Extrapolated Yield Stress Research Articles

A Study on the Effects of Three Types of Deflocculants and the Increase in the pH on the Rheological Behavior of Nano Carbon Suspensions

In this study, the rheological behavior of carbon black suspension with different amounts of three deflocculants (Dispex G40, Dispex N40 and CMC) has been investigated. As the rheological behavior of carbon black is markedly dependent on pH, the effect of the increase in pH has been studied. Dispex G40 and Sodium carboxymethycellulose (CMC), are effective in promoting complete deflocculation of carbon black suspensions with 20, 30 and 40 wt% solids concentrations for Dispex G40, and 40 wt% for CMC. 40 wt% suspensions containing Dispex N40 exhibit a yield stress at all levels of deflocculant investigated. However, a minimum in the extrapolated yield stress and apparent viscosity curve indicates that there is an optimum deflocculation level. The addition of alkali enhances the deflocculating power of CMC and Dispex G40, reducing any existing yield stress to zero. However, it would appear that Dispex N40 is desorbed when the pH is increased as rapid coagulation of the system is apparent, arising from a reduction in the repulsive forces.

Rheological characterization of food thickeners marketed in Australia in various media for the management of dysphagia. III. Fruit juice as a dispersing medium

Apple, orange and pineapple juices were used to prepare thickened fluids from six Australian commercially available food thickeners that are based on guar gum, modified starch and xanthan gum. Using a strain-controlled rheometer, changes in shear stress with the rate of shear (1–100 s −1) at 20 °C were independent of the thickener or fruit juice. As the solids content of the fluids increased, so were the viscosity, density and extrapolated yield stress. The density, yield stress and viscosity of the thickened fluids were not significantly influenced ( p > 0.05) by fruit juice, but the type of thickener significantly ( p < 0.05) affected these properties. The Herschel–Bulkley model was found to be the most suitable in describing the rheological data of the thickeners in the fruit juices. The relevant parameters obtained for the recommended models can be used to obtain a known viscosity of the thickened fluids, match to fluids used in videofluoroscopy and obtain objective classification of the thickened fluids. Sample calculations are included.

Comment on “Synthesis and electrorheological characterization of polymer containing amino and carboxy groups”

The comments for the recent article on electrorheological (ER) characterization of polymer containing amino and carboxy groups based ER fluids are given by analyzing its extrapolated yield stress data as a function of electric field strengths. Using the critical electric field strengths deduced, we found that the universal yield stress equation collapses their data onto a single curve.

The importance of the interfacial stabilising layer on the macroscopic flow properties of suspensions dispersed in non-adsorbing polymer solution

In this paper, the rheological properties, microscopic appearance and macroscopic sedimentation behaviour of 147- and 482-nm polystyrene latices in HEC solutions, bearing different adsorbed poly(ethyleneoxide)–poly(propyleneoxide)–poly(ethyleneoxide) (PEO–PPO–PEO) copolymers are presented and compared with previous results with a 67-nm latex (Langmuir 13 (1997) 2922). The ratio of the steric layer thickness to the particle radius varies from 1:5 to 1:40 for the three latex sizes covering a range of particle softness. The 147-nm latex showed gas, liquid and solid phases, including three phase coexistence with increasing concentrations of HEC. The solid phase was a viscoelastic gel that sedimented slowly and showed initially slow, then faster sedimentation rates for HEC concentrations close to the fluid–gel phase boundary. These properties depended on the adsorbed PEO–PPO–PEO copolymers; the fluid–gel phase boundary moved to lower HEC concentrations with increasing PEO chain length. Oscillatory shear measurements were sensitive to the floc network structure and showed the transition from the fluid to gel phases. The values for the elastic modulus in the gel region were independent of the PEO chain length in the stabiliser implying the presence of similar floc structures with each of the different PEO–PPO–PEO copolymers. Stress relaxation measurements gave long relaxation times (>10 3 s) and showed that the suspensions were viscoelastic fluids with high zero shear viscosities. Higher values were obtained with longer PEO chain lengths. Extrapolated yield stress values showed stronger flocculation with increasing PEO chain length in the adsorbed stabilising layer. There was good correlation between the extrapolated yield stress and the sedimentation velocity, indicating that the collapse of the floc network is governed by the strength of the interparticle bonds (for the same floc structure) and also with the long-time behaviour from the stress relaxation measurements. With the 482-nm latex there was less effect of the adsorbed copolymer both for the rheology and sedimentation behaviour, with the particles behaving more like hard spheres. The transition between hard and soft sphere behaviour, interpreted here as the ratio of the steric layer thickness to the particle radius at which the adsorbed stabilising layer starts to have an effect on the rheology and phase behaviour is estimated to be approximately 1:20.

The rheology of concentrated suspensions of depletion-flocculated latex particles

The effect of adding non-adsorbing polymer, poly(acrylic acid) (PAA), on the rheological properties of concentrated electrostatically-stabilised polystyrene latex suspensions was investigated. The extrapolated yield stress of the depletion-flocculated suspensions was studied as a function of the concentration and the molecular weight of the free polymer. Specifically, the Bingham yield value was observed to increase with either an increase in the weight fraction of the polymer or through the use of a longer chain polyacid. Unlike the sterically stabilised colloidal suspensions studied in the literature, at high polymer concentrations these charge-stabilised latex particles exhibited plateauing in the yield stress for each polyacid. The energy of separating particles within an aggregate into single units was calculated using the yield stress and average particle co-ordination number. In contrast to what was commonly done in the literature, the latter was not assumed to be constant but estimated from the aggregate mass fractal dimension as obtained from static light scattering techniques. It was found that the separation energy showed similar trends to those in the yield stress with both varying the polymer concentration and molecular weight. These trends also bear remarkable similarities to those in the depth of the secondary potential energy well as measured using atomic force microscopy (AFM).

Magnetorheological fluid composites

An interesting extension in the use of magnetic fluids has resulted from the development of magnetic fluid composites obtained by dispersing micrometre-sized non-magnetic particles in a magnetic fluid. The composites possess a yield stress in a magnetic field which can be described at sufficiently high strain rates by the Bingham relation , where is the shear stress perpendicular to the applied field, the extrapolated yield stress, the strain rate and the plastic viscosity. Thus, a composite, particle concentration , in a field 0.036 T with has a yield stress of 26 Pa. The yield stresses obtained experimentally for different and correspond well to values predicted theoretically by Rosensweig using a determination of based on a continuum concept of unsymmetric stress that develops in the deformed but unyielded anisotropic medium.

The derivation of a strain hardening modulus from true stress-strain curves for thermoplastics

Some problems in the measurement of stress-strain curves for thermoplastics are considered and the importance of measuring true stress-strain curves is emphasized. However, an increasing number of suitable curves have now been published of which the large majority have been found to comply with the following Gaussian equation: σ true =Y+G p (λ 2− 1 λ ) where σ true is the true stress, Y is the extrapolated yield stress, G P is the strain hardening modulus and λ is the extension ratio. It is shown that the Considere condition for necking requires that Y G P > 3 and the available results support the proposition that this is a necessary condition for necking to occur. High values of G P are observed in polymers with an extended chain conformation.

The Effect of Surface Modification by an Organosilane on the Electrochemical Properties of Kaolinite

AbstractThe electrochemical properties of kaolinite before and after modification with chlorodimethyl-octadecylsilane have been studied by electrophoretic mobility, surface charge titration, and extrapolated yield stress measurements as a function of pH and ionic strength. A heteropolar model of kaolinite, which views the particles as having a pH-independent permanent negative charge on the basal planes and a pH-dependent charge on the edges, has been used to model the data. The zeta potential and surface charge titration experimental data have been used simultaneously to calculate acid and ion complexation equilibrium constants using a surface complex model of the oxide-solution interface. The experimental data were modeled following subtraction of the basal plane constant negative charge, describing only the edge electrical double layer properties. Extrapolated yield stress measurements along with the electrochemical data were used to determine the edge isoelectric points for both the unmodified and modified kaolinite and were found to occur at pH values of 5.25 and 6.75, respectively. Acidity and ion complexation constants were calculated for both sets of data before and after surface modification. The acidity constants, pKa1 = 5.0 and pKa2 = 6.0, calculated for unmodified kaolinite, correlate closely with acidity constants determined by oxide studies for acidic sites on alumina and silica, respectively, and were, therefore, assigned to pH-dependent specific chemical surface hydroxyl groups on the edges of kaolinite. The parameters calculated for the modified kaolinite indicate that the silane has reacted with these pH-dependent hydroxyl groups causing both a change in their acidity and a concomitant decrease in their ionization capacity. Infrared data show that the long chain hydrocarbon silane is held by strong bonding to the kaolinite surface as it remains attached after washing with cyclohexane, heating, and dispersion in an aqueous environment.

Depletion flocculation of concentrated latex suspensions by surfactant micelles

The influence of addition of a high concentration of non-ionic surfactants on the rheology of a concentrated (volume fraction φ p = 0.4) polystyrene latex suspension was investigated. Four different surfactants containing the same hydrophobic group (C 9H 19C 6H 5(CH 2CH(CH 3)O) 13) and increasingly large hydrophilic chains (poly(ethylene oxide) with 27, 48, 79 and 174 ethylene oxide (EO) units) were used. The rheology was studied using steady-state shear stress (τ)—shear rate (γ) measurements as well as oscillatory measurements. From the τ—γ curves, the extrapolated yield stress τ β and plastic viscosity η pl were obtained as a function of surfactant concentration. From oscillatory measurements, the complex modulus G*, the storage modulus G′ and loss modulus G″ were obtained as a function of frequency at different surfactant concentrations. All results showed a rapid increase in the rheological parameters with increase of surfactant concentration, once the latter reached a critical concentration. This rapid increase (non-Newtonian flow) was considered to be due to depletion flocculation. The latter was thought to occur at a surfactant concentration in excess of that required for maximum random packing of surfactant micelles, which were assumed to be spherical. A simple calculation (using a value of 0.63 for random packing) predicted the surfactant concentration at the onset of depletion flocculation, using the aggregation number of surfactant molecules in the micelle (obtained from surface-tension or light-scattering measurements). The extrapolated yield value was used to calculate the energy of separation E sep between contact points in a floc. E sep was compared with the theoretical free energy of depletion attraction G dep that was calculated using the Asakura and Oosawa theory. Agreement between the calculated G dep and experimental E sep values was fair.

Use of viscoelastic measurements for investigating the stability/flocculation of concentrated dispersions

The use of viscoelastic measurements for studying stability/flocculation of concentrated dispersions is discussed. With electrostatically stabilised dispersions, the system becomes predominantly elastic when significant double-layer overlap occurs. This was demonstrated using polystyrene latex dispersions in 10–5 and 10–3 mol dm–3 NaCl. Plots of the elastic modulus G′versus surface-to-surface separation distance h showed a rapid increase when h was less than twice the double-layer thickness. The experimental G′ values were compared with theoretical values calculated from the second differential of the interaction energy vs. distance relationship. With sterically stabilised latex dispersion [containing grafted poly(ethylene oxide) chains], predominantly elastic response was also obtained when h became less than twice the adsorbed layer thickness (2δ). The G′vs. volume fraction curves were converted to G′vs. h and this was compared with the values of G′ calculated from direct force, F, vs. distance curves. In both cases there was a rapid increase in G′ with decrease in h when h < 2δ.Viscoelastic measurements could also be applied for flocculated dispersions. With weakly flocculated systems such as those obtained by addition of a free non-adsorbing polymer (depletion flocculation), the systems showed pronounced non-Newtonian behaviour above a critical volume fraction of free polymer (ϕ+P). The occurrence of this behaviour decreased with increasing molecular weight of the free polymer. The extrapolated yield stress was used to calculate the energy of separation between particles, Esep, in the flocculated dispersion. Esep was compared with the theoretical value of the free energy of depletion, Gdep, that was calculated using available theories. With strongly flocculated dispersions, scaling concepts could be applied and the power exponent in ϕ(G′∼ϕn) could be used as a measure of the strength of flocculation. From G′ and the critical strain γc, above which non-linear response is obtained, the cohesive energy of the flocculated structure, Ec, was calculated. log–log plots of Ecversus ϕ were used to obtain the power exponent in ϕ and this should give a measure of the strength of flocculation.

Viscoelastic properties of sodium montmorillonite (Gelwhite H) suspensions

The swelling of a commercial sodium montmorillonite clay suspension, namely Gelwhite H, has been investigated at pH 8.8–8.9 at various clay concentrations. Swelling was investigated using rheological measurements by following the storage modulus G′(t) as a function of time t. The exponential increase of G′(t) with t was used to calculate the modulus at infinite time G′ t → ∞ as well as the gelation time t g. The results showed a rapid increase in G′ t → ∞ with an increase in clay concentration from 30 to 60 g liter −. However, within experimental error, t g was constant and independent of clay concentration. A plot of G∗ (complex modulus), G′, and G′' (loss modulus) (at.1 Hz) versus Gelwhite H concentration (pH 8.8–8.9) showed a rapid increase in G∗ and G′ (which were identical) above a clay concentration of 30 g liter −1. G′' remained very low and showed a slight increase with an increase in clay concentration. Similar trends were obtained in the variation of shear modulus G∞ and the extrapolated yield stress τ B. This means that the “gel point” for this clay sample is about 30 g liter −1, above which the elasticity increases very rapidly with a further increase in clay concentration. The cohesive energy, E c , in the gel structure was obtained by measuring the viscoelastic parameters as a function of applied strain amplitude (at constant frequency). The results showed that G′(t), E c , and the critical stress σ c increase rapidly with an increase in Gelwhite H concentration. The results could be fitted to a power law with an exponent n in the concentration. This exponent was in the region 3.1–3.7 and was lower than that obtained previously with another commercial bentonite sample. The results confirmed the previously held view that gel formation in these commercial samples is most likely due to a face-to-edge association mechanism. This mechanism is favorable at intermediate to high electrolyte concentrations (usually present in commercial clay suspensions) whereby the double layers are compressed, thus obtaining close approach of the edges to the faces. Plots of G∗, G′, G′', G, and τ b versus pH showed a primary maximum at pH 7, indicating maximum interaction at this pH. At this pH, the edges are most likely positively charged and hence edge-to-face association is possible. The reduction at pH >7 is due to the reduction of positive charges on the edges. However, the reduction at pH <7 may also be due to the reduction in the number of units available for the build up of the double-T junctions.

Plastic banding in glassy polycarbonate under plane simple shear

Samples of amorphous polycarbonate were tested in plane simple shear at various temperatures (−100 to +150‡ C) and shear rates (3×10−5 to 3×10−2sec−1). In the glassy state, it was observed that the deformation concentrated at yield inside a single shear band whose elongation and widening phases correspond to well marked stages of the recorded stress-strain curve. Birefringence and X-ray diffraction in the growing band show that the molecular orientation follows a pseudoaffine evolution with the local plastic strain. Although the shear is inhomogeneous during the growth of the shear band, it is fairly uniform inside the band itself, down to the scale of 100 nm. After the band has completed its widening (for an overall shear of about 0.9) the overall shear in the whole specimen is homogeneous and then one can deduce the constitutive equation for steady state plasticity of the glassy material, up to shear strains as large as 2.0. It is characterized by a linear strain hardening whose value, such as the extrapolated yield stress, decreases gradually with temperature.

Effect of grain size and free interstitials on yield stress, flow stress and Lüders strain in iron and an iron-titanium alloy

The grain size dependence of yield and flow stresses was studied and compared in an impure iron (Ferrovac-E) with 75 p.p.m. C + N and an essentially interstitial-free iron–0.2 w/o Ti alloy. The Hall-Petch relation was obeyed in the case of both materials. In the absence of interstitials, the extrapolated yield stress showed little or no grain size dependence. The dependence of flow stress on grain size in this alloy increased with increasing strain and can be explained by a work-hardening model. In impure iron containing interstitials, the possibility of two mechanisms, one governing the magnitude of the stress during inhomogeneous yielding and the other the work-hardening characteristics during the homogeneous plastic flow that follows, is discussed. The factors which govern the extent of Lüders strain in Ferrovac-E and their relationship to the stress-strain curve for iron-Ti alloy are also discussed.

The mechanical properties of pure iron tested in compression over the temperature range 2 to 293 °K

The mechanical properties of pure iron single crystals and of polycrystalline specimens of a zone-refined iron have been measured in compression over the temperature and strain rate ranges 2.2 to 293 °K and 7 x 10 -7 to 7 x 10 -3 s -1 respectively. Various yield stress parameters were determined as functions of both temperature and strain rate, and the reversible changes in flow stress produced by isothermal changes of strain rate or by changes of temperature at constant strain rate were also measured as functions of temperature, strain and strain rate. Both the temperature variation of the flow stress and the strain rate sensitivity of the flow stress were generally identical for the single crystals ( ca. 0.005/M carbon) and the polycrystalline specimens ( ca. 9/M carbon). At low temperatures, the temperature dependence of the yield stress was smaller than that of the flow stress at high strains, probably because of the effects of mechanical twinning, but once again the behaviour of single and polycrystalline specimens was very similar. Below 10 °K, both the flow stress and the extrapolated yield stress were independent of temperature. The results show that macroscopic yielding and flow at low temperatures are both governed by the same deformation mechanism, which is not very impurity sensitive, even in the very low carbon range covered by the experiments. The flow stress near 0 °K is ca. 5.8 x 10 -3 u where [i is the shear modulus. On the basis of a model for thermally activated flow, the activation volume at low temperatures (high stresses) is found to be ca. 5 b 3 . The exponent in the empirical power law for the dislocation velocity against stress relation is ca. 3 near room temperature, but becomes quite large at low temperatures. The results indicate that macroscopic deformation at low temperatures is governed by some kind of lattice frictional stress (Peierls-Nabarro force) acting on dislocations.