Rheology suspension

Rheology is the study of flow and deformahon of matter (Barnes et al., 1989). It encompasses a wide range of mechanical behaviour from Hookian elashc 

in this section, the influence of volume fraction of particles is discussed in the case where there are no surface forces between particles. Only hydrodynamic forces and Brownian motion are considered in this case, which is known as the non-interacting hard sphere model. The influence of surface forces is considered in the following section. 

Consider a molecular liquid with Newtonian behaviour (see Chapter 4) such as water, benzene, alcohol, decane, etc. The addition of a spherical particle to the liquid will increase its viscosity due to the additional energy dissipation related to the hydrodynamic interaction between the liquid and the sphere. Further addition of spherical particles increases the viscosity of the suspension linearly. Einstein developed the relationship between the viscosity of a dilute suspension and the volume fraction of solid spherical particles as follows (Einstein, 1906)  

Einstein s analysis was based on the assumption that the particles are far enough apart so that they do not influence each other. Once the volume fraction of solids reaches about 10%, the average separation distance between particles is about equal to their diameter. This is when the hydrodynamic disturbance of the liquid by one sphere begins to influence other spheres. In this semi-dilute concentration regime (about 7-15 vol% solids), the hydrodynamic interactions between spheres results in positive deviation for Einstein s relationship. Batchelor (1977) extended the analysis to include higher order terms in volume fraction and found that the suspension viscosities are still Newtonian but increase with volume fraction according to  

At even higher concentrations of particles, the particle-particle hydrodynamic interactions become even more significant and the suspension viscosity increases even faster than predicted by Batchelor and the suspension rheology becomes shear thinning (see Chapter 4) rather than Newtonian. 

In deriving an equation for the viscosity of a suspension of spherical particles, Einstein considered particles which were far enough apart to be treated independently. The particle volume fraction (p is defined by 

The suspension could be assigned an effective viscosity, rj, given by 

A charged particle in suspension with its inner immobile Stern layer and outer diffuse Gouy (or Debye-ffiickel) layer presents a different problem from that arising with a smooth and small nonpolar sphere. In movement such particles experience electroviscous effects which have two sources (a) the resistance of the ion cloud to deformation, and (b) the repulsion between particles in close contact. When particles interact, for example to form pairs in the system, the new particle will have a different shape from the original and will have different flow properties. The coefficient 2.5 in Einstein s equation (7.30) 

Other problems in deriving a priori equations result from the polydisperse namre of pharmaceutical suspensions. The particle size distribution will determine rj. A polydisperse suspension of spheres has a lower viscosity than a similar monodisperse suspension. 

Stmcture formation during flow is an additional complication. Stmcture breakdown occurs also and is evident particularly in clay suspensions, which are generally flocculated at rest. Under flow there is a loss of the stmcture and the suspension exhibits thixotropy and a yield point. The viscosity decreases with increasing shear stress (Fig. 7.33). 

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Binders in Ceramics, Powder Metallurgy, and Water-Based Coatings of Fluorescent Lamps. In coatings and ceramics appHcations, the suspension rheology needs to be modified to obtain a uniform dispersion of fine particles in the finished product. When PEO is used as a binder in aqueous suspensions, it is possible to remove PEO completely in less than 5 min by baking at temperatures of 400°C. This property has been successfully commercialized in several ceramic appHcations, in powder metallurgy, and in water-based coatings of fluorescent lamps (164—168). 

For a given suspension rheology and flow rate there is a critical permeability of the filter, below which no cake will be formed. The model also suggests that the equilibrium cake thickness can be precisely controlled by an appropriate choice of suspension flow rate and filter permeability. 

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. 

Metzner AB (1977) Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction Phys Fluids 20 145... 

Suspension Rheology. Particles suspended in a material, such as in filled or reinforced polymers, have a direct effect on the properties of the final article and on the viscosity during... 

For reviews and more information on the principles and practice of mineral-slurry pipelining see Refs. [90,615-618]. The relationships among suspension rheology, flow rate, and pressure drop in a pipeline are discussed in Section 6.7.1 and oil pipelining is discussed in Section 11.3.4. 

Leal, Advanced Transport Phenomena Fluid Mechanics and Convective Transport Mewis and Wagner, Colloidal Suspension Rheology... 

Applications of computer simulations to dense suspension rheology. 

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). 

Cell-type models are still in use (Adler, 1979 Russel and Benzing, 1981) because of their simplicity. Predicted results are often quite reasonable, exhibiting features intuitively anticipated. On the other hand, such models fail to provide definitive answers to many of the fundamental issues encountered in suspension rheology. Moreover, because of their strictly ad hoc geometric nature, no obvious way exists for their rational improvement. 

Finally, we direct attention to Barnes et al. (1987), for their extensive review of applications of computer simulations to dense suspension rheology, and also to Hassonjee et al. (1988), for their numerical scheme for dealing with large clusters of spherical particles. 

Intimately related to these magnetic-field suspension rheology developments is the growing field of electrorheology, which involves comparable electric fields and was the subject of an international symposium (Carlson and Conrad, 1987). 

In Chapter 12 of this book, the mechanical properties of ceramic suspensions, pastes, and diy ceramic powders are discussed. Ceramic suspension rheology is dependent on the viscosity of the solvent with polymeric additives, particle volume fraction, particle size distribution, particle morphology, and interparticle interaction energy. The interparticle forces play a veiy important role in determining the colloidal stability of the suspension. If a suspension... 

FIGURE 12.2 Constitutive equations for ceramic suspension rheology. 

Ceramic Suspension Rheology son to the particle radius. This equation is given by... 

If we are to use a direct analogy of suspension rheology to the Cross equation derived for polymer solutions, we should consider that the... 

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