Shear viscosity behavior of highly concentrated suspensions at low and high shear-rates

A method is proposed for determining the shear viscosity behavior of highly concentrated suspensions at low and high shear-rates through the use of a formulation that is a function of three parameters signifying the effects of particle size distribution. These parameters are the intrinsic viscosity [], a parametern that reflects the level of particle association at the initiation of motion and the maximum packing concentration _m. The formulation reduces to the modified Eilers equation withn = 2 for high shear rates. An analytical method was used for the calculation of maximum packing concentration which was subsequently correlated with the experimental values to account for the surface induced interaction of particles with the fluid. The calculated values of viscosities at low and high shear-rates were found to be in good agreement with various experimental data reported in literature. A brief discussion is also offered on the reliability of the methods of measuring the maximum packing concentration. _r = /₀ relative viscosity of the suspension - volumetric concentration of solids - k _n coefficient which characterizes a specific effect of particle interactions - _m maximum packing concentration - _r,0 relative viscosity at low shear-rates - [] intrinsic viscosity - n, n parameter that reflects the level of particle interactions at low and high shear-rates, respectively - _r, relative viscosity at high shear-rates - (_m)_s, (_m)_i, (_m)_l packing factors for small, intermediate and large diameter classes - v _s, v_i, v_l volume fractions of small, intermediate and large diameter classes, respectively - _si, _sl coefficient to be used in relating a smaller to an intermediate and larger particle group, respectively - _is, _il coefficient to be used in relating an intermediate to a smaller and larger particle group, respectively - _ls, _li coefficient to be used in relating a larger to a smaller and intermediate particle group, respectively - _m0 maximum packing concentration for binary mixtures - _m,e measured maximum packing concentration - _m,c calculated maximum packing concentration     

Time periodic viscosity of concentrated kaolin suspensions at constant shear rates

Knowledge of the viscosity of concentrated suspensions is required for several technical applications, e.g. process control in mechanical engineering, casting of ceramics and pipeline transport of solids. Our previous viscometric investigations of concentrated suspensions showed, under particular shear conditions, an apparent viscosity that was periodic in time for a constant shear rate and temperature. These results were obtained with rotational viscometers with a set coaxial geometry. The inner cylinder was rigidly coupled to the viscometer driving axis. In this paper we describe a viscosity time behavior which was found using another type of coupling. Measurements were performed with rotational viscometers with a non-rigidly linked inner cylinder (small sample adapter supplied by Brookfield). Using kaolin suspensions of 30% solid mass content, viscosity oscillations appear. They show a regular time pattern at certain intervals of low shear rates. The amplitudes reach up to 20% of the viscosity mean value. In addition a motion of the inner cylinder away from the coaxial position is observed. This dislocation is followed by a relocation into the coaxial position. A maximum in the viscosity value is correlated with a maximum of the dislocation position. The process of dislocation and relocation of the inner cylinder is assumed to be caused by local anisotropically distributed inhomogeneities, which originate from shear-induced agglomeration and deglomeration of suspended particles. The motion of the inner cylinder is described by introducing a perturbation term into the equation of motion. The parameters of the perturbation term are fitted to the experimental data. Received: 10 September 1998 Accepted: 28 April 1999     

Shear viscosity of settling suspensions

Summary A new apparatus is presented which allows the determination of the viscosity of suspensions of high density particles in low viscosity media. Results obtained on suspensions of low density particles compare well with those obtained on a Weissenberg Rheogoniometer equipped with a cone-and-plate and a bob-and-cup. Also, a very interesting observation is that the Eilers equation, conveniently modified to take into account the shape of the particles by means of the intrinsic viscosity, can well correlate all the data.

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Zusammenfassung Es wird ein neues Gerät beschrieben, das die Bestimmung der Viskosität von Suspensionen mit Teilchen hoher Dichte in niedrig viskosen Flüssigkeiten ermöglicht. Die an Suspensionen von Teilchen mit niedriger Dichte erhaltenen Ergebnisse stimmen gut mit den mittels eines Weissenberg-Rheogoniometers gewonnenen überein, das entweder mit einer Kegel-Platte- oder einer Koaxial-Zylinder-Meßeinrichtung ausgerüstet war. Als ein überraschendes Ergebnis stellt sich heraus, daß die Eilers-Gleichung, zum Zweck der Erfassung der Teilchenform mit Hilfe des Staudinger-Index in bequemer Weise modifiziert, alle experimentellen Daten gut zu korrelieren imstande ist.

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Nomenclature shear rate (sec^–1) - viscosity (Poise) - _r relative viscosity - [] intrinsic viscosity - volume concentration - _max maximum volume concentration With 7 figures and 3 tables     

Shear induced periodic structure changes in concentrated alumina suspensions at constant shear rate monitored by FBRM

Concentrated aqueous suspensions of alumina as disperse phase show a particular non-Newtonian time dependent flow behavior. The apparent viscosity measured by means of a rotational viscometer with coaxial cylinders at constant shear rate oscillates with time. The period of the oscillations varies on a scale of several hundred seconds. It is assumed that this behavior is caused by shear induced self-organized structure changes. In order to detect structure changes during the shear process a particle analysis system based on the focused beam reflectance measurement (FBRM) technique was applied. We have found a significant correlation between the oscillations of the viscosity and alterations of the chord length distribution.     

Rheology of low viscosity,high concentration brown coal suspensions

The paper describes how the theology of low concentration brown coal suspensions can be exploited to produce high concentration, low viscosity suspensions which are attractive as a potential coal-water fuel. Brown coal suspensions with solid concentrations approaching those of bituminous black coal have been prepared. The high inherent water content ( 60 wt %) and macroporosity of the brown coal have been reduced by thermal and chemical means. The hydrophobicity of the coal surface has been increased sufficiently to reduce the tendency for swelling and water uptake. This, together with densification, has allowed the solids content to be progressively improved from 30 wt % solids with raw coal to 65 wt% solids with modified coals while maintaining the viscosity of the suspension at a low level. The high solid concentration was achieved without additives.     

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. Received: 19 January 1999 Accepted: 17 June 1999     

Stability of some shear flows for concentrated suspensions

In this paper we investigate the stability of some viscometric flows for a concentrated suspension model which allows for the effects of shear-induced migration, including plane and circular Couette and Poiseulle flows, and unbounded and bounded torsional flows. In the bounded torsional flow, where its radial outer boundary is assumed frictionless, an exact closeform solution is given. With the exception of torsional flows, we find that a limit point for all the steady-state solutions can exist for certain range in the parameter values. In all cases, disturbances can persist for a long time, O (H ²/a ²), where H is a dimension of the flow field, and a is the particles' radius.     

On viscous flow and effective viscosity of concentrated suspensions and emulsions

Summary Previous analysis byHappel (3) of viscous flow in concentrated solid suspensions has been extended to include concentrated emulsions of slightly deformable fluid particles in the presence or absence of surfactant impurities.General expressions were obtained for viscous flow in multi-particle systems when arbitrary shear fields are imposed. Specific relations were then derived for uniform,Couette and hyperbolic fields. The behavior is found to be strongly dependent upon particle concentration and surfactant concentration. The theoretical expressions obtained for effective viscosity of emulsions compare favorably with experimental data ofNeogy andGhosh (18),Sibree (15),Sherman (17), andBroughton andWindebank (16). These results support other studies on ensemble velocities [(10), (12), and in particular (22)], which strongly indicate the practical value and factual reliability of cell models in predicting the behavior of suspensions and emulsions.     

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.     

Steady shear viscosity of short fibre suspensions in thermoplastics

The rheological behaviour of a polyethylene, two polyamides and a silicone oil filled with different fibre contents are studied in capillary rheometry. The viscosity increase induced by the fibres is important for the silicone oil, and negligible for the polyethylene. The polyamide is intermediate. The same classification stands for the pressure loss in the convergent channel upstream from the capillary. A constitutive equation based on a cell model which takes into account the shear-thinning behaviour of the matrix is built. The predictions of the model are in correct agreement with the measurements. Received: 22 September 1997 Accepted: 5 March 1998     

Experiments on the effective viscosity of concentrated suspensions of solid spheres

The effective viscosity of concentrated suspensions of solid spherical particles was determined experimentally, under zero shear conditions, by means of a convection experiment. For solid concentrations in the range 30–50 per cent the results verify extrapolations to low shear rates of previously reported conventional viscosity measurements, and suggest that, in this range of concentrations and at low shear, a suspension of neutrally bouyant spheres behaves effectively as an equivalent Newtonian fluid.     

Primary normal-stress coefficient prediction at high shear rates

On the basis of a brief analysis of well known normal-stress calculation methods, the necessity of improved models of prediction is elaborated. A modified form of the so-called mirror relation which meets these requirements is presented. In combination with the Carreau viscosity equation, an analytical solution is given which leads to a Carreau normal-stress coefficient equation and, thus, to a simple method of calculation. The comparison between measured normal stresses and those determined by experiments shows that the values calculated in accordance with the presented method agree well with the measured values, especially within the range of high shear rates. The parameters andK to be selected for this purpose are determined in dependence on the slope of the viscosity function ₁ at high shear rates for each polymer individually, using empirical relations so that the global selection of parameters, which is common practice with other methods, is obviated. In an appendix a method for deriving the relations between material functions on the basis of operator calculation is given.Extended version of a paper read at the 2^nd Symposium on Rheology of the GDR in Tabarz/Thuringia, December 7–11, 1987     

Concentration-dependent behaviour of the shear viscosity of coal-fuel oil suspensions

A function correlating the relative viscosity of a suspension of solid particles in liquids to their concentration is derived here theoretically using only general thermodynamic ideas, with out any consideration of microscopic hydrodynamic models. This function ( _r = exp (1/2B ^* C ²)) has a great advantage over the many different functions proposed in literature, for it depends on a single parameter,B ^*, and is therefore concise. To test the validity of this function, a least-squares regression analysis was undertaken of available data on the viscosity and concentration of suspensions of coal particles in fuel oil, which promise to be a useful alternative to fuel oil in the near future. The proposed function was found to accurately describe the concentration-dependent behaviour of the relative viscosity of these suspensions. Furthermore, an attempt was made to obtain information about the factors affecting the value ofB ^*, however the results were only qualitative because of, among other things, the inaccuracy of the viscosity measurements in such highly viscous fluids. shear viscosity of the suspension - ₀ shear viscosity of the Newtonian suspending medium - _r = /₀ relative viscosity - solid volume concentration - c solid weight concentration - _m maximum attainable volume concentration of solids - solid volume concentration at which the relative viscosity of the suspension becomes infinite - c _m maximum attainable solid weight concentration - _s density of the solid phase - _l density of the liquid phase - _m density of the suspension - k _n coefficients of theø-power series expansion of _r - { _j } sets of parameters specifying the thermodynamic state of the solid phase of a suspension - T absolute temperature (K) - f (c, T, _j) formal expression for the relative variation of the viscosity with concentration = [1 / (/c)] _T,j - d median size of the granulometric distribution - _B plastic or Bingham viscosity - K consistency factor - n flow index - g ([c _m –c],T, _j ) function including an asymptotic divergence asc tends toc _m , formally describing the concentration dependent behaviour of the shear viscosity of a suspension - A (T, _j) regression analysis parameters - B (T, _j) regression analysis parameters - B ^* (T, _j ) regression analysis parameters     

Rheology and birefringence of Fomblin YR at very high shear rates

The rheological and structural properties of perfluoropolyether (PFPE) lubricant films including viscosity, shear stress, and birefringence were measured at relatively low to extremely high shear rates using a rotational optical rheometer. The viscosity of various films with different thicknesses exhibit Newtonian behavior up to a shear rate 1 × 10⁴ s⁻¹, with a transition to shear-thinning behavior obvious at higher shear rates. Birefringence of these films was also measured for the first time, and these results indicate chain alignment with shear in the shear-thinning regime. The shear rate at which alignment occurs is similar to that of the onset of shear thinning. This correlation between chain alignment and shear thinning provides direct evidence that the ability of PFPEs to lubricate hard drives at high shear rates is a direct consequence of the ability of the applied shear field to align the molecules on a molecular level.     

Viscosity of some clay-based coating colors at high shear rates

The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s^–1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 10⁵ – 10⁶ s^–1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.     

A self-similar behavior for the relative viscosity of concentrated suspensions of rigid spheroids

A viscosity model for suspensions of rigid particles with predictive capability over a wide range of particle volume fraction and shear conditions is of interest to quantify the transport of suspensions in fluid flow models. We study the shear viscosity of suspensions and focus on the effect of particle aspect ratio and shear conditions on the rheological behavior of suspensions of rigid bi-axially symmetric ellipsoids (spheroids). We propose a framework that forms the basis to microscopically parameterize the evolution of the suspension microstructures and its effect on the shear viscosity of suspensions. We find that two state variables, the intrinsic viscosity in concentrated limit and the self-crowding factor, control the state of dispersion of the suspension. A combination of these two variables is shown to be invariant with the imposed shear stress (or shear rate) and depends only on the particle aspect ratio. This self-similar behavior, tested against available experimental and numerical data, allows us to derive a predictive model for the relative viscosity of concentrated suspensions of spheroids subjected to low (near zero) strain rates. At higher imposed strain rates, one needs to constrain one of the state variables independently to constrain the state of dispersion of the suspension and its shear dynamic viscosity. Alternatively, the obtained self-similar behavior provides the means to estimate the state variables from the viscosity measurements made in the laboratory, and to relate them to microstructure rearrangements and evolution occurring during deformation.     

Instability and localization of plastic flow in shear at high strain rates

Shear band formation in a thermal viscoplastic heat conducting material is described in a simple shear test at high strain rate with inertia effects. The classical perturbation method is discussed, and a new relative perturbation method accounting for non-steadiness of plastic flow is presented. They respectively provide instability and localization criteria which are compared. Furthermore both are compared to available nonlinear exact results and to experimental data. The influence of material parameters, initial imperfections, and boundary conditions is described.