Rheology concentrated suspensions

The rheological characterisation of non-Newtonian fluids is widely acknowledged to be far from straightforward. In some non-Newtonian systems, such as concentrated suspensions, rheological measurements may be complicated by non-linear, dispersive, dissipative and thixotropic mechanical properties and the rheometrical challenges posed by these features may be compoimded by an apparent yield stress. 

Detailed treatments of the rheology of various dispersed systems are available (71—73), as are reviews of the viscous and elastic behavior of dispersions (74,75), of the flow properties of concentrated suspensions (75—82), and of viscoelastic properties (83—85). References are also available that deal with blood red ceU suspensions (69,70,86). 

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

It is convenient to distinguish between particle or fluid rotation about axes normal and parallel to the direction of relative motion. These two types of motion may be termed respectively top spin and screw motion (Til). Top spin is of more general importance since this corresponds to particle rotation caused by fluid shear or by collision with rigid surfaces. Workers concerned with suspension rheology and allied topics have concentrated on motion at low Re, while very high Reynolds numbers have concerned aerodynamicists. The gap between these two ranges is wide and uncharted, and we make no attempt to close it here. 

Now the technique provides the basis for simulating concentrated suspensions at conditions extending from the diffusion-dominated equilibrium state to highly nonequilibrium states produced by shear or external forces. The results to date, e.g., for structure and viscosity, are promising but limited to a relatively small number of particles in two dimensions by the demands of the hydrodynamic calculation. Nonetheless, at least one simplified analytical approximation has emerged [44], As supercomputers increase in power and availability, many important problems—addressing non-Newtonian rheology, consolidation via sedimentation and filtration, phase transitions, and flocculation—should yield to the approach. 

This chapter will focus on infinitely-extended suspensions in which potential complications introduced by the presence of walls are avoided. The only wall-effect case that can be treated with relative ease is the interaction of a sphere with a plane wall (Goldman et ai, 1967a,b). The presence of walls can lead to relevant suspension rheological effects (Tozeren and Skalak, 1977 Brunn, 1981), which result from the existence of particle depeletion boundary layers (Cox and Brenner, 1971) in the proximity of the walls arising from the finite size of the suspended spheres. Going beyond the dilute and semidilute regions considered by the authors just mentioned is the ad hoc percolation approach, in which an infinite cluster—assumed to occur above some threshold particle concentration—necessarily interacts with the walls (cf. Section VI). 

Tg and . This is shown in Fig. 7 both for the extrapolated (Bingham) and Casson s yield value. In both cases the linear relationship is maintained indicating that such crude models may be applied to the rheology of the complex system of bentonite clay plus pesticide suspension. It should be mentioned, however, that the elastic floe model is a more realistic description of the system, since the assumption of a maximum of doublets in the floe rupture model is not justified with a concentrated suspension with many body interactions. 

This section on concentrated suspensions discusses the rheological behavior of sj tems which are colloidally stable and colloidally unstable suspensions. For stable sj tems, the rheology of sterically stabilized and electrostatically stabilized systems wiU be considered. For sterically stabilized suspensions, a hard sphere (or hard particle) model has been successfid. Concentrated suspensions in some cases behave rheologically like concentrated polymer solutions. For this reason, a discussion of the viscosity of concentrated polymer solutions is discussed next before a discussion of concentrated ceramic suspensions. 

This section draws heavily from two good books Colloidal Dispersions by Russel, Seville, and Schowalter [31] and Colloidal Hydrodynamics by Van de Ven [32] and a review paper by Jeffiey and Acrivos [33]. Concentrated suspensions exhibit rheological behavior which are time dependent. Time dependent rheological behavior is called thixotropy. This is because a particular shear rate creates a dynamic structure that is different than the structure of a suspension at rest. If a particular shear rate is imposed for a long period of time, a steady state stress can be measured, as shown in Figure 12.10 [34]. The time constant for structure reorganization is several times the shear rate, y, in flow reversal experiments [34] and depends on the volume fraction of solids. The viscosities discussed in Sections 12.42.2 to 12.42.9 are always the steady shear viscosity and not the transient ones. 

Monodiefperse Spheres The rheology of concentrated ceramic suspensions is very important for good mold filling. For concentrated suspensions that are colloidally stable (by steric means, giving a hard sphere model), there is a particle volume fraction (i.e., = 0.63 for... 

At this voliime fraction, the viscosity diverges because the shear stress is now given by the particle-particle contact in the tightly packed structure. As a result, we obtain a fluid with visco-elastic properties similar to polymeric solids. In ceramic processing, we extrude and press these pastes into green shapes. As a result, the rheology of ceramic pastes is of importance. The rheology of very concentrated suspensions is not particularly well developed, with the exception of model systems of monodisperse spheres. This section first discusses visco-elastic fluids and second the visco-elastic properties of ceramic pastes of monodisperse spheres. The material on visco-elastic fluids draws heavily from the book Colloidal Dispersions by Russel, Saville, and Schowalter [31]. 

Tsai, S. C. and Zammouri, K. 1988. Role of interparticular van der Waals force in rheology of concentrated suspensions. J. Rheol. 32 737-750. 

Maschmeyer, R. 0. and Hill, C. T. 1977. Rheology of concentrated suspensions of fibers in tube flow. Trans. Soc. Rheol. 21 183-194. 

Bergstrom, L., Rheology of concentrated suspension, in Surface and Colloidal Chemistry in Advanced Ceramic Processing, R.J. Pugh and L. Berstrom, Eds., Marcel Dekker, New York, 1994. 

Bergstrom, L., and Sjostroum, E., Temperature-induced flocculation of concentrated ceramic suspensions rheological properties, J. Eur. Ceram. Soc., 19, 2117, 1999. 

The rheology of pastes, which are highly concentrated suspensions, is very important for the process of extrusion and spheronization to produce pellets. 

In many cases, where precision is more important than accuracy, CLD measurements are adequate to monitor dynamic changes in process parameters related to the particle size and shape, concentration, and rheology of fluid suspensions. 

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