Rheological peculiarities of concentrated suspensions

The rheological properties of concentrated suspensions of metal oxides dispersed in transformer oil, which are used as electrorheological fluids, are systematically studied. Colloidal particles have intermediate sizes between nano- and microsized scales. Low-amplitude dynamic measurements show that the storage moduli of the examined suspensions are independent of frequency and these materials should be considered as solidlike elastic media. The storage modulus is proportional to the five-powdered particle volume concentration. At the same time, a transition through an apparent yield stress with a reduction in the viscosity by approximately six orders of magnitude is distinctly seen upon shear deformation. The character of the rheological behavior depends on the regime of suspension deformation. At very low shear rates, a steady flow is possible; however, upon an increase in the rate, an unsteady regime is realized with development of self-oscillations. When constant shear stresses are preset, in some range of stresses, thickening of the medium takes place, which can also be accompanied by self-oscillations. In order to gain insight into the nature of this effect, measurements are performed for samples with different volume/surface ratios, which show that, in some deformation regimes, suspension is separated into layers and slipping occurs along a low-viscosity layer with a thickness of several dozen microns. Direct observations show a distinct structural inhomogeneity of the flow. The separation and motion of layers with different compositions explain the transition to the flow with the lowest apparent Newtonian viscosity. Thus, the deformation of concentrated suspensions is associated with self-oscillations of stresses and slipping along a low-viscosity interlayer.     

Electrokinetic study on concentrated suspensions using colloid vibration potential measurements

-potentials of a silica suspension and three types of polystyrene latex suspensions with different surface charge groups were measured, as a function of the particle concentration () in the suspension over a wide range, using the colloid vibration potential (CVP) technique. The concentration dependence of the-potential in silica suspension is explained well by Levine et al.s [1] cell model theory, verifying the applicability of the cell model to the CVP in silica suspension. However, the-potential of latex suspensions ordinarily decreases as the particle concentration increases, even after being corrected by the term of (1-). This tendency is especially noticeable in the systems that have particles with high surface charge densities. Furthermore, the conductivity measurements of these suspensions reveal that the conductivity of these systems, especially in their highly charged state, increases as the particle concentration is increased; opposite in tendency to silica suspensions. These new findings can be explained as follows: on the highly charged surface of a latex particle, a polyelectrolyte-like (hairy) layer is present, which overlaps at some point. This permits interparticle surface conduction and results in the abnormal behavior of CVP in these systems.     

Colloidal stabilization of nanoparticles in concentrated suspensions

The stabilization of nanoparticles in concentrated aqueous suspensions is required in many manufacturing technologies and industrial products. Nanoparticles are commonly stabilized through the adsorption of a dispersant layer around the particle surface. The formation of a dispersant layer (adlayer) of appropriate thickness is crucial for the stabilization of suspensions containing high nanoparticle concentrations. Thick adlayers result in an excessive excluded volume around the particles, whereas thin adlayers lead to particle agglomeration. Both effects reduce the maximum concentration of nanoparticles in the suspension. However, conventional dispersants do not allow for a systematic control of the adlayer thickness on the particle surface. In this study, we synthesized dispersants with a molecular architecture that enables better control over the particle adlayer thickness. By tailoring the chemistry and length of these novel dispersants, we were able to prepare fluid suspensions (viscosity < 1 Pa.s at 100 s-1) with more than 40 vol % of 65-nm alumina particles in water, as opposed to the 30 vol % achieved with a state-of-the-art dispersing agent. This remarkably high concentration facilitates the fabrication of a wide range of products and intermediates in materials technology, cosmetics, pharmacy, and in all other areas where concentrated nanoparticle suspensions are required. On the basis of the proposed molecular architecture, one can also envisage other similar molecules that could be successfully applied for the functionalization of surfaces for biosensing, chromatography, medical imaging, drug delivery, and aqueous lubrication, among others.     

The viscoelastic properties of concentrated suspensions

The viscoelastic properties of concentrated, well dispersed, sterically stabilised polymethyl methacrylate particles were studied using a specially developed low frequency, controlled shear stress rheometer. The experimental results show a well defined viscoelastic transition over a narrow frequency range. Evidence is produced to show that the particles act as hard, non-interacting spheres. It is argued that the transition represents a change from a randomly packed assemblage with particle motion dominated by Browniandiffusion processes to a lower packing density shear flow regime.     

A simple model of the high-frequency dynamic mobility in concentrated suspensions

Because electroacoustic techniques are gaining interest in many fields of colloid science, a number of theories dealing with the phenomenon of electrophoresis in high-frequency (on the order of the MHz) electric fields have been developed. In the present work we propose a straightforward derivation of a simple formula for the dynamic mobility of colloidal particles in mildly concentrated systems. Starting with a simple expression for the electrophoretic mobility in dilute suspensions, given as a function of the zeta potential and of the dipole coefficient, we introduce successive corrections related to: (i) the back flow of fluid induced by the electrophoretic motion of the particles; (ii) the electrostatic interactions among particles; (iii) the difference between the macroscopic and the external electric fields; (iv) the difference between the zero-momentum and the laboratory reference frames. Considering furthermore that the frequency dependence of the dipole coefficient is due to the Maxwell-Wagner-O'Konski double-layer relaxation, we obtain a mobility expression that compares well with other (semi)analytical models and (in proper conditions) with numerical cell-model calculations. However, its main merit is that it allows to understand, to a large extent, the physical origin of the frequency and volume fraction dependences of the dynamic mobility.     

Rheology of concentrated carbon nanotube suspensions

The rheological properties of non-Brownian carbon nanotube suspensions are measured over a range of nanotube volume fractions spanning the transition from semidilute to concentrated. The polymer-stabilized nanotubes are "sticky" and form a quiescent elastic network with a well-defined shear modulus and yield stress that both depend strongly on nanotube volume fraction with different but related critical exponents. We compare controlled-strain-rate and controlled-stress measurements of yielding in shear flow, and we study the effect of slow periodic stress reversal on yielding and the arrest of flow. Our measurements support a universal scaling of both the linear viscoelastic and steady-shear viscometric response. The former allows us to extract the elastic shear modulus of semidilute nanotube networks for values that are near or below the resolution limit of the rheometers used, while the latter provides a similar extrapolation of the yield stress. A simple scaling argument is used to model the dependence of yield stress and elastic modulus on concentration.     

A theory for concentrated fiber suspensions with strong fiber-fiber interactions

A theory is presented for the flow-induced fiber orientation and stress in fiber-reinforced polymer composites with planar fiber orientation. The rate of change of fiber orientation is given as a function of the strain rate in the continuum and the probabilistic effects of physical inter-fiber contacts. The continuum stress is calculated from the stress in the fluid and fibers, where fiber stress is a result of the local disturbance in the fluid velocity field and of the inter-fiber contact forces. Fiber orientation is described via a probability density function whose transport equation has the form of a standard advection-diffusion equation with an orientation-dependent rotary diffusion. This equation is solved using a finite difference scheme and the results are presented.     

Time dependent viscosity of concentrated alumina suspensions

Viscometric investigations of concentrated aqueous alumina suspensions with particles smaller than 5 μm have been performed. Experimental flow curves indicate thixotropy in the shear rate interval between =20 and 640 s⁻¹. In the range smaller than =200 s⁻¹ we found pseudoplastic flow behavior, in the higher range the material shows dilatancy. The non-Newtonian behavior results from a small content of sodium aluminum oxide in the alumina suspension. This gives rise to interparticle forces that can drive the suspension into a gel-like state. The time scale of this process is some days. On the short-time scale of some hours the material ages slowly increasing moderately the apparent viscosity. Studying the relaxation process after a shear rate jump, the shear stress time dependency at constant shear rate follows an exponential law. There is a single particular relaxation time for each shear rate. The relaxation towards a steady state occurs asymptotically over some 10³ s. Flow curves calculated from steady state data after relaxation processes are below the experimental flow curves which were measured during some 100 s. The flow curves follow the Herschel–Bulkley formula. The shape of the viscosity curves indicates changes of suspension structure at ca. =200 and 400 s⁻¹. At constant shear rates in the interval between =400 and 450 s⁻¹ the apparent viscosity of the alumina suspension fluctuates periodically in time in the same manner found for other suspensions. This effect is interpreted as periodic organization of agglomeration and deglomeration processes. Supposing, that the stabilisation energy of agglomerates is of the order of the energy introduced by the mechanical shear field, the observation of oscillations at =400 s⁻¹ is in agreement with the drastic slope change in the viscosity curves.     

Shear response of concentrated calcium carbonate suspensions

The rheology of concentrated calcium carbonate suspensions is investigated with respect to addition of solution and dispersion polymers. System materials and composition are chosen to be similar, generically, to those in use in the coating of paper. Specifically, we investigate the particle volume fraction dependence of the relative viscosity, using both capillary and steady-shear concentric cylinder measurement methods to cover a broad range of concentrations. The results are interpreted in terms of semi-empirical models, such as the Krieger-Dougherty model. Oscillatory shear measurements are also employed to investigate the viscoelastic behavior of the concentrated suspensions. The measurements indicate that a common solution polymer thickener, carboxymethyl cellulose (CMC), causes depletion flocculation of calcium carbonate suspensions.     

Temperature-induced gelation of concentrated silicon carbide suspensions

Due to the steric barrier provided by the adsorption of the dispersant hypermer KD1 (a polyester/polyamine condensation polymer), stable and low-viscosity suspensions of SiC, Y(2)O(3), and Al(2)O(3) powder mixtures could be prepared in methyl ethyl ketone (MEK)/ethanol (E) solvent with solids loading as high as 60 vol%. The solvency of the dispersant in MEK/E decreased dramatically on cooling. Steady shear viscosity and oscillatory measurements were performed as a function of temperature for suspensions with different solids loading. The viscosity and elastic modulus of suspension increased with decreasing temperature and became more sensitive with the increase of solids loading. The suspensions with solids loading higher than 40 vol% could be solidified with decreasing temperature, but gelation temperature and gelation stiffness decreased with decreasing solids loading. The 60 vol% solid-loaded suspension was a stable and free-flowing fluid at 20 degrees C and gradually transformed to a very highly viscous and elastic system upon cooling to about 13 degrees C. Complete solidification occurred when the temperature was decreased to 5 degrees C. The gelation mechanism was mainly based on the collapse of the adsorbed layer as the temperature decreases, which induced incipient flocculation and formed a stiff network. The gelled body was further strengthened by separation of the dispersant from the suspension.     

Temperature-induced crystallization in concentrated suspensions of multiarm star polymers: a molecular dynamics study

In this work, we study temperature-induced crystallization in dense suspensions of multiarm star polymers. This is a continuation of a previous study, which identified and studied the emergence of "glassy" amorphous states, in accordance with experimental observations. We performed molecular dynamics simulations on two types of star polymers: 128-arm stars and 64-arm stars dissolved in n-decane in the temperature range of 20-60 degrees C. These supramolecules are modeled as "soft spheres" interacting via a theoretically developed potential of mean field. Both systems attain a crystalline structure with the characteristics of a face-centered-cubic (fcc) crystal beyond a certain temperature. Kinetics is sensitive on initial configuration. Interestingly, kinetic trapping in "temporary" energy wells leads to highly crystalline structures, yet less ordered than their genuine equilibrium fcc structure. This complication illustrates the difficulty in reaching the equilibrium state, which is crystalline at high temperatures. A structural analysis of the final conformations is presented. The effect of size dispersity and star functionality of soft spheres on microstructure is also examined. Both factors influence crystallization and their effect is quantified by our study.     

The rheology of concentrated suspensions of deformable particles

The rheology of slightly deformable particles, in particular their dilatant behaviour, has been investigated using waxy maize starch as a ‘model’ suspension. Suspensions of such large particles present considerable experimental problems in rheological terms in that they exhibit phenomena such as wall slip and sedimentation. These are discussed in some detail, along with the methodologies developed to overcome them. Comparisons of the results with hard sphere data in the literature indicate that whilst the deformability of the starch granules does not play a significant role in the high shear limiting viscosity, the dilatant transition does appear to be strongly affected.     

Rotational and translational self-diffusion in concentrated suspensions of permeable particles

In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.     

Measuring the electrophoretic mobility of concentrated suspensions in nonaqueous media

We present a new method of measuring the electrophoretic mobility of a particle in a concentrated suspension. The method is used to measure the electrophoretic mobility of PMMA particles (diameter 10 microm) suspended in a mixture of liquid hydrocarbons. The particle volume fraction of the suspension is varied from 0 up to 0.30 and the resulting variation of the electrophoretic mobility is discussed. The suspending liquid is such that its refractive index is very close to that of the particles. Thus the suspension is almost transparent and it is possible to follow through a microscope the motion of one particle. The suspension is subjected to a low-frequency electric field (0.5 Hz). The cell containing the suspension is mounted on a piezoelectric crystal. The displacement that compensates for the particle motion (when the particle image is steady) is determined.     

Viscosity of concentrated suspensions: influence of cluster formation

Dispersed particles can form clusters even at low concentrations. Colloidal and hydrodynamic forces are responsible for this phenomenon and these forces determine both structure and size of clusters. We assume that the viscosity of a concentrated suspension is completely determined by cluster size distribution, regardless if clusters form under the action of colloidal, hydrodynamic interactions or applied shear rates. Based on this assumption an equation, which describes dependency of viscosity on a concentration of dispersed particles taking into account cluster formation, is deduced. Under special restrictions the deduced dependency coincides with the well-known Dougherty-Krieger's equation except for a clear physical meaning of parameters entered. Our consideration shows that Dougherty-Krieger's equation has deeper physical background than it has been supposed earlier. Experimental verification of the suggested model shows a good agreement with the theory predictions and proves a presence of clusters even at low concentrations of dispersed particles.     

Studies in thixotropy

Summary The author adopts the original Freundlich-Peterfi definition of thixotropy, that is the reversible isothermal gel/sol/gel/transformation induced by shear and subsequent rest. The criterion of a gel is the presence of a “Yield Value”, and that of a sol the absence of a “Yield Value”. It is recognised, that most of Freundlich's “thixotropic” systems did not conform to this definition; rather they were gels which became less viscous on shearing but never became true sols: such systems the author describes as “false-body” systems. The author briefly describes his electromagnetic thixotrometer, the “constant reading viscometer”, and the “twin-Couette” viscometer, and illustrates their application to the study of the influence of the rate of shear, the measurement of “Yield Value”, the influence of the concentration of solid and the effects of the “dispersion power” of the liquid. Figures are shown of curves of “elastic recoil” in such systems as heather honey, mayonnaise, cream, paints and bentonite suspensions; and the applications of “elastic recoil” to the study of structural viscosity. Illustrations are given of the different Theological states obtained by dispersing fine particles in Newtonian liquids and in non-Newtonian fluids. A range of curves illustrates the variations in the effects of time on different types of colloidal systems; and it is shown how these curves can be applied to predict the behaviour of such systems over long periods of time. Finally a generalised diagram is used to show how the degree of dispersion can be determined from the rheological state of a colloidal system; and it is shown that dispersion increases as we pass along the rheological states: Structural viscosity — false-body — thixotropy —dilatancy — Newtonian flow.

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Zusammenfassung Der Verfasser übernimmt die Originaldefinition der Thixotropie von Freundlich-Peterfi, das hei\t die reversible, isotherme Gel/Sol/Gel-Umwandlung, verursacht durch Scherung und darauf folgende Ruhe. Das Kriterium für ein Gel ist das Vorhandensein einer ‘Flie\-festigkeit‘. Es ist bemerkenswert, da\ die meisten der Freundlichschen thixotropen Systeme nicht dieser Definition entsprechen, vielmehr werden sie nur weniger viskos beim Scheren, werden aber nicht wahre Sole; solche Systeme werden vom Verfasser als ‘false-body’-(= Schleimk?rper) bezeichnet. Verf. beschreibt kurz das elektromagnetische Thixotrometer, das ‚konstant anzeigende Viskosimeter‘ und das ‚Zwillings-Couette-Viskosimeter‘, und stellt ihre Anwendung zum Studium des Einflusses der Schergeschwindigkeit, zur Messung der Flie\festigkeit, des Einflusses der Konzentration und der Effekte des Dispersionsverm?gens einer Flüssigkeit dar. Kurven der elastischen Nachwirkung in Systemen wie Heidehonig, Mayonnaisen, Creme, Farbpigmenten und Bentonit-Suspensionen werden gezeigt, ebenso die Anwendung der elastischen Nachwirkung zum Studium der Strukturviskosit?t. Es werden Beispiele für die verschiedenen Theologischen Zust?nde gegeben, die durch Dispersion feiner Teilchen in Newtonschen Flüssigkeiten und nicht-Newtonschen Flüssigkeiten erzielt werden. Eine Reihe von Kurven erl?utert die Unterschiede der Zeiteffekte bei den verschiedenen Typen kolloider Systeme und es wird gezeigt, wie solche Kurven zur Voraussage des Verhaltens derartiger Systeme für lange Zeiten verwendet werden k?nnen. Schlie\lich wird in einem verallgemeinerten Diagramm skizziert, wie der Dispersionsgrad aus dem Theologischen Zustand eines kolloidalen Systems bestimmt werden kann; es wird gezeigt, da\ die Dispersion in dem Ma\e steigt, in dem folgende Theologische Zust?nde durchlaufen werden: Strukturviskosit?t — Schleimk?rper — Thixotropie Dilatanz — Newtonsches Flie\en.

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Vorgetragen auf der Rheologie-Tagung Berlin, September 1952.     

Electrical conductivity and stability of concentrated aqueous alumina suspensions

This work describes the effect of solids load and ionic strength on the electrical conductivity (K(S)) of concentrated aqueous suspensions of commercial alpha-alumina (1-35 vol% solids). The results obtained show that the dependency of the electrical conductivity of the suspending liquid (K(L)) on the volume fraction of solids is well described by Maxwell's model. The change in the conductivity of the suspensions relative to that of the suspending liquid (K(S)/K(L)) was found to be inversely proportional to the solids content, as predicted by Maxwell's model. The relative conductivity rate, DeltaK, could be interpreted in terms of the DLVO theory and the particles double layer parameter, kappaa, and used as a stability criterion. As kappaa changes, in response to the changes in ionic strength, so does the conducting to insulating character of the particles and, as such, their contribution to the overall suspension conductivity (expressed by DeltaK). When the particles become insulating, the suspension conductivity decreases when the solids load increases. The turning point in this particle behaviour corresponds to a critical concentration of ions in the solution that destabilises the suspension and is associated with the critical coagulation concentration (ccc). It is the electrical double layer that ultimately determines the conducting or insulating character of the particles, and that character can be made to change, as required for suspension stability, and accessed by the relative conductivity rate.