Concentrated suspensions forces

In a concentrated suspension, the drag force on a particle will be a function of its velocity up relative to the liquid and will be influenced by the concentration of particles that is, it will be a function of the voidage e of the suspension. 

The colloidal chemistry of very diluted clay suspensions is usually described by the double layer theory (3). In more concentrated suspensions or thick pastes, where the average distance between sheets is shorter, the Van der Waals forces have to be considered. The combination of all these effects influences the distribution of the individual sheets and, thus, the viscosity of the slurry. From the viewpoint of this review, these spatial distributions of the individual sheets affect the availability of the surface area with the important consequence that the surface area is no longer an extensive property of the material. Disordered... 

For concentrated suspensions ( 9 >0.25), on the other hand, there is no free-fall sedimentation because the intra-aggregate water is forced out slowly as the settled floes merge. 

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. 

In this chapter, we described the fundamentals of suspension iheol-ogy from dilute suspensions to concentrated suspensions. Attention has been paid to interparticle forces and the structure of the suspension because these things drastically influence suspension iheology. In addition, visco-elastic properties of concentrated suspensions including ceramic pastes have been discussed. Finally, the mechanical properties of dry ceramic powders have been discussed in terms of the dJoulomb yield criterion, which gives the stress necessary for flow (or deformation) of the powder. These mechanical prc rties will be used in the next chapter to predict the ease with vdiich dry powders, pastes, and suspensions can be made into green bodies by various techniques. 

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

Lionberger and Russel (1994) suggested that the stabilizing layers on the spheres of van der Werff et al. produce different lubrication forces than those between bare particles, such as those of Shikata and Pearson, and that this accounts for the differences between the high-frequency moduli of these two systems. Thus, it would appear, perhaps not surprisingly, that the high-frequency behavior of concentrated suspensions is sensitive to the details of interactions between spheres in near contact. 

Shear thinning of concentrated suspensions is typical for submicron particles dispersed in a low viscosity Newtonian fluid.At low shear strain rates. Brownian motion leads to a random distribution of the particles in the suspension, and particle collision will result in viscous behavior. At high shear strain rates, however, particles will arrange in layers, which can slide over each other in the direction of flow. This results in a reduced viscosity of the system in agreement with the principles of shear thinning. A pro-noimced apparent yield stress can be found for shear thinning suspensions, if the Brownian motion is suppressed by electrostatic repulsion forces, which result in three-dimensional crystal-like structures of the particles with low mobility. 

The gel-sol method involves aging a concentrated gel or iron polynuelear species at 100 °C for some days (Sugimoto and Sakata, 1992). The yield from this technique (in contrast to the forced hydrolysis method) is elose on 100% and because a concentrated suspension is used, the yield can be considerable. This method has been applied mainly to haematite. It can also be used to produce small, uniform rods of akaganeite (Paterson and Tait, 1978 and Fig. 9.1b). 

We have seen that it can be difficult to reach the critical concentration required to observe an isotropic-anisotropic transition because concentrated suspensions of colloids are not always stable. However, orientation of flexible polymers as well as of anisotropic particles in suspension can be induced by flow, a phenomenon that has long been observed, reported, and studied. This phenomenon is especially strong when a pretransitional effect exists, which can be easily observed by the naked eye on a sample that is shaken between crossed polarizers (see for example the section on clays). In these systems, birefringence is induced via mechanical forces, like the shear stresses in a laminar flow ( Maxwell-dy-namo-optic effect ). 

Some examples of suspension structures are illustrated in Figure 5. Figure 5a depicts a stable suspension with only short-range repulsive forces between the suspended fine particles. Hence, this system may settle as the particles move around each other into positions of lowest free energy, a consequence of the fact that the repulsive forces act between them. Figure 5b is a stable system for a more concentrated suspension. The... 

Following the descriptions of Probstein and Sengun (1987) and Sengun and Probstein (1989b), we shall examine the forces in concentrated suspensions. We reserve our discussion of the effect of volume fraction for the sections that follow. 

From the above observations and from the discussion of the forces governing suspension rheology, Probstein Sengun (1987) (see also Sengun Probstein 1989b) introduced a model to characterize the viscous behavior of concentrated suspensions. In their model the suspension is bimodal, wherein it is made up of a colloidal fine fraction and a coarse fraction of noncolloidal particles. 

Unlike the cooked corn flour in the first part of this experiment, the starch polymer remains trapped in the starch granules and the fluid is a concentrated suspension rather than a polymer solution. When the suspension is sheared gently a layer of water between the starch granules lubricates their flow past each other. However, fast deformation forces the water out from between the granules so there is much greater friction between them and they cannot flow. Quicksand behaves in a similar manner. Ice cream mixes, the matrix and ice cream itself are all shear-thinning if these were shear-thickening like the concentrated custard powder suspension, ice cream would be impossible to process, and would become solid every time you tried to chew it ... 

Up to now we were limited to considering the behavior of isolated particles or hydrodynamic interactions of two particles (pair interactions). However, in concentrated suspensions multi-particle interactions are possible, and one cannot neglect them. The problem of determining force and torque acting on a particle in suspension in the presence of other particles is very difficult and so far has not been completely solved. However, in the last years, a significant progress [13] in... 

Of the particular value is the case of concentrated suspensions for which the volume concentration of disperse phase is not small. The microstmcture of such suspensions depends on relations between hydrodynamic forces of particle interactions and thermodynamic forces causing Brownian motion. In the last years the research of dynamics of concentrated suspensions (Stokes s dynamics [30]) was based on use of the Langevin equation for ensemble of N particles... 

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