Properties of Concentrated Suspensions

One of the main features of concentrated suspensions is the formation of three-dimensional structure units, which determine their properties and, in particular, their rheology. The formation of these units is determined by the interparticle interactions, which need to be clearly defined and quantified. It is usefiil to define the concentration range above which a suspension may be considered as concentrated. The particle number concentration and volume fraction, q , above which a suspension may be considered to be concentrated, is best defined in terms of 

At one extreme, a suspension may be considered dilute if the thermal motion (Brownian diffusion) of the particles predominate over the imposed interparticle interaction [30-32]. In this case, the particle translational motion is large and only occasional contacts will occur between the particles that is, the particles do not see each other until a collision occurs, giving a random arrangement of particles. 

With solid-in-liquid dispersions, such a highly ordered structure - which is close to the maximum packing fraction (q = 0.74 for hexagonally closed packed array of monodisperse particles) - is referred to as a soHd suspension. In such a system, any particle in the system interacts with many neighbours and the vibrational amplitude is small relative to particle size thus, the properties of the system are essentially time-independent [30-32]. In between the random arrangement of particles in dilute suspensions and the highly ordered structure of solid suspensions, concentrated suspensions may be easily defined. In this case, the particle interactions occur by many body collisions and the translational motion of the particles is restricted. However, this reduced translational motion is less than with solid suspensions - that is, the vibrational motion of the particles is large compared to the particle size. Consequently, a time-dependent system arises in which there will be both spatial and temporal correlation. 

On standing, concentrated suspensions reach various states (stractures) that are determined by  

The magnitude and balance of the various interaction forces, electrostatic repulsion, steric repulsion and van der Waals attraction. 

Thus by measuring the 0-point (CFT or CFV) for the polymer chains (A) in the medium under investigation (which could be obtained from viscosity measurements) one can establish the stability conditions for a dispersion, before its preparation. This procedure also helps in designing effective steric stabilisers such as block and graft copolymers. 

Between the random arrangement of partides in dilute suspensions and the highly ordered structure of solid suspensions one may easily define concentrated suspensions. In this case, the partide interactions occur by many-body collisions and the translational motion of the particles is restricted. However, this reduced translational motion is not as great as with solid suspensions, i.e. the vibrational motion of the particles is large compared with particle size. A time-dependent system arises in which there will be spatial and temporal correlations. 

On standing, concentrated suspensions reach various states (structures) that are determined by (1) Magnitude and balance of the various interaction forces, electrostatic repulsion, steric repulsion and van der Waals attraction. (2) Particle size and shape distribution. (3) Density difference between disperse phase and medium, which determines the sedimentation characteristics. (4) Conditions and prehistory of the suspension, e.g. agitation, which determines the structure of the floes formed (chain aggregates, compact clusters, etc.). (5) Presence of additives, e.g. high molecular weight polymers that may cause bridging or depletion flocculation. 

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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). 

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. 

Ottewill, R.H. (1987) Properties of concentrated suspensions, in Solid/Liquid Dispersions (ed. T.F. Tadros), Academic Press, London. 

Cell models have also been applied to the approximate determination of the properties of concentrated suspensions. This is touched upon in our discussion of suspension viscosity at high shear rate in Section 9.3. 

Cell models akin to those discussed in Section 8.5 have also been applied to the determination of the properties of concentrated suspensions (Happel Brenner 1983, van de Ven 1989). Although it is another method which has been used to obtaining approximate expressions for the high shear relative viscosity, we choose not to expand upon it here, instead referring the reader to the references cited. One of the difficulties is that the determination of the boundary conditions at the cell surface is somewhat arbitrary. Furthermore, expressions obtained by this approach indicate that the cell model is inappropriate for highly concentrated suspensions and is most satisfactory only at low to moderate concentrations. 

The rheological properties of concentrated suspensions are often time-dependent. If the apparent viscosity continuously decreases with time under shear, with a subsequent recovery of the viscosity when the flow is stopped, the system is said to be thixotropic. The opposite behaviour is called antithixotropy, or sometimes rheopexy. Thixotropy should not be confused with shear-thinning which is a time-independent characteristic of a system. Systems which show an irreversible decrease in viscosity with shear should be termed shear-destructive and not thixotropic. 

Nevertheless, on closer examination there appear to be very clear differences between stable suspensions (in which the particles retain their individual independence) and flocculated systems (in which the particles adhere to one another). These differences are shown, among other things, in the mechanical properties of concentrated suspensions and the sediments formed from them. 

The rheological properties of concentrated suspensions often depend not only on the shear rate but also on the time. When the viscosity decreases with time under shear but recovers to its original value after flow ceases, the behavior is known as thixotropic (Fig. 4.36). This type of behavior is more often observed in flocculated suspensions and colloidal gels. When the suspension is sheared, the floes are broken down leading a distribution of floe sizes. Often the regeneration of the floes is slow which causes the resistance to flow to decrease. The opposite behavior, when the viscosity increases with shear rate and is also time dependent, is known as rheopectic. 

Ottewill, R.FI., Properties of Concentrated Suspensions , in Solid/Liquid Dispersions ,... 

It is clear from the materials presented above that coupling between flow and orientation of fibers is necessary to accurately describe or predict the rheological properties of concentrated suspensions of fibers. Several other research groups (Altan et al. 1989, 1990, 1992 Ranganathan and Advani 1991 Shanker et al. 1991 Shaqfeh and Fredrickson 1990 Tucker and Advani 1974) reported on flow-induced fiber orientation in semicon-centrated or concentrated suspensions closely related to the processing of thermoplastic composite materials. In Chapter 13 of Volume 2 we discuss the importance of fiber orientation in the processing of thermoset/fiber composites. 

The construction of calibration curves is recommended in nephelometric and turbidimetric determinations, since the relationship between the optical properties of the suspension and the concentration of the disperse phase is, at best, semi-empirical. If the cloudiness or turbidity is to be reproducible, the utmost care must be taken in its preparation. The precipitate must be very fine, so as not to settle rapidly. The intensity of the scattered light depends upon the number and the size of the particles in suspension, and provided that the average size of particles is fairly reproducible, analytical applications are possible. 

The rheological properties of a suspension depend upon factors such as the size, shape and concentration of the particles, the stability of the suspension and the viscosity of the medium. Flow properties can be modified by altering the surface charge... 

Cerpa, A. Garcia-Gonzalez, M.T. Tartaj, P. Re-quena, J. Garcell, L. Serna, C.J. (1999) Mineral-content and particle-size effects on the colloidal properties of concentrated lateri-tic suspensions. Clays Clay Min. 47 515-521 Cervini-Silva, J. Sposito, G. (2002) Steady-state dissolution kinetics of aluminum-goethite in the presence of desferrioxamine-B and oxalate. Environ. Sci. Technol. 36 337-342 Cesco, S. Rdmheld.V. Varanini, Z. Pinton,... 

It appears that one can develop a qualitative understanding of the simple flow properties at moderate concentration without going beyond concepts which are already inherent either in the dilute solution theory of polymers or in the properties of particulate suspensions. The dependence of viscosity on c[i ] is believed to reflect a particle-like or equivalent sphere (127) hydrodynamics in solutions of low to moderate concentration. In particular, the experimental facts do not force the consideration of effects which might arise from the permanent connectedness of the polymer backbones. Situations conducive to the entangling of molecules may be present, e.g., overlap of the coils, but either entanglement contributions are small, or else they are overwhelmed by the c[f ] interactions. 

For full evaluation of the flow behaviour (rheology) of structured pesticide suspension concentrates and their settling characteristics, it is necessary to carry out measurements at small and large deformations. Such investigations provide valuable information on the viscoelastic properties of the suspension and if sufficiently analysed may be... 

Alexander, M., Rojas-Ochoa, L.F., Leser, M.E., and Schurtenberger, P. (2002). Stmcture, dynamics and optical properties of concentrated milk suspensions an analogy to hard-sphere liquids. J. ColloidInterf. Sci. 253, 35- 6. 

The macroscopic properties of liquid suspensions of fumed powders of silica, alumina etc. are not only affected by the size and structure of primary particles and aggregates, which are determined by the particle synthesis, but as well by the size and structure of agglomerates or mesoscopic clusters, which are determined by the particle-particle interactions, hence by a variety of product- and process-specific factors like the suspending medium, solutes, the solid concentration, or the employed mechanical stress. However, it is still unclear how these secondary and tertiary particle structures can be adequately characterized, and we are a long way from calculating product properties from them [1,2]. 

Until now the discussion has mciinly been on the properties of monodisperse dilute dispersions. In coating dispersions used in practice this is usually not the case. For example, alumina and zirconia coating suspensions for macroporous support coatings consist of irregular particles having a log normal size distribution. This has a profound effect on the interactions between the particles and the flow behaviour of concentrated suspensions. The principles discussed above are still relevant but the consequences are much more complicated. Surface roughness... 

Cerpa, A. et al.. Mineral-content and particle-size effects on the colloidal properties of concentrated lateritic suspensions. Clays Clay Miner, 47, 515, 1999. 

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