Suspensions, solids fraction

FIGURE 12.24 Viscosity (at y 50 sec ) and apparent yield stress (at y = 1 sec ) versus suspension solids fraction for ion-exchanged kaolinite. Data taken from Langs-... 

The presence of a gas in the suspension results in an increase of the stirrer speed required to establish the state of complete suspension. The propeller usually requires a higher speed than the turbine. Furthermore, a critical volume gas flow exists above which drastic sedimentation of particles occurs. Hence, homogenisation of the suspension requires an increase of the rotational speed and/or a decrease of the gas flow rate. The hydrodynamics of suspensions with a solid fraction exceeding 0.25-0.3 becomes very complex because such suspensions behave like non-Newtonian liquids. This produces problems in the scale-up of operations. Hydrodynamics, gas hold-up, mass-transfer coefficients, etc. have been widely studied and many correlations can be found in literature (see e.g. Shah, 1991). 

To a solution of 4 g. of silver nitrate in 8 ml. of water is added 60 ml. of 3.4% aqueous sodium hydroxide plus 1.3 g. of 2-(4-acetyl-5-methylpyrrole-2)diglycolaldehyde. The mixture is heated under reflux on a steam bath for forty minutes. After cooling, the suspension is filtered and the filtrate is neutralized (to Congo Red) with dilute nitric acid. On further cooling, a solid separates this is slightly soluble in water and very soluble in ether. Additional product is obtained by extracting the filtrate three times with ether. The united ether extracts are dried with anhydrous sodium sulfate, filtered, and the filtrate evaporated to dryness. The residue is combined with the first solid fraction, and recrystallized from ether, affording pale-yellow crystals yield, lg. m. p., 200°. 

Among other drawbacks of slurry reactors are the high axial dispersion and the low solid fraction that can be held in suspension. Concerning the flow capacity, it should be emphasized that the slurry reactors are less sensitive to gas flow rates, whereas in monolith reactors the gas flow rate is limited by the restrictions of slug flow. 

C = f (porosity, permeability, capillary pressure, suspension solids volume fraction, compact solids volume fraction)... 

Such a value for the average density is only approximately correct for power calculations (although it is appropriate in most cases), as the solids fraction in the impeller region may differ from 0 depending on N, i.e., on the solids suspension state. 

Although both expressions are commonly used, they fail to predict some important macroscopic properties of solid-fluid suspensions, such as the expansion and sedimentation profiles. To overcome this limitation Mazzei Lettieri (2007) developed a relationship for the drag coefficient that is based on the empirical correlation by Richardson Zaki (1954) describing the expansion profiles of homogeneous fluid-solid suspensions. Its main feature resides in the fact that the expression is consistent with the Richardson and Zaki correlation over the whole range of fluid-dynamic regimes and for any value of the suspension void fraction. It has the following formulation ... 

Figure 4 Particle packing dynamics and structures of stabilized AI2O3 suspensions with different solid fractions and the corresponding size distributions of smallest particles. The initial state (a) is identical with the initial state in Fig. 2(a), and is therefore omitted here.

Figure 2. Fractional removal of Cd onto Fe(OH) and an Fe-Si binary suspension. Solids concentrations are given in Table I.

Similarly as the processes of coagulation and break-up characterized for mixtures of fluids, the processes of micelles crystallization, colloidal agglomeration, and process of dispersion occurring in colloidal suspensions, can be simulated by using multilevel particle models described in Section ll.E. This time, however, solid fraction, colloidal beads, has to be simulated by using different interaction paradigm. 

The viscosity of a slurry can be measured if the particles settle slowly. For dilute suspensions of fine particles, slurries may exhibit Newtonian behaviour. In this case, the viscosity of a very dilute suspension (solids volume fraction less than 2%) of uniform, spherical particles can be described by the theoretical equation derived by Einstein (Einstein, 1906). Einstein s equation is ... 

The solids fraction only slightly influences the necessary shaft speed for suspension, as shown in Equation 13.17 and in Figure 13.8. When applying the 90% solids level criterion, the influence is more significant. The viscosity behavior of the suspension usually remains Newtonian up to a fraction range of 0.25-0.3. 

Material is continuously removed through the interaction of the SiC particles below the moving wire and the silicon surface. The abrasive action of the SiC depends on many factors such as the wire speed, the force between the wire and the crystal, the solid fraction of SiC in the suspension, the viscosity of the suspension, the size distribution and the shape of the SiC particles. The viscosity of the slurry depends on the temperature and the solid fraction of particles and changes because of the continuous abrasion of silicon and iron from the wire. This gradually deteriorates the abrasive action and the slurry finally has to be replaced. The kerf loss... 

To make such comparisons, the differences and similarities are worthwhile to consider, and we begin with what appear to be the key differences. The first very readily noted difference is the flexibility in solid fraction, <(), for suspension, while granular materials are found in a rather narrow range of solid fractions close... 

Figure 11.1 At top is a schematic showing spherical particles, typically relatively monodisperse with radius a in (Newtonian) liquid, with the mixture subjected to shear flow. A key issue in suspensions is the structure developed, and in the lower panels is the pair distribution function g(r) for a suspension of solid fraction 4> = 0.45 shown in a plane for the equilibrium at lower left, and for the plane of shear at dimensionless shear rate of Pe = 6nr Qya )/kT = 25 at lower right. The strong anisotropy induced by flow at elevated shear rate is evident.

Lenoble et al. (2005) studied a suspension of heavy particles at an initial solid fraction of ( ) = 0.59, a mixture they in fact termed a "wet granular material," in a simple shear flow configuration (between parallel plates) and found a sheared layer over a static layer. Granular avalanche flows under liquid have also been studied to determine the normal stress response, specifically through the pore pressure at the base of the flow (Cassar et al. 2005), and a model for the development of the steady state in such flows was presented by Pailha and Pouliquen (2009). 

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