Shear Viscosity Of Suspensions Research Articles

Electrorheological properties and microstructure of silica suspensions

We present experimental and theoretical results on the electrorheological response and microstructure of colloidal suspensions composed of silica nanoparticles dispersed in a silicon oil, as a function of electric field strength and silica water content. Using small-angle neutrons scattering experiments, we determined the evolution of the static structure factor of the suspensions when an electric field is applied. Experimental data were fitted with model calculations using the Percus-Yevick solution for Baxter's hard-sphere adhesive potential. The obtained stickiness parameter is directly related to the polarization interactions that depend on the water content of silica particles. The influence of the polarization interparticle potential on the rheology of the silica dispersions was investigated in a second time. A microscopic theory for the shear viscosity of adhesive hard-sphere suspensions was successfully used which describes the steady shear viscosity of suspension in terms of the fractal concept.

A new approach to prepare highly loaded aqueous alumina suspensions with temperature sensitive rheological properties

Abstract Poly(acrylic acid) (PAA)-free alumina suspensions with temperature sensitive rheological properties have been successfully produced using the combination of tri-ammonium citrate and magnesium citrate powders with slurry loading up to 60 vol.%. A new approach using the DLVO concept is proposed to design the suspension composition. Both the shear viscosity and the shear modulus of the suspensions start to increase when the suspension temperature is above a critical value. The flocculation of the suspensions is controlled by the dissolution of the magnesium citrate that increases the ionic strength in the suspensions. The dissolution is controlled by the pH of the suspensions, which decreases with increasing temperature. Compared with the same solid loading suspensions containing PAA, the suspension shear viscosity of 25 °C can be reduced, which is useful in developing new near net shape forming technologies.

Shear viscosity of suspensions of aligned non-Brownian fibres

We report on the steady-state shear viscosity of suspensions of fibres dispersed in Newtonian fluids, in a wide range of volume fractions throughout the dilute and semi-dilute regimes. We show that the apparent shear-thinning behaviour, which is sometimes observed in the semi-dilute regime at intermediate shear rates, is an experimental artefact due to the presence of transient clusters of entangled fibres in the suspensions. At high shear rates, the fibres are aligned and the suspensions exhibit Newtonian behaviour. In this regime, the viscosity is a function of volume fraction and fibre aspect ratio only. The data can be rescaled onto a universal curve using a variable that accounts for the average contribution of the particles to the bulk stress. All these results are discussed in relation to recent theories.

Rheology of bubble-bearing magmas

The rheology of bubble-bearing suspensions is investigated through a series of three-dimensional boundary integral calculations in which the effects of bubble deformation, volume fraction, and shear rate are considered. The behaviour of bubbles in viscous flows is characterized by the capillary number, Ca, the ratio of viscous shear stresses that promote deformation to surface tension stresses that resist bubble deformation. Estimates of Ca in natural lava flows are highly variable, reflecting variations in shear rate and melt viscosity. In the low capillary number limit (e.g., in carbonatite flows) bubbles remain spherical and may contribute greater shear stress to the suspension than in high capillary number flows, in which bubble deformation is significant. At higher Ca, deformed bubbles become aligned in the direction of flow, and as a result, contribute less shear stress to the suspension. Calculations indicate that the effective shear viscosity of bubbly suspensions, at least for Ca<0.5, is a weakly increasing function of volume fraction and that suspensions of bubbles are shear thinning. Field observations and qualitative arguments, however, suggest that for sufficiently large Ca ( Ca greater than about 1) the effective shear viscosity may be less than that of the suspending liquid. Bubbles reach their quasi-steady deformed shapes after strains of order one; for shorter times, the continuous deformation of the bubbles results in continual changes of rheological properties. In particular, for small strains, the effective shear viscosity of the suspension may be less than that of the liquid phase, even for small Ca. Results of this study may help explain previous experimental, theoretical, and field based observations regarding the effects of bubbles on flow rheology.

Quantitative predictions of suspension rheology by nonequilibrium Brownian dynamics and hydrodynamic preaveraging

Nonequilibrium Brownian dynamics simulations are applied to model a highly concentrated dispersion of charged particles at high ionic strength. Through the use of hydrodynamic preaveraging, as applied to the overdamped Langevin equation, and correlations appropriate for hard spheres, good predictions are obtained for the suspension shear viscosity at low to moderate shear rates. At higher shear rates, the influence of near-field hydrodynamic interactions on the suspension microstructure invalidates the preaveraging approach.

A constitutive approach for studying concentrated suspensions of rigid fibers in a non ‐ Newtonian Ellis fluid

Abstract A constitutive model for a semi‐concentrated suspension of rigid fibers in a non‐Newtonian fluid is derived in the present study. This work is extended from a previous work by Dinh and Armstrong which counted rigid fibers suspended in a Newtonian fluid. To investigate the effect of the shear‐dependent suspending fluid on the shear viscosity of suspension, the Ellis fluid is assumed to model such a non‐linear matrix. It is shown that the present derivation, via a cell model, gives an analytic form to calculate the drag coefficient of fibers and to illustrate the influence of material parameters of matrix fluid. The resulting equation gives the bulk stress in terms of an integral over a fourth‐order orientation vector, e, similar to the expression of Doi and Edwards for dense macromolecular fluid. For the purpose of evaluation, the present model attempts to predict the rheological behavior in the inception of flow, steady simple shear flow and stress‐growth experiments.

Convergence of multiple scattering series for two-body hydrodynamic effects on shear viscosity of suspensions of spheres

An efficient computational scheme has been developed that includes many-body hydrodynamics for viscosity in a suspension of spheres following the approach of Jones and Muthukumar [J. Chem. Phys. 89, 6406 (1988)] for friction coefficients. The method combines the hydrodynamic scattering formalism of Freed and Muthukumar [J. Chem. Phys. 76, 6186 (1982)] with angular momentum diagrammatic techniques from quantum mechanics. The concentration dependence of the viscosity is expressed as a series of finite integrals labeled by the equivalent of angular momentum quantum numbers. This series is smoothly convergent in contrast to the case of the alternate formalism of a series of terms of inverse powers of the sphere separation. A comparison between different methods and the slowness of convergence of the series are addressed in detail. At the two-body level, the virial expansion for the shear viscosity η of a suspension of hard spheres of volume fraction Φ is determined to be η/η0=1+2.5Φ+4.8292Φ2+O(Φ3), where η0 is the viscosity of the fluid and the correction for the Brownian motion [G. K. Batchelor, J. Fluid Mech. 83, 97 (1977)] has been ignored. Our value for the two-body coefficient differs in 3.4% from the extrapolated value 5.0019 obtained by Cichocki and Felderhof [J. Chem. Phys. 89, 1049 (1988)].

Bulk properties of composite media. II. Evaluation of bounds on the shear modulus of suspensions of impenetrable spheres

We evaluate third-order bounds due to Milton and Phan-Thien on the effective shear modulus Ge of a random dispersion of identical impenetrable spheres in a matrix up to sphere-volume fractions near the random close-packing value. The third-order bounds, which incorporate two parameters, ζ2 and η2, that depend upon the three-point probability function of the composite medium, are shown to significantly improve upon the second-order Hashin–Shtrikman (or, more general, Walpole) bounds which do not utilize this information, for a wide range of volume fraction and phase property values. The physical significance of the microstructural parameter η2 for general microstructures is briefly discussed. The third-order bounds on Ge are found to be sharp enough to yield good estimates of the effective shear modulus for a wide range of sphere-volume fractions, even when the individual shear moduli differ by as much as two orders of magnitude. Moreover, when the spheres are highly rigid relative to the matrix, the third-order lower bound on the effective property provides a useful estimate of it. The third-order bounds are compared with experimental data for the shear modulus of composites composed of glass spheres in an epoxy matrix and the shear viscosity of suspensions of bituminous particles in water. In general, the third-order lower bound (rather than the upper bound) on Ge tends to provide a good estimate of the data.

Bulk rheology of dilute suspensions in viscoelastic liquids

A theoretical relation is derived for the bulk stress in dilute suspensions of neutrally buoyant, uniform size, spherical drops in a viscoelastic liquid medium. This is achieved by the classic volume-averaging procedure of Landau and Lifschitz which excludes Brownian motion. The disturbance velocity and pressure fields interior and exterior to a second-order fluid drop suspended in a simple shear flow of another second-order fluid were derived by Peery [9] for small Weissenberg number (We), omitting inertia. The results of the averaging procedure include terms up to orderWe2. The shear viscosity of a suspension of Newtonian droplets in a viscoelastic liquid is derived as $$\eta _{susp} = \eta _0 \left[ {1 + \frac{{5k + 2}}{{2(k + 1)}}\varphi - \frac{{\psi _{10}^2 \dot \gamma ^2 }}{{\eta _0^2 }}\varphi f_1 (k, \varepsilon _0 )} \right],$$ whereη0, andω10 are the viscosity and primary normal stress coefficient of the medium,e0 is a ratio typically between −0.5 and −0.86,k is the ratio of viscosities of disperse and continuous phases, and\(\dot \gamma \) is the bulk rate of shear strain. This relation includes, in addition to the Taylor result, a shear-thinning factor (f1 > 0) which is associated with the elasticity of the medium. This explains observed trends in relative shear viscosity of suspensions with rigid particles reported by Highgate and Whorlow [6] and with drops reported by Han and King [8]. The expressions (atO (We2)) for normal-stress coefficients do not include any strain rate dependence; the calculated values of primary normal-stress difference match values observed at very low strain rates.

Cluster theory for concentration dependence of shear viscosity for suspensions of interacting spheres. I

We present a general divergent-integral-free cluster theory for the concentration dependence, to any order in concentration, of the shear viscosity of a suspension of interacting colloidal spheres. Treating the solvent as a viscous hydrodynamic continuum, the steady state limit of vanishing shear rate is considered, so the sphere–sphere interactions enter through the Mayer cluster expansion of the various sphere equilibrium distribution functions. The spheres are taken to move such that the net hydrodynamic forces and torques acting on them identically vanish. We present general formulas for all coefficients in a virial type expansion of the suspension shear viscosity in powers of the concentration for any prescribed spherically symmetric direct interaction potential between the spheres. Previous work has been limited to the two-sphere contributions only. Every virial coefficient in our complete expansion involves integrals of the sphere equilibrium distribution functions multiplied by functions of hydrodynamic origin. These virial coefficients are perfectly convergent because of the nature of the various equilibrium distribution functions present in the integrals for the virial coefficients.