higher shear.     

Melt shear rheology of carbon nanofiber/polystyrene composites

The rheological behavior and morphology of carbon nanofiber/polystyrene (CNF/PS) composites in their melt phase have been characterized both through experimental measurements and modeling. Composites prepared in the two different processes of solvent casting and melt blending are contrasted; melt-blended and solvent-cast composites were each prepared with CNF loadings of 2, 5, and 10 wt%. A morphological study revealed that the melt blending process results in composites with shorter CNFs than in the solvent-cast composites, due to damage caused by the higher stresses the CNFs encounter in melt blending, and that both processes retain the diameter of the as-received CNFs. The addition of carbon nanofiber to the polystyrene through either melt blending or solvent casting increases the linear viscoelastic moduli, G′ and G″, and steady-state viscosity, η, in the melt phase monotonically with CNF concentration, more so in solvent cast composites with their longer CNFs. The melt phase of solvent-cast composites with higher CNF concentrations exhibit a plateau of the elastic modulus, G′, at low frequencies, an apparent yield stress, and large first normal stress difference, N ₁, at low strain rates, which can be attributed to contact-based network nanostructure formed by the long CNFs. A nanostructurally-based model for CNF/PS composites in their melt phase is presented which considers the composite system as rigid rods in a viscoelastic fluid matrix. Except for two coupling parameters, all material constants in the model for the composite systems are deduced from morphological and shear flow measurements of its separate nanofiber and polymer melt constituents of the composite. These two coupling parameters are polymer–fiber interaction parameter, σ, and interfiber interaction parameter, C _I. Through comparison with our experimental measurements of the composite systems, we deduce that σ is effectively 1 (corresponding to no polymer–fiber interaction) for all CNF/PS nanocomposites studied. The dependence of CNF orientation on strain rate which we observe in our experiments is captured in the model by considering the interfiber interaction parameter, C _I, as a function of strain rate. Applied to shear flows, the model predicts the melt-phase, steady-state viscosities, and normal stress differences of the CNF/PS composites as functions of shear rate, polymer matrix properties, fiber length, and mass concentration consistent with our experimental measurements.     

Some correlations involving the shear viscosity of polystyrene melts

Based upon a compilation of steady-shear and dynamic-shear viscosity data from the literature for polystyrene melts, an assessment has been made concerning the relative merits of the Cross and Carreau models in describing the shear-rate dependence of such viscosities. It is shown that the Cross model is decidedly more appropriate for PS of BMWD. Based upon master plots, it is demonstrated that the Cox-Merz relation applies to PS of both BMWD and NMWD. It is also shown that the Cox-Merz relation applies even into the second-Newtonian regime, with being independent ofM _w and MWD. In addition, the applicability of the Prest-Porter-O'Reilly relationship between shear viscosity and recoverable shear compliance is corroborated in the case of PS of NMWD.     

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.     

Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology

Complex viscosity ^* = -i predictions of the Dasbach-Manke-Williams (DMW) internal viscosity (IV) model for dilute polymer solutions, which employs a mathematically rigorous formulation of the IV forces, are examined in the limit of infinite IV over the full range of frequency number of submolecules N, and hydrodynamic interaction h ^*. Although the DMW model employs linear entropic spring forces, infinite IV makes the submolecules rigid by suppressing spring deformations, thereby emulating the dynamics of a freely jointed chain of rigid links. The DMW () and () predictions are in close agreement with results for true freely jointed chain models obtained by Hassager (1974) and Fixman and Kovac (1974 a, b) with far more complicated formalisms. The infinite-frequency dynamic viscosity predicted by the DMW infinite-IV model is also found to be in remarkable agreement with the calculations of Doi et al. (1975). In contrast to the other freely jointed chain models cited above, however, the DMW model yields a simple closed-form solution for complex viscosity expressed in terms of Rouse-Zimm relaxation times.     

Dynamics and rheology of a dilute suspension of dipolar nonspherical particles in an external field: Part 1. Steady shear flows

Suspensions of small nonspherical particles having dipolar moments exhibit non-Newtonian behavior under the influence of shear and external fields. Numerical methods are presented for calculating the rheological and rheo-optical properties of dilute suspensions of Brownian particles having permanent dipoles subject to time-dependent shear and external fields. The numerical methods employ the Galerkin method of weighted residuals to solve the differential equation for the particle orientation distribution function. The steady-state shear flow intrinsic viscosity of suspensions of particles with sufficiently extreme aspect ratio is predicted to exhibit a maximum value attained for intermediate shear rates at selected field orientations. These numerical results provide valuable insight into the coupling which occurs between the effects of rotary Brownian motion, the hydrodynamic resistance of nonspherical particles, and the external torque exerted on dipolar particles. The results are applicable to both suspensions of magnetic particles and electrically dipolar particles.     

Foam rheology: Relation between extensional and shear deformations in high gas fraction foams

A two-dimensional hexagonal foam cell model is used to derive analytic expressions for the bulk stress tensor and foam microstructure for any small homogeneous deformation. We show that calculations done for deformations where the principal axes of stress and strain coincide, such as in extension, are sufficient to provide all information about shear deformation. The stresses and foam structure for any given strain and initial cell orientation in shear bears a unique relation to a different strain and orientation in extension. Such a mapping is obtained using the assumption that the principal axes of strain and stress corotate with each other. This in turn implies that high gas fraction foams follow the Lodge-Meissner relation, i.e. the ratio of the normal-stress difference to the shear stress equals the shear strain. The spatially periodic structure of foam along with the fact that the cell centers move affinely with the bulk, makes the above assumption a justifiable one.     

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.     

Elongational and shear rheology of carbon nanotube suspensions

Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.     

The shear viscosity dependence on concentration,molecular weight,and shear rate of polystyrene solutions

The solution viscosity of narrow molecular weight distribution polystyrene samples dissolved in toluene and trans-decalin was investigated. The effect of polymer concentration, molecular weight and shear rate on viscosity was determined. The molecular weights lay between 5 10⁴ and 24 10⁶ and the concentrations covered a range of values below and above the critical valuec ^*, at which the macromolecular coils begin to overlap. Flow curves were generated for the solutions studied by plotting log versus log . Different molecular weights were found to have the same viscosity in the non-Newtonian region of the flow curves and follow a straight line with a slope of – 0.83. A plot of log ₀ versus logM _w for 3 wt-% polystyrene in toluene showed a slope of approximately 3.4 in the high molecular weight regime. Increasing the shear rate resulted in a viscosity that was independent of molecular weight. The sloped (log)/d (logM _w ) was found to be zero for molecular weights at which the corresponding viscosities lay on the straight line in the power-law region.On the basis of a relation between _sp and the dimensionless productc · [], simple three-term equations were developed for polystyrene in toluene andt-decalin to correlate the zero-shear viscosity with the concentration and molecular weight. These are valid over a wide concentration range, but they are restricted to molar masses greater than approximately 20000. In the limit of high molecular weights the exponent ofM _w in the dominant term in the equations for both solvents is close to the value 3.4. That is, the correlation between _sp andc · [] results in a sloped(log _sp)/d(logc · []) of approximately 3.4/a at high values ofc · [] wherea is the Mark-Houwink constant. This slope of 3.4/a is also the power ofc in the plot of ₀ versusc at high concentrations. a Mark-Houwink constant - B ₁,B ₂,B _n constants - c concentration (g · cm^–3) - c ^* critical concentration (g · cm^–3) - K, K constants - K _H Huggins constant - M molecular weight - M _c critical molecular weight - M _n number-average molecular weight - M _w weight-average molecular weight - n sloped(log _sp)/d (logc · []) at highc · [] - PS polystyrene - T temperature (K) - shear rate (s^–1) - critical shear rate (s^–1) - viscosity (Pa · s) - ₀ zero-shear viscosity (Pa · s) - _s solvent viscosity (Pa · s) - _sp specific viscosity - [] intrinsic viscosity (cm³ · g^–1) - dynamic viscosity (Pa · s) - | ^*| complex dynamic viscosity (Pa · s) - angular frequency (rad/s) - density of polymer solution (g · cm^–3) - ₁₂ shear stress (Pa) Dedicated to Prof. Dr. J. Schurz on the occasion of his 60^th birthday.Excerpt from the dissertation of Reinhard Kniewske: Bedeutung der molekularen Parameter von Polymeren auf die viskoelastischen Eigenschaften in wäßrigen und nichtwäßrigen Medien, Technische Universität Braunschweig 1983.     

Steady and dynamic shear properties of non-aqueous drag-reducing polymer solutions

The steady and dynamic shear properties of two non-aqueous drag-reducers (a medium molecular weight polyisobutylene and a commercial organic drag-reducer) in kerosene solutions over a wide range of temperature and concentration were presented. The intrinsic and zero-shear viscosity results were used to identify the concentrate regimes of these solutions. A characteristic time constant λ₀, which was based on the spring-bead model for dilute solutions, was employed as the scaling parameter for both steady-shear and dynamic data over a wide range of concentration and temperature. The inadequacy of the Graessley reduced-variable method in the dilute region was illustrated. The shear-thinning behaviour of these polymer solutions could be described by the Carreau model. The dynamic data followed the Zimm and Rouse-like behaviour in the low and high frequency limits. The Cox-Merz rule was obeyed in the low shear rate and frequency regions. The Carreau and the zero-frequency Maxwell time constants appeared to be related to λ₀ by a constant factor over a wide range of polymer concentrations. The finding provides a method for extrapolating viscoelastic information into the drag reduction regime, and could be useful for interpretation of drag reduction results.     

Rheology and microstructure of heat-induced egg yolk gels

The evolution of native egg yolk undergoing a thermal-induced sol-gel transition was studied by using temperature controlled small amplitude oscillatory shear measurements. The critical gel point was determined according to Winters criterion: 1) from the measurements of storage and loss moduli as a function of heating time at different frequencies, and 2) from the exponents of the power law mechanical spectra obtained after cure experiments performed up to a maximum temperature (60–90 °C) followed by a sudden decrease in temperature up to 20 °C. Differential Scanning Calorimetry (DSC) was performed in order to investigate thermal transitions in egg yolk. Microstructure of gels was evaluated by Transmission and Scanning Electron Microscopy. The results obtained were discussed in terms of the processes involved in protein gelation: change in the protein system, aggregation of partially denaturated protein molecules and association of aggregates. As a result, an elastic gel network was always obtained. The influence of frequency, heating rate, solids concentration and maximum temperature of processing, was analysed. Most of the transformations found during thermal processing were found to be basically irreversible, even at the sol state and gel point. However, some reversible phenomena were detected during constant temperature processing depending on the maximum temperature performed.     

Research on the effect of particle of two-dimensional shear flow

ＩｎｔｒｏｄｕｃｔｉｏｎＴｕｒｂｕｌｅｎｔｆｌｏｗｌａｄｅｎｗｉｔｈｐａｒｔｉｃｌｅｓｉｓｃｏｍｍｏｎｉｎｂｏｔｈｎａｔｕｒｅａｎｄｉｎｄｕｓｔｒｙ .Ｔｈｅｍｉｘｉｎｇｄｅｇｒｅｅｏｆｐａｒｔｉｃｌｅｓｉｎｔｈｅｇａｓ＿ｓｏｌｉｄｆｌｏｗｉｓｓｉｇｎｉｆｉｃａｎｔｔｏｉｎｄｕｓｔｒｉａｌａｐｐｌｉｃａｔｉｏｎｓ.Ｔｈｅｒｅｃｅｎｔｒｅｓｅａｒｃｈｅｓｉｎｄｉｃａｔｅｔｈａｔｔｈｅｃｏｈｅｒｅｎｔｓｔｒｕｃｔｕｒｅｓｅｘｉｓｔｉｎｔｈｅｍｉｘｉｎｇｌａｙｅｒ.Ｃｒｏｗｅｅｔａｌ.[1]ｅｖａｌｕａｔｅｄ…     

Hexagonal Defect Array Formed under Steady Shear Flow in Water-in-Cholesteric Liquid Crystal Emulsions

The relation between the liquid crystalline textures and the steady shear viscosity has been investigated in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the surfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. Under a steady shear flow with the shear rate below 100 s^–1, we observed that point defects spontaneously appear, and tend to adopt a regular hexagonal arrangement in the low shear-rate range of 1–20 s^–1. In viscosity measurements, the shear-thinning behavior was found, showing a clear correspondence to the texture change. We estimated the height of point defects in the hexagonal array from the viscosity increase in the shear-thinning, assuming that the shear-thinning behavior is caused by the reduction of the effective gap between cone and plate, owing to the presence of the hexagonal array anchored on the plate. The relation between the estimated height and the measured lateral size of point defects agreed with that of the quadrilateral array, which is formed after termination of the shear. This agreement informs that the shape of a point defect is preserved in both defect arrays, independently of shearing conditions.     

Hydrodynamic interactions of dilute polymer solutions under shear flow in a narrow channel

Hydrodynamic interactions on dilute solutions of spherical beads under shear flow are calculated with the method of induced forces. The Navier-Stokes equation is considered in the Stokes approximation. Hydrodynamic interactions cause the drag to be anisotropic in space.Numerical solutions are obtained for the added stress, caused by polymeric molecules in solution in a narrow channel under shear flow. The polymeric molecules are considered as Hookean spring-dumbbells.Slip velocity and the effective viscosity are obtained taking different dumbbells' bead radii. Transversal migration in the channel is obtained for different bead radii.     

Modelling elongational and shear rheology of two LDPE melts

Experimental data of two low-density polyethylene (LDPE) melts at 200°C for both shear flow (transient and steady shear viscosity as well as transient and steady first normal stress coefficient) and elongational flow (transient and steady-state elongational viscosity) as published by Pivokonsky et al. (J Non-Newtonian Fluid Mech 135:58–67, 2006) were analysed using the molecular stress function model for broadly distributed, randomly branched molecular structures. For quantitative modelling of melt rheology in both types of flow and in a very wide range of deformation rates, only three nonlinear viscoelastic material parameters are needed: Whilst the rotational parameter, a ₂, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter describing maximum stretch of the polymer chains.     

Drop shape under slow steady shear flow and during relaxation. Experimental results and comparison with theory

The three-dimensional small deformation of a single Newtonian drop immersed in an immiscible Newtonian liquid was investigated, both in slow steady shear and during retraction after cessation of shear. The experiments were performed in a parallel plate apparatus equipped with video- enhanced microscopy. The drop was observed from two perpendicular directions, and accurate measurements were obtained in each view by image analysis. The results were compared to existing theoretical predictions from the exact fluid dynamic problem, obtained perturbatively for the case of small deformations of the drop. Excellent agreement between data and theory was found, thus providing the first assessment of drop shape predictions in steady flow and relaxation for Newtonian fluids. Received: 6 February 2000 Accepted: 24 May 2000     

Steady motion of a rigid disk of finite thickness on a horizontal plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady-state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line or in a circle. Oscillations about steady state are discussed and conditions for stable motion established. The bifurcations of steady motions on a smooth surface are also considered.     

Rheology of concentrated coagulating suspensions in non-aqueous media

The rheology of concentrated coagulating suspensions is analysed on the basis of the following model: (i) at low shear rates, the shear is not distributed homogeneously but limited to certain shear planes; (ii) the energy dissipation during steady flow is due primarily to the overcoming of viscous drag by the suspended particles during motion caused by encounters of particles in the shear planes. This model is called the giant floc model.With increasing shear rate the distance between successive shear planes diminishes, approaching the suspended particles' diameter at average shear stresses of 88–117 Pa in suspensions of 78 µm particles (glass ballotini coated by a hydrophobic layer) in glycerol — water mixtures, at solid volume fractions between 0.35 and 0.40. Smaller particles form a more persistent coagulation structure. The average force necessary to separate two touching 78 µm particles is too large to be accounted for by London-van der Waels forces; thus coagulation is attributed to bridging connections between polymer chains protruding from the hydrophobic coatings.The frictional ratio of the glass particles in these suspensions is of the order of 10. Coagulation leads to build-up of larger structural units at lower shear rates; on doubling the shear rate the average distance between the shear planes decreases by a factor of 0.81 to 0.88. A inter-shear plane distance - A Hamaker constant - b radius of primary particles - f frictional ratio - F _A attractive force between two particles - g acceleration due to gravity - H distance between the surfaces of two particles - K proportionality constant in power law - l fraction of distance by which a moving particle entrains its neighbours - l effective length of inner cylinder in the rheometer - M torque experienced by inner cylinder during measurements - n exponent in power law - n ₀ ,n ₁ ,n ₂ constants in extended power law - NC _hex number of contacts, per mm², between particles in adjacent layers with an average degree of occupation, assuming a hexagonal arrangement of the particles within the layers - NC _cub asNC _hex, but with a cubical arrangement - p () d increase of slippage probability when the shear stress increases from to + d - q average coordination number of a particle in a coagulate - R _i radius of inner cylinder of rheometer - R _u radius of outer cylinder of rheometer - t _i time during which particlei moves - t ₀ time during which a particle bordering a shear plane moves from its rectilinear course, on meeting another particle - u angle between the direction of motion, and the line connecting the centers of two successive particles bordering a shear plane - V _A attractive energy between two particles - x, y, z Cartesian coordinates:x — the direction of motion;y — the direction of the velocity gradient - y ₀ ,z ₀ y, z value of a particle meeting another particle, when both are far removed from each other - y ₀ spread iny ₀ values - —2/n - ₀ capture efficiency - shear rate - average shear rate calculated for a Newtonian liquid - _i distance by which particlei moves - ₀ distance by which a particle bordering a shear plane moves from its rectilinear course, when it encounters another particle - square root of area occupied by a particle bordering a shear plane, in this plane - _c energy dissipated during one encounter of two particles bordering a shear plane - _p energy dissipated by one particle - energy dissipated per unit of volume and time during steady flow - viscosity - _app calculated as if the liquid is Newtonian - ₀ viscosity of suspension medium - _PL lim - [] intrinsic viscosity - _diff - _{diff, rel diff}/ ₀ - standard deviation of distribution ofy ₀ values - shear stress - _n average shear stress at the highest values applied - mass average particle diameter - _n number average particle diameter - solid volume fraction - _eff effective solid volume fraction in Dougherty-Krieger relation - _max maximum solid volume fraction permitting flow - _i angular velocity of inner cylinder in rheometer during measurements