Rheological properties of poly(dimethylsiloxane) filled with fumed silica: II. Stress relaxation and stress growth

The steady-state viscosity, stress relaxation, and stress growth function were measured for a 3.0% by weight dispersion of fumed silica in poly(dimethylsiloxane); using a two-step shear rate history. For short rest times the stress growth function η⁺ increased monotonically towards steady-state, while at long rest times η⁺ exhibited large overshoot followed by a monotonic decrease to steady-state. For intermediate rest times η⁺ exhibited more complicated transient behaviour. The effect of both shear rates in the two-step shear-rate history on η⁺ have been studied, and the resulting rheological behaviour is discussed in terms of phenomenological microstructural models.     

The effect of molecular weight on the rheological properties of poly(dimethylsiloxane) filled with fumed silica

The viscometric, stress relaxation, and stress growth rheological properties were measured for various molecular weight PDMS fluids filled with fumed silica. The stress growth function exhibited significant overshoot, when the continuous phase molecular weight was slightly greater than the entanglement molecular weight; however, significant overshoot peaks were not observed, when the continuous phase molecular weight was less than or much greater than the molecular weight between entanglements. The experimentally observed transient rheological properties are rationalized in terms of a molecular model, where interparticle interactions occur via entanglements of the polymer adsorbed on the silica surface. When the molecular weight of the adsorbed polymer is greater than the entanglement molecular weight, the strength of the interparticle interaction will increase substantially and the particle diffusivity will substantially decrease.     

A structural model for thixotropy of colloidal dispersions

The present study proposes a structural model to describe the thixotropic behavior of colloidal dispersions. This model uses structural viscosity and elasticity as internal parameters, and predicts the evolution of shear stress when shear rate varies over time. Viscosity represents the structural level of colloidal aggregates and is dependent upon their alignment. Changes in alignment are linked to changes in shear rate, are regarded as instantaneous and are not believed to cause thixotropic behavior. Only changes in the structural level or structural viscosity and in the elastic deformation of colloidal aggregates cause measurable thixotropic behavior. Variations in structural viscosity over time, and at a fixed shear rate, follow a first-order kinetic equation based on two characteristic thixotropic times. This model incorporates several parameters, which are fitted independently by the appropriate rheological tests, in order to avoid any mathematical coupling. This model has been tested in 3 wt% Laponite aqueous dispersions using different ionic strengths.     

Influence of medium viscosity and adsorbed polymer on the reversible shear thickening transition in concentrated colloidal dispersions

The influence of medium viscosity on the onset of shear thickening of silica dispersions is investigated with two different methods. In the first method, the sample temperature is varied over a narrow range for two different suspensions. For the first suspension, the stress at the onset of shear thickening, or the critical stress, was found to be independent of sample viscosity, and the shear viscosity scaled with Peclet number, as expected. The critical stress for the second suspension was not independent of sample viscosity, and the Peclet number scaling was only moderately successful. The differences were attributed to changes in particle interactions with temperature. In the second method, the molecular weight of an oligomeric silicone oil medium is varied. In principle, this method should maintain constant chemical interactions as medium viscosity varies; however the polymer is found to adsorb onto the silica surface and delay shear thickening to higher stresses with increasing molecular weight. The critical stress for the highest molecular weight systems, which is highly dependent on particle loading, overlays with an effective volume fraction based on the hydrodynamic diameter of the polymer-stabilized colloids. The results of both methods suggest that if all other properties of the dispersion are held constant, critical stress is independent of medium viscosity.     

Study of magnetorheological fluids at high shear rates

The tunable rheological properties of magnetorheological (MR) materials at high shear rates are studied using a piston-driven flow-mode-type rheometer. The proposed method provides measurement of the apparent viscosity and yield stress of MR fluids for a shear rate range of 50 to 40,000 s⁻¹. The rheological properties of a commercial MR fluid, as well as a newly developed MR polymeric gel, and a ferrofluid-based MR fluid are investigated. The results for apparent viscosity and dynamic and static shear stresses under different applied magnetic fields are reported.     

Rheological behaviour of spray-dried egg yolk/xanthan gum aqueous dispersions

This paper provides information on the microstructure of, and reports particle size distributions and rheological results for, aqueous dispersions of spray-dried egg yolk and xanthan gum prepared on a laboratory scale using two types of homogenisers. Laser light scattering results demonstrated that higher energy input during homogenisation yielded a dispersion with a lower average particle size and a wider polydispersity, slightly influencing the linear dynamic viscoelastic functions due to the low concentration of egg yolk particles. These dispersions exhibited weak gel properties at the composition studied. The mechanical spectrum and the corresponding relaxation spectrum were dominated by the xanthan/gum-water matrix which controls the structure of the continuous phase. This fact explained the lack of any wall depletion effects. Several controlled-rate and controlled-stress rotational rheometers and a capillary rheometer were used to obtain information on flow properties. The shear rate dependence of steady state viscosity was determined through twelve decades, and was fitted using the Carreau equation. The kinetics of structural recovery after steady-state shear was studied by start-up at the inception of shear and flow interrupted experiments under controlled shear history. The results were analysed in terms of the ratio of a time-dependent amount of overshoot to the amount of overshoot of the original sample, using the addition of two first order equations. Additionally, combined steady state flow properties at fixed shear stress/oscillatory shear experiments were also used. The increase of the storage modulus with time, checking a linear viscoelastic response, tracked the structural recovery after steady shear. Laser light scattering of sheared samples helped gain a better understanding of the role of egg yolk particles on the rheology of these dispersions. Received: 6 February 2000 Accepted: 5 September 2000     

Possibility of a master plot for material functions of high-polymer solutions

A new systematic method has been developed for estimating rheological properties (such as relaxation time, viscosity, primary normal stress difference) for various polymer solutions form the zero-shear-rate specific viscosity and a dimensionless shear rate.A linear relation has been found between the relaxation time and the zero-shear-rate specific viscosity on a double-logarithmic plot, and a new master plot for the primary normal stress difference has been established. In addition the applicability of the FENE-P dumbbell model to high-polymer solutions is discussed.     

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.     

Rheological properties of disperse systems at low shear stresses

Three-dimensional network structures can be built up in disperse systems due to long-range colloidal interactions between the dispersed particles. The rheological behaviour of such coagulation structures has been studied by means of creep and recovery experiments at low shear stresses, i.e. by measuring the shear strain as a function of time under constant stress and after removal of stress. Measurements of this type give insight into the elastic and viscous deformations and the retardation times necessary to reach equilibrium or steady-state conditions.Results obtained with dispersions of pigments in polymer solutions and with monodisperse polymer latexes indicate the existence of an equilibrium state at low shear stresses with a predominant elastic deformation and a high viscosity suggesting that the disperse systems investigated do not behave exactly as rigid gels but apparently exhibit a dynamic equilibrium of structural break-down and formation under applied stress. This behaviour is approximately described by a 4-parameter-model with an instantaneous and a steady-state compliance, one retardation time, and a viscosity.At higher shear stresses thixotropic structural break-down occurs resulting in a transition from the rheological behaviour described here to a liquid-like state with a comparatively low viscosity. In this stress range the viscoelastic properties become strongly time-dependent.These measurements give evidence of the presence of two types of deformation: an instantaneous, purely elastic deformation attributable to the unperturbed coagulation structure and the creep-recovery behaviour of an elastic liquid apparently related to the breaking and re-forming of bonds.     

Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

A thermodynamic approach to the rheology of highly interactive filler-polymer mixtures. Part II. Comparison with polystyrene/nanosilica mixtures

The dynamic properties as a function of frequency and strain amplitude, steady-state viscosity as a function of shear rate, and transient shear stresses at startup and cessation of shear flow of polystyrene (PS)/fumed silica mixtures of various concentrations were investigated. An abrupt change in the viscoelastic properties was noticed at a concentration above 1% by volume. Observations by means of scanning electron microscopy (SEM) indicate the presence of a three-dimensional network through the bridging of filler particles by the adsorbed polymer. The viscoelastic behavior is simulated utilizing a theory proposed in Part I (Havet and Isayev 2001) based on a double network created by the entangled polymer matrix and the adsorbed polymer with filler concentration taken into account through the bridging density of polymer-filler interactions and a hydrodynamic reinforcement. The steps taken for determining the model parameters required to carry out the simulation are described. The major features of the rheological behavior of highly interactive polymer-filler mixtures are captured qualitatively and in some cases, quantitatively predicted.     

Rheology and structure of precipitated silica and poly(dimethyl siloxane) system

The reinforcing capability of precipitated silica in poly(dimethyl siloxane: PDMS) was characterized by means of bound rubber formation, solvent swelling, yield stress, rheological and dynamic properties. Volume concentration of precipitated silica in PDMS was varied from 0 to 0.16. The homogeneity of the compounds after mixing was confirmed by studying a uniformity of dispersion of silica particles in PDMS via SEM morphology of vulcanizates. Bound rubber measurements of the compounds and solvent swelling studies of vulcanizates showed that the precipitated silica exhibited much stronger interaction with PDMS than that of typical carbon black with rubbers but less than that of fumed silica with PDMS. At high volume concentrations of silica (0.128 and 0.160), a yield behavior was evident from the storage modulus measurements. The network formation due to an interaction between the precipitated silica and PDMS was visualized via dynamic property measurements.     

New insights on fumed colloidal rheology—shear thickening and vorticity-aligned structures in flocculating dispersions

We investigate the rheology of dilute dispersions of fumed colloidal particles with attractive interactions in hydrocarbon liquids. Surprisingly, these systems display shear thickening due to the breakdown of densified flocs and a concomitant increase in the effective volume fraction of the fractal particles in the fluid. We show that this shear thickening is controlled by a critical stress and accompanied by a positive increase in the first normal stress difference, N ₁, at the shear thickening transition. This is in contrast to the well-known hydrocluster mechanism of shear thickening in concentrated hard-sphere and repulsive systems. Gel elasticity depends strongly on the stress applied to suspensions in preshear, scaling roughly as \(G'\sim\sigma_{\text{preshear}}^{2}\). We propose a simple model to account for these results in terms of the cluster number density determined by the preshear stress. At low shear rates, vorticity-aligned aggregates are present at \(\dot\gamma\approx 10^0 {\rm{s}}^{-1}\) . In this regime, the system displays a small but noticeable increase in viscosity on increasing shear rate. We investigate the effect of tool roughness and find that wall slip is not responsible for the observed phenomena. Instead, the increase in the apparent viscosity results from increased flow resistance due to the presence of gap-spanning log-like flocs in rolling flow.     

Rheological characterization of continuous fiber—reinforced viscous fluid

The present paper describes a micromechanical technique to determine rheological properties of viscous fluid reinforced with unidirectional continuous fibers. Fluid viscosity is described by a shear thinning model and high viscosity is considered for continuous fibers having considerable rigidity compared to net fluid. The microstructure is identified by a representative volume element that is subjected to equivalent macroscopic deformation fields. The energy balance and periodicity conditions are considered to relate deformation and stress in macro and micro-levels. It is shown that response of viscous fluid reinforced with rigid fibers depends on deformation history as well as rate-of-deformation in the transverse intraply shear and transverse squeeze flows. An orthotropic viscous constitutive equation is derived to describe response of such materials. The material viscosities are evaluated for viscous fluid reinforced with different fiber volume fractions during deformation applied in different rates of deformation. The results are used to derive the functions predicting effective anisotropic viscosities of reinforced fluid.     

Shear flow rheological properties of vinylon- and glass-fiber reinforced polyethylene melts

Shear viscosity, shear stress and first normal-stress difference have been investigated for glass- and vinylon-fiber filled polyethylene melts over a wide range of shear rate by means of three kinds of instruments. The influence of fiber content and fiber properties on the rheological properties is discussed. The viscosity increases with increasing aspect ratio and fiber content, and the influence of these parameters on the flow properties is evident at low shear rates. The first normalstress difference increases more rapidly with increasing glass fiber content, especially at low shear stresses. The influence of vinylon fibers on the first normal stress-difference vs. shear-stress relationship is different from that of glass fibers.     

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.     

Fibre spinning of a weakly elastic liquid

This paper presents a study of a silicone oil (poly(dimethyl siloxane)) in extensional deformation using an instrument developed recently by the authors. Data from steady shear and low amplitude sinusoidal deformation of this liquid clearly establish that it is weakly elastic. The viscometric data, for shear rates less than 100 s ⁻¹, are best represented by either the Maxwell model or the Jeffrey's model, the latter being marginally superior. The extensional data show that at low deformation rates, this fluid exhibits a Newtonian behavior with an apparent extensional viscosity equal to three times the shear viscosity. Under these conditions the velocity profiles along the spinline are also well represented by the Newtonian model. However, at higher deformation rates better predictions of the velocity profiles are obtained from the Jeffrey's and Maxwell models. At deformation rates above 100 s ⁻¹ none of these simple models is adequate. Under the conditions used in these experiments, the fractional increase in tensile stress along the fiber is shown both theoretically and experimentally to be a unique function of the total strain. Furthermore, the apparent extensional viscosity at any point on the spinline can be calculated from steady state expressions if allowance is made for the variation of stretch rates by defining a time averaged stretch rate.The results obtained here show that elasticity must be considered if these model liquids are used to conduct rheological experiments at high deformation rates. Additionally, it is found that elastic effects in extension can be predicted using simple constitutive equations provided viscometric data can be represented properly in the deformation rate range of interest. Finally, the present research further substantiates the utility of the extensional viscometer developed by the authors.     

Rheological behavior of silica suspensions flocculated by bridging

The viscosity and stress relaxation behavior of silica suspensions in polyacrylamide (PAAm) solutions have been studied as a function of particle concentration, particle diameter, and molecular weight of PAAm by the use of a coaxial cylinder type rheometer. The effects of polymer adsorption on the flocculation of particles and the rheological behavior are discussed in terms of bridging. The suspensions of 10-nm silica are remarkably pseudoplastic because the particles are easily flocculated by bridging. The ability of PAAm to flocculate silica particles is very extensive at a molecular weight of 5.5 × 10⁶. For suspensions of 20-nm silica in a solution of PAAm with M_W = 5.5 × 10⁶ − 1 × 10⁷, the apparent viscosity irreversibly increases with shearing time at shear rates beyond a certain value. This may be due to the flocculation by the shear-induced bridging. The suspensions of 40-nm silica show similar flow behavior to the medium irrespective of molecular weight of PAAm. The bridging flocculation is not expected for large particles as one polymer molecule cannot bridge through many particles.     

Rheology modification of montmorillonite dispersions by colloidal silica

We have studied the effect of additions of both anionic and cationic spherical silica colloids of different sizes on the rheology of dispersions of a well-characterised montmorillonite clay, SWy-2. The systems have been studied above and below the critical hydrodynamic overlap concentration, c*, of the clay. For dispersions at c < c* on replacement of ～10 % w/w of the clay content by silica, it was found that whereas a cationic silica additive transformed a liquid-like, non-gelling montmorillonite dispersion into a substantial gel, anionic silica destroyed any nascent structure in the fluids, reducing the effective viscosity and virtually eliminating the rheological hysteresis characteristic of structured fluids. On the other hand, in the regime of c > c*, replacement of ～10 % w/w of the clay content by silica leads to enhancements of all the rheological parameters characteristic of a gelling system, for the addition of both anionic and cationic silica. A simple tentative microstructural model for this complex behaviour is presented. This work, alongside our previous studies, confirms significant rheological modification by the addition of small quantities of nanoparticles as a general phenomenon of clay-colloid systems. It further suggests that viscosity enhancement and control of the rates of sol-gel transitions for product applications can be achieved using relatively low-cost, commercially available materials, such as silica nanoparticles and natural clays of different mineralogy.     

Structure and dynamics of a polymer solution subject to flow-induced phase separation

Experiments combining mechanical rheometry with polarimetry (birefringence and scattering dichroism) have been conducted on a 6% solution of polystyrene (1.86x10⁶ molecular weight) in dioctyl phthalate. Birefringence is used to measure the extent of segmental orientation, whereas the dichroism is sensitive to orientation and deformation of concentration fluctuations associated with the process of flow-induced phase separation. The results indicate that these fluctuations grow predominately along the neutral (or vorticity axis) of a simple shear flow. At higher rates of shear, orientation in the flow direction is favored. The transition in orientation direction is accompanied by time-dependent behavior in the optical properties of the solution during shear and the onset of shear thickening of the viscosity and the first normal stress difference coefficient.