Fragile networks and rheology of concentrated suspensions

Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic -Fe₂O₃ and non-magnetic -Fe₂O₃ particles in mineral oil are interpreted with the model proposed.Non-zero elastic modulus appeared at threshold particle concentrations of about 0.7 vol.% and 0.4 vol.% of the magnetic and non-magnetic suspensions, respectively. The difference is attributed to the denser flocs formed by magnetic suspensions. The volume fraction of particles in the flocs was estimated from the threshold particle concentration by transforming this concentration into a critical volume concentration of flocs, and identifying this critical concentration with the theoretical percolation threshold of three-dimensional networks of different coordination numbers. The results obtained indicate that the flocs are low-density structures, in agreement with cryo-scanning electron micrographs. Above the critical concentration the dynamic elastic modulus G was found to follow a scaling law of the type G ( _f - _f ^c ) ^f , where _f is the volume fraction of flocs in suspension, and _f ^c is its threshold value. For magnetic suspensions the exponent f was found to rise from a low value of about 1.0 to a value of 2.26 as particle concentration was increased. For the non-magnetic a similar change in f was observed; f changed from 0.95 to 3.6. Two other flocculated suspension systems taken from the literature showed a similar change in exponent. This suggests the possibility of a change in the mechanism of stress transport in the suspension as concentration increases, i.e., from a floc-floc bond-bending force mechanism to a rigidity percolation mechanism.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

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.     

Zum Einfluß von Füllstoffen auf das rheologische Verhalten von hochmolekularen Polyethylenschmelzen I. Das Fließverhalten in Scher- und Dehnströmungen

Zusammenfassung Das Fließverhalten von Polymersuspensionen in verschiedenen Strömungsformen wird anhand von mit isotropen und anisotropen Partikeln (Glaskugeln bzw. Glasfasern) gefüllten hochmolekularen Schmelzen untersucht. Zur Anwendung kommen dabei sowohl lineare als auch verzweigte Polymere, nämlich Polyethylene mit hoher Dichte (HDPE) und mit niedriger Dichte (LDPE).Alle untersuchten Systeme zeigen in der Scherströmung im Rotationsrheometer bei Zugabe von Füllstoff eine Verringerung der elastischen Eigenschaften. Solches Verhalten ist für Suspensionen isotroper Teilchen zu erwarten, bei Fasersuspensionen wird jedoch gewöhnlich ein verstärktes Anwachsen der ersten Normalspannungsdifferenz mit zunehmender Füllung gefunden. Bei höheren Schergeschwindigkeiten (Messungen im Kapillarviskosimeter) wird die durch die Füllstoffe bewirkte Viskositätserhöhung zunehmend geringer, die Suspensionen verhalten sich also mit zunehmendem Füllgrad stärker scherentzähend. Das Einsetzen der für das lineare HDPE typischen Instabilitäten (stick-slip, Wandgleiten) läßt sich durch den Ersatz von (elastischem) Polymer durch (starre) Kugeln nicht beeinflussen, diese Form des Schmelzenbruchs setzt bei gleichen Schubspannungen ein und ist so wegen der höheren Viskosität der Suspension sogar zu niedrigeren Durchsätzen hin verschoben.Um die Lücke zwischen den Messungen im Rotations- und im Kapillarviskosimeter (niedrige bzw. hohe Schergeschwindigkeiten) zu schließen, wurden Experimente bei oszillatorischer Scherbeanspruchung durchgeführt. Die bekannte Cox-Merz-Beziehung vermag das Verhalten der ungefüllten Schmelzen zwar recht gut zu beschreiben, versagt jedoch bei den Suspensionen gerade im Bereich niedriger Schergeschwindigkeiten, ebenso wie andere vorgeschlagene Korrelationen zwischen dynamischen und stationären Kenngrößen.Zur Bestimmung des Materialverhaltens bei uniaxialer Dehnbeanspruchung wurde ein Rotationsrheometer in geeigneter Weise modifiziert, so daß für die verwendeten sehr hochviskosen Stoffsysteme eine Messung möglich wurde. Die verschiedenen reinen Schmelzen zeigen ein wenig unterschiedliches Dehnverhalten mit ausgeprägten Verfestigungserscheinungen. Eine stationäre Dehnviskosität konnte in keinem Fall gemessen werden. Die Zugabe von Glaskugeln ändert die Dehnviskosität nicht wesentlich, der Zusatz von Glasfasern jedoch bewirkt eine merkliche Erhöhung der instationären Dehnviskosität im Anlaufbereich.

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The flow behaviour of suspensions is examined in different flow geometries using linear and branched high-molecular-weight polyethylene melts as suspension media containing isotropic (glass beads) and anisotropic (glass fibre) particles.In shear flow in a rotational rheometer, all suspensions show a decrease of the elastic properties with increasing filler content. While this behaviour has to be expected with suspensions of isotropic particles, fibre-filled polymer fluids usually show increasing normal stress differences with increasing fibre content. At higher shear rates (in a capillary viscometer) the particle-induced viscosity increase deminishes, hence the suspensions tend to be more shear thinning with increased filler content.The onset point of instabilities typically found with the linear HDPE is not shifted towards higher volumetric flow rates by replacement of elastic polymer by inelastic fillers as might be expected; on the contrary, the so-called stick-slip behaviour is initiated at constant values of shear stress and hence — because of the higher viscosity of the suspensions — at lower flow rates.Additionally, experiments were carried out with oscillating shear strain. Neither the well-known Cox-Merz relation nor similar relations, discussed in the literature, could properly correlate oscillatory and steady-state fluid behaviour of the suspensions, especially in the low shear rate range, whereas the former worked rather well for the unfilled melts.To allow for measurements of extensional properties, a rotational rheometer was slightly modified, thus being capable of determining the extensional viscosity of highly viscous polymeric materials. The pure melts showed only a slightly different behaviour with pronounced strain hardening. No stationary values of the Trouton viscosity could be obtained. While addition of glass beads was of little influence on material behaviour, addition of glass fibres showed remarkable increase of the extensional viscosity in the start-up region.

Erster Teil einer vom Fachbereich Chemietechnik der Universität Dortmund genehmigten Dissertation     

Flow mechanisms in dense silica-metal oxide-water suspensions

The rheological properties of dense silica in water suspensions (approx. 50% solids by volume) containing additions of metal oxides were examined. Metal oxides used were ferric, zinc and stannic. To prevent settling, testing was performed in a rheometer which was modified to provide for continual stirring of the materials. Relatively small oxide additions had the effect of thickening the mixtures and making them non-Newtonian. Different rate-limiting steps for flow were identified depending on the particular mixture, testing temperature and shear strain rate. Flow could be described using empirical equations which are identical to those often used to describe plastic flow in solid crystalline materials.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment

The rheological behavior of stable slurries is shown to be characterized by a bimodal model that represents a slurry as made up of a coarse fraction and a colloidal size fine fraction. According to the model, the two fractions behave independently of each other, and the non-Newtonian behavior of the viscosity is solely caused by the colloidal fraction, while the coarse fraction increases the viscosity level through hydrodynamic interactions. Data from experiments run with colloidal coal particles of about 2–3 µm average size dispersed in water show the viscosity of these colloidal suspensions to exhibit a highly shearrate-dependent behavior and, in the high shear limit, to match very closely the viscosity of suspensions of uniform size rigid spheres although the coal volume fraction must be determined semi-empirically. Different amounts of coarse coal particles are added to the colloidal suspension and the viscosity of the truly bimodal slurries measured as a function of shear rate. In agreement with the bimodal model, the measured shear viscosities show the coarse fraction to behave independently of the colloidal fraction and its contribution to the viscosity rise to be independent of the shear rate. It is shown that the shear rate exerted on the colloidal fraction is higher than that applied by the viscometer as a result of hydrodynamic interactions between the coarse particles, and that it is this effective higher shear rate which is necessary to apply in the correlations. For determining the coal volume fraction a relatively simple and quite accurate measurement technique is developed for determining the density and void fraction of coarse porous particles; the technique directly relates volume fraction to mass fraction.     

Rheological determination of peptizing agents in bentonite clays

This paper presents the results of an evaluation of the rheological properties of commercial bentonite suspensions made from peptized and unpeptized clay samples collected over a six year time span. The rheological properties of these suspensions were measured between shear rates of 5.11 to 1022 s^–1 at concentrations of 15, 30, 45, 64.2 and 70 kg/m³. Bingham, power-law and Casson models were then fitted to the shear stress and shear rate values. Parameters derived from these models were then subjected to further analyses. Four rheological methods (termed peptization index tests) were developed to differentiate between peptized and unpeptized bentonite samples.     

Investigation of influence of coal properties on dense-phase pneumatic conveying at high pressure

Experiments of dense-phase pneumatic conveying of pulverized coal using nitrogen were carried out in a test facility at pressures of up to 3.7 MPa to study the effects of coal type, particle size and moisture content on flow characteristics. The Jenike shear test and scanning electron microscopy (SEM) were employed to provide a better understanding of effects of the material properties on flow characteristics. Two kinds of pulverized coals, Yanzhou and Datong, with similar particle size, moisture content and density, were used in the test. Pressure drop increases with increasing the particle size at similar solid–gas ratio, superficial velocity and pressure in the receiving hopper, and pressure drops through different test sections decrease firstly and then rise with increasing the conveying velocity for the same particle size, mass flow rate and pressure in the receiving hopper. The flowability of pulverized coal decreases with increasing the moisture content in the range from 3.24% to 8.18%. Unconfined yield strength (UYS) increases and flow function (FF) decreases with increasing the moisture content. Results of the shearing tests are consistent with the results of the conveying study. Pressure drops through different test sections are discussed and analyzed.     

Characterization of yield stress fluids with concentric cylinder viscometers

The methods normally employed for shear rate calculations from concentric cylinder viscometer data generally are not applicable for fluids with a yield stress. In cylindrical systems with large radius ratios, as usually is the case with suspensions, the yield stress induces two possible flow regimes in the annulus. Unless the yield value is exceeded everywhere in the gap only part of the fluid can be sheared while the remaining region behaves like a solid plug. A correct calculation of the shear rate must take into account the presence of a variable effective gap width determined by the extent of the sheared layer. For time-independent yield stress fluids, a two-step procedure, which does not require any specific flow model, is proposed for analysing the experimental torque-speed data. Under the partially sheared condition, the shear rate can be computed exactly, whereas for the fully sheared flow the Krieger and Elrod approximation is satisfactory. The method is assessed by examining both semi-ideal data generated with a Casson fluid with known properties, and experimental data with an industrial suspension. A more complicated problem associated with characterization of time-dependent yield stress fluids is also identified and discussed. An approximate procedure is used to illustrate the dependence of the shear rate on time of shear in constant-speed experiments.     

Flow birefringence and rheological measurements on shear induced micellar structures

Aqueous solutions of cationic surfactant systems with strongly binding counterions show the striking phenomenon of shear induced phase transitions. At low shear rates or angular frequencies, the solutions exhibit Newtonian flow. At high rates of shear, however, the rheological properties change dramatically. Above a well defined threshold value of the velocity gradient, a supermolecular structure can be formed from micellar aggregates. This shear induced structure (SIS) behaves like a gel and exhibits strong flow birefringence. The formation of the shear induced structure is very complicated and depends on the specific conditions of the surfactant system. In this paper we discuss new results which have been obtained from rheological measurements and from flow birefringence data. We examine the stability of the shear induced state as a function of temperature, surfactant concentration and salt concentration and we analyse the effect of solubilisation of alcohols and hydrocarbons. The results are interpreted in terms of a kinetic model which accounts for the observed behavior.Dedicated to the 60. birthday of Prof. H. Harnisch, Hoechst AGPartly presented at the 2nd Conference of European Rheologists, Prague, June 17–20, 1986     

Transient rheology in a new type of couette apparatus. Application to blood

By using our new air-bearing viscometer different types of transient flow can be studied; in the present work this viscometer was specifically applied to non-Newtonian blood suspensions. To observe the influence of both the aggregation and the deformation of red blood cells (RBCs), different concentrations of fibrinogen and dextran were used: the suspended RBCs were simply washed or rigidified with diamide. From the data three rheological parameters were determined, two of which are relative to the behavior at low and at high shear gradients, respectively. Their values were related to the theory of Taylor, and the internal viscosity of RBCs was estimated to be around 3 cp.     

Dynamic-mechanical properties of interfacially modified glass sphere filled polyethylene

Model composites of spherical glass particles dispersed in a matrix of high density polyethylene were prepared both with and without interfacial modification by an azidofunctional trialkoxysilane. Dynamic mechanical measurements of the composites in the melt state were recorded. The unmodified composites behave as theoretically predicted and the effect of particle—particle interaction at high volume fractions can be measured. The composites with a modified interfacial region have greater shear moduli due to the effect of a region surrounding the particle modified by the silane. The material in this region is largely bound to the glass surface and was examined by Fourier transform infrared spectroscopy after extraction of the bulk matrix. Theoretical calculations are shown to be useful in calculating the mechanical properties and volume fraction of the interfacial region.     

Shear and extensional flow of polyacrylamide solutions

As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made.The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution.Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Finite difference solutions have been obtained by the perturbation method to investigate the influence of shear thinning and elasticity on the flow around an inclined circular cylinder of finite length in a uniform flow. In this numerical analysis a generalized upper-convected Maxwell model, in which the viscosity changes according to the Cross model, has been used.The local flow over the cylinder is only slightly deflected. However, in the wake flow behind the cylinder the particle path is remarkably influenced by the axial flow and rapidly flows up parallel to the cylinder's axis. Then it gradually rejoins direction of the incoming flow. It is found that viscoelastic fluids are prone to flow axially in the vicinity of the cylinder. The numerical predictions generally agree with the flow visualization results.The numerical solutions also demonstrate that elasticity has a strong effect on the velocity profile especially around both ends of the cylinder; elasticity increases the asymmetric profiles of both circumferential velocity and axial velocity with respect to equal to 90° and decreases a difference in the circumferential velocity between the windward end and the leeward end.For non-Newtonian fluids, the length of the wake flow is influenced by not only the Reynolds number but also the cylinder diameter and it is larger for the cylinder with the smaller diameter at the same Reynolds number.Partly presented at the 9th Australasian Fluid Mechanics Conference, University of Auckland, New Zealand, 8–12 December, 1986     

Hydrodynamisch induzierte Eigenbewegung von idealisierten Teilchen in newtonschen Suspensionsmedien unter Berücksichtigung begrenzender Wände.

Zusammenfassung Die hydrodynamisch induzierte Bewegung starrer und elastischer Teilchen, die in einem newtonschen Medium suspendiert sind, wird unter Berücksichtigung gekrümmter Begrenzungen untersucht. Die Geometrie eines hyperbolischen Zylinders erlaubt die Simulation einer Strömung durch poröse Medien und in den Grenzfällen durch ein Rohr und ein kreisförmiges Loch. Der Einfluß des inhomogenen Strömungsfeldes verursacht eine Migrationsbewegung der suspendierten Teilchen quer zu den Stromlinien. Es wird gezeigt, daß eine inhomogene Suspension elastischer Teilchen nach Durchlauf eines konvergenten und eines divergenten Bereiches eine Entmischung erfährt. Die Konzentration der Teilchen nimmt sowohl im Kernbereich der Strömung als auch aufgrund des abstoßenden Wandeffektes in unmittelbarer Wandnähe ab.

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The flow-induced migration of rigid and elastic particles suspended in a Newtonian medium is studied. The flow situation investigated consists of pressuredriven flow through a hyperbolic cylinder. This permits the simulation of flow through a porous medium and in the limiting cases through a tube and through a circular hole. The influence of the nonhomogeneous flow field effects a migration of the suspended particles across the streamlines. It is deduced that nonhomogeneous suspensions of elastic particles receive a separation according to size after passing a converging and diverging section. The results imply that the particle concentration decreases in the centre of the flow as well as in the immediate neighbourhood of the walls.

Zweiter Teil einer vom Fachbereich Chemietechnik der Universität Dortmund genehmigten Dissertation     

The behaviour of polymer solutions in extension-dominated flows,with applications to Enhanced Oil Recovery

The rheometry and flow behaviour of aqueous solutions of polyacrylamide and xanthan gum are discussed, with the expectation that the results will be of use in Enhanced Oil Recovery (EOR). The rheometrical study gives particular prominence to the dramatically high values of extensional viscosity which are possible in aqueous solutions of flexible polymers such as polyacrylamide. The effect of such factors as polymer concentration, salt concentration and mechanical degradation on rheometrical properties is outlined. Reference is also made to the qualitatively-different rheometrical behaviour experienced by comparable solutions of xanthan gum.Further evidence is advanced that some dilute polymer solutions of potential use in EOR experience abnormally high resistance in flows which are dominated by extension. Since flow through a porous medium involves a substantial extensional component, it is argued that there is justification for studying the effect of this high extensional-viscosity behaviour in a number of idealized geometries of relevance to EOR conditions. The resulting experiments indicate that, at low flow rates,shear viscosity is the dominant influence, but that, after a critical set of conditions,extensional-viscosity considerations can become all important and the observed pressure losses are against any expectation based on conventional fluid mechanics.Flow visualization studies support the pressure-drop measurements in emphasising the strong influence of high extensional viscosities in flows through tortuous geometries.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

The motion of rodlike particles in the pressure-driven flow between two flat plates

The motion of freely suspended rodlike particles has been observed in the pressure-driven flow between the two flat plates of a Hele Shaw flow cell at low Reynolds numbers. Data are reported for rodlike particles with aspect ratios of 12.0 suspended in a Newtonian fluid for gap thickness to particle length ratios of 3, 6, and 20; and for rodlike particles with aspect ratios between 5 and 8 in a non-Newtonian fluid (79.25 wt.% water, 20.2 wt.% glycerine, and 0.55 wt.% polyacrylamide). For the Newtonian fluid, the time-dependent orientation of the particles near and far from walls was shown to be in quantitative agreement with Jeffery's theory for ellipsoids suspended in a simple shear flow if an effective aspect ratio is calculated from the experimental period of rotation. Particles aligned with the flow direction and less than a particle half-length from a wall interacted irreversibly with the wall. For the non-Newtonian fluid, the timedependent orientation far from a wall was shown to be in qualitative agreement with Leal's theory for a second-order fluid; however, particles that were aligned with the flow direction and were near walls did not rotate.     

Orientation and rheology of rodlike particles with weak Brownian diffusion in a second-order fluid under simple shear flow

An analysis of particle orientation in a dilute suspension of rodlike particles in a second-order fluid was performed to examine the effects of the elasticity of the fluid and of weak Brownian diffusion of the particle on its orientation. Distributions of particle orientation under a simple shear flow with rate of shearg have been obtained as a function of a single nondimensional parameter, ^* =/r _e ² (D/g), which combines the effects of the particle aspect ratior _e , the weak fluid elasticity, and the weak Brownian rotation diffusion coefficientD of the particle. In the limit of larger _e , when the fluid elasticity is strong enough to overcome the rotational diffusion effect on the particle motion, most of the particles will orient close to the vorticity axis. A new shear-thinning mechanism of the shear viscosity of such systems is predicted by the theory.