Richard Buscall

The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory

The properties of aqueous solutions of model HEUR associative thickeners under dynamic and steady shear have been studied as a function of concentration, molecular weight, temperature, and hydrophobic end‐cap length. It is shown that solutions of AT behave as near perfect Maxwell fluids inasmuch that Cole–Cole plots of the dynamic moduli are almost exactly semi‐circular. An Arrhenius law temperature dependence of the static viscosity and relaxation time is also observed, providing confirmation of a single relaxation process. In certain other respects, AT solutions show more complex behavior, e.g., the Cox–Merz rule is not obeyed, with the steady shear viscosity showing a weaker dependence on shear rate than does the complex viscosity upon frequency. Furthermore, weak shear thickening is seen to precede shear thinning in steady shear. The above results are consistent with the predictions of a transient network theory presented recently by Tanaka and Edwards and Jenkins (generalized Green–Tobolsky theory). ...

The consolidation of concentrated suspensions. Part 1.—The theory of sedimentation

The concentration or consolidation of suspensions of fine particles under the influence of a gravitational field has been analysed. The rate and extent of consolidation depends upon a balance of three forces, the gravitational driving force, the viscous drag force associated with flow of liquid in the sediment and a particle or network stress developed as a result of direct particle–particle interactions. In the case of colloidally stable suspensions, this particle stress is the osmotic pressure of the particles; in the case of flocculated or coagulated suspensions, it is the elastic stress developed in the network of particles. A constitutive equation is suggested for irreversibly flocculated suspensions undergoing consolidation which embodies the concept of a concentration-dependent yield stress Py(ϕ). This is then used to analyse the sedimentation behaviour of flocculated sediments and to derive expressions for the initial sedimentation rate. The initial rate of change of sediment height with time in a uniform gravitational or centrifugal field is given approximately by: [graphic ommitted] where B=Δρgϕ0H0/Py(ϕ0), u0 is the sedimentation rate of an isolated particle, ϕ0 is the initial (uniform) volume fraction of solids, r(ϕ0) is a dimensionless hydrodynamic interaction parameter, Δρ is the difference in density between solid and liquid, g is the gravitational or centrifugal acceleration and H0 is the initial sediment height. The theory accounts correctly for the equilibrium consolidation behaviour of strongly flocculated suspensions, and preliminary experimental data suggest that it is not inconsistent with their dynamic behaviour. The estimation of the yield stress Py(ϕ) from a batch centrifuge experiment is also described.

Scaling behaviour of the rheology of aggregate networks formed from colloidal particles

The instantaneous shear modulus G and compactive strength Py of aggregate networks formed from silica particles with a mean diameter of 26 nm have been determined as a function of particle concentration. The data are compared with similar data obtained earlier for a range of polystyrene spheres with diameters between 60 and 960 nm and with compactive strength data obtained for polystyrene spheres at higher volume fractions by Sutherland. It is shown that clusters of submicron spheres formed by rapid aggregation become spacefilling and form a network at a critical volume fraction Φg of ca. 0.05. Above this concentration the data for Py and G suggest that aggregate networks show universal behaviour which is consistent with the scalings G∼ϕµ, dPy(ϕ)//d ln ϕ∼G(ϕ), with µ= 4 ± 0.5. This latter value for the exponent agrees well with that predicted by Ball and Brown by assuming the clusters comprising the network are fractal. For diffusion-limited cluster–cluster aggregation (DCA) they obtained a value of µ= 3.6. The data for Py imply a particle size dependence of the type Py∼am with m between –2 and –3, where a is the particle radius. More data are required to establish the precise dependence; the observed trend is, however, not inconsistent with what might be expected from a consideration of interparticle forces which implies a scaling of a–2.3. The scaling behaviour of the yield stress in shear flow and the dependence of the shear modulus on strain for non-negligible strains is also discussed.

The rheology of strongly-flocculated suspensions

Abstract The rheology of strongly-flocculated dispersions of colloidal particles has been investigated at particle concentrations where a continuous network is formed rather than a collection of discrete flocs. Such networks are shown to possess a true yield stress in both shear and in uniaxial compression (as realised in a centrifuge). Properties measured as a function of particle concentration and particle size include the yield stresses in shear (σ y ) and compression ( P y ); the limiting and strain-dependent, instantaneous shear moduli G O and G (γ); the elastic recovery at finite strains, and the rate of centrifugally-driven compaction. The yield stresses and moduli appear to show a power-law dependence on particle concentration with G O and P y , having the same power-law index and σ y a somewhat lower one. The data are in part consistent with predictions based on the idea that the networks have a heterogeneous structure comprising a collection of interconnected fractal aggregates. The behaviour as a function of particle size and concentration is however not completely scaleable as might be expected on this basis. Thus, whereas the shear yield stress could be scaled to remove its dependence on particle radius a and volume fraction φ (over the measured range 0.25 μm ⩽ a ⩽ 3.4 μm; 0.05 ⩽ φ ⩽ 0.25) as could the strain dependent modulus (0.25 ⩽ a ⩽ 1.3 μm; 0.08 ⩽ 0.25), the particle-size and concentration dependence of P y and G O could only be scaled for particles with radii between 0.16 and 0.5 μm, smaller and larger particles having different and much higher power-law index in respect of their concentration dependencies. In the case of the smaller particles the failure of the scaling is thought to be due to an anomaly since these particles distort significantly under the influence of the strong van der Waals forces and this causes the aggregates to be more compact then they otherwise would be. The reasons for the failure at larger sizes is not clear.

Rheological evidence of adsorbate-mediated short-range steric forces in concentrated dispersions

In order to examine quantitatively the effect of short-range forces on the state of dispersion in dense suspensions, the effect of a series of anionic adsorbates on the rheology of a model zirconia concentrated suspension has been studied in detail. The anionic additives include sulfate, phosphate, pyrophosphate and polyphosphates as well as simple organic acid anions such as lactate, malate and citrate. The adsorbates shifted the pH of maximum static yield stress and, equivalently, the pH of zero zeta potential (ζ), to lower pH values. The additives also lowered the magnitude of the maximum yield stress at ζ= 0. The results are all consistent with the adsorbates producing a steric barrier equivalent to the size of the adsorbed molecule along the attractive van der Waals interaction. Separately the polyphosphate adsorbates are shown to assume a flat orientation and do not appear to produce a thick electro-steric barrier to coagulation.

The rheology of concentrated dispersions of weakly attracting colloidal particles with and without wall slip

It is demonstrated that weakly flocculated, concentrated colloidal dispersions show slip flow when sheared between smooth concentric cylinders. The precise pattern of behavior seen depends upon the stress and upon how long the flow is left to establish prior to measurement. With delay times of order hours, slip is not seen until a critical stress is exceeded (typically about 1 Pa) and, thus, the true low‐shear viscosity can be determined provided care is taken to ensure the stress does not exceed the critical level. With short delay times of order minutes, slip is seen irrespective of how small the stress is and the low‐shear viscosity can be underestimated by several orders of magnitude. Comparisons of flow curves obtained using smooth and roughened cylinders show that slip only occurs at the inner cylinder, and also that bulk flow is re‐established at higher stresses where the dispersions start to shear thin. The apparent low‐shear, relative viscosity measured in the presence of slip appears, to a first...

Shear thickening in model suspensions of sterically stabilized particles

The onset of shear thickening (dilatancy) has been studied in submicron model suspensions of sterically stabilized spherical particles. Stress controlled rheometers have been used for this purpose, so that measurements can be performed beyond the onset of sudden shear thickening. Systematic data are presented for the effect of particle size, particle concentration, and the nature of the suspending medium on the onset of shear thickening. As a first approximation, the critical shear rate changes inversely proportional with the medium viscosity. The changing solvency of the medium for the stabilizer polymer introduces additional changes through effects on the thickness and stiffness of the steric barrier. Thinner, stiffer barriers cause lower critical shear rates. In the softer systems the critical shear stress becomes independent of particle concentration in dense suspensions. This does not seem to be the case for the harder systems. The effect of particle radius a could shed some light on the underlying m...

Letter to the Editor: Wall slip in dispersion rheometry

Even though our appreciation of the importance and ubiquity of wall slip has grown substantially over the last decade or two, it is still common to find papers on disperse systems wherein scant details of the measurement methods are given and where no mention of the possibility of slip is made. It seems then that there is a need still to raise awareness and to promote the idea that the rheometry of disperse systems is not so straightfoward as it might seem. It takes experience, judgment, and skill to make meaningful measurements on disperse systems and it is suspected that the nature of the experimental challenge is under-estimated grossly by too many workers even now. Slip is not merely a rheometric complication; of course, it an intrinsic feature of the response of disperse systems and one deserving of more attention in its own right.

Viscoelastic properties of concentrated latices. Part 2.—Theoretical analysis

Shear-modulus data for polystyrene latices at various volume fractions and sodium chloride concentrations are compared with a simple model based on the theory of interaction between electrical double layers. Stress relaxation and low shear-rate viscosity are also discussed in the context of particle interaction forces.

Viscoelastic properties of concentrated latices. Part 1.—Methods of examination

Concentrated polystyrene latices form strongly interacting systems, and under appropriate conditions of particle radii, volume fraction and ionic strength the repulsive forces can be strong enough to give rise to measurable viscoelastic behaviour. In this paper an experimental investigation of the viscoelastic behaviour of concentrated latices is described. The methods used included creep compliance and shear-wave propagation. The former was used to determine the low stress viscosities and the latter to determine the shear modulus. The particle radii were varied from 26 to 98 nm and the volume fraction range was 0.2–0.4.