Fluid-particle suspensions

The equation due to Zweitering (1958) has been shown to be of wide applicability for estimating the minimum impeller speed, N, to suspend all the particles smaller than a certain size, d  

The terminal velocities of crystals suspended in agitated vessels may be predicted from the equations 

For crystals of intermediate size, an interpolated mean value should be used. The just-suspended slip velocity is given by 

The types of agitator commercially available to maintain crystals dispersed in a crystallizer are many and varied. They include anchors, gates, flat paddles, propellers, radial-flow flat-bladed turbines, axial-flow angle-bladed turbines, and so on. Each has its own fluid mixing and crystal dispersion characteristics. The selection of the most appropriate agitator for a given duty is a highly skilled task and reference should be made to specialist publications and technical brochures. 

Good accounts of process mixing and agitation equipment for liquid-solid systems are given by Sterbacek and Tausk (1965), Uhl and Gray (1986), Old-shue (1983, 1992) and Harnby, Edwards and Nienow (1992). 

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Joseph DD, Lundgren TS, Jackson R, SaviUe DA (1990) Ensemble Averaged and Mixture Theory Equations for Incompressible Fluid-Particle Suspensions. Int J Multiphase Flow 16 (l) 35-42... 

The particle settling velocity in a fluid-particle suspension ... 

Joseph DD, Jjmdgren TS, Jackson R, Savflle DA (1990) Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions. Int J Multiph Row 16(1) 35-42... 

Fluid mixing and particle suspension in unbaffled vessels (Figure 7.1(a)) may be poor, experiencing vortexing but this can be improved by the addition of wall... 

Reticulated Bacterial Cellulose. A cellulose with an intertwined reticulated structure, produced from bacteria, has unique properties and functionalities unlike other conventional celluloses. When added to aqueous systems, reticulated bacterial cellulose improves the fluid rheology and the particle suspension over a wide range of conditions [1836]. Test results showed advantages in fluid performance and significant economic benefits by the addition of reticulated bacterial cellulose. 

Significance. What is the significance of these observations For succinoglycan solutions the answer is obvious, above the transition temperature they have little or no viscosity, which may be undesirable. Such polymers are usually used as viscosifiers or for particle suspension. On the other hand, a drop in viscosity may be an advantage if fluid penetrates a formation hotter than the well as there could be little or no subsequent formation damage. 

Khan, A. R. and Richardson, J. F. Chem. Eng. Comm. 78 (1989) 111. Fluid-particle interactions and flow characteristics of fluidized beds and settling suspensions of spherical particles. 

DISPERSANTS. Dispersants are materials that help maintain fine solid particles in a state of suspension, and inhibit their agglomeration or settling in a fluid medium. With the help of mechanical agitation, dispersants can also hit-.tk up agglomerates of particles to form particle suspensions. Another use of dispersants is to inhibit the growth of crystallites in a supersaturated solution. This characteristic is also known us precipitation... 

These six equations are insufficient to give a closure of the EMMS model that involves eight variables. The closure is provided by the most unique part of the EMMS model, that is, the introduction of stability condition to constraint dynamics equations. It is expressed mathematically as Nst = min, which expresses the compromise between the tendency of the fluid to choose an upward path through the particle suspension with least resistance, characterized by Wst = min, and the tendency of the particle to maintain least gravitational potential, characterized by g = min (Li and Kwauk, 1994). 

The Basset force may be negligible when the fluid-particle density ratio is small, e.g., in most gas-solid suspensions, and the time change is much longer than the Stokes relaxation time or the acceleration rate is low. 

There are many pitfalls in measuring the properties of aerosols. One of the most critical is sampling of particulate matter without disturbing the aerial suspension. There are some optical devices that make measurements of an aerosol in situ without disturbance. However, most devices requires that a small sample be taken from the gas-particle suspension. Because of inertial forces acting on particles, it can be deduced readily that siphoning part of the fluid... 

In vivo, however, various further aspects have to be taken into account such as variability in stomach emptying, intestinal transit, effect of the dilution of the particle suspension in the Gl-tract fluids, and mixing with ingested food (Ponchel and Irache 1998). 

For small catalyst particles completely different reactor types are used. The catalyst is now suspended in the flowing reaction mixture and has to be separated at the reactor exit or is carried along with the fluid. Particle sizes are now from 10 fim up to 1 mm. In Figure 1.2 some of the common reactor types are shown. Figure 1.2(a) shows the fluid bed reactor, where the gaseous feed keeps the small catalyst particle in suspension. Catalyst carried over in the exit stream is separated, for example, in cyclones. For even shorter contact times, riser reactors are used in which the solid catalyst is transported in the gas stream. Fluid bed reactors are also used for feed mixtures of a liquid and a gas. 

We further mention that at low values of the Reynolds number (that is at very low fluid velocities or for very small particles) for flow through packed beds the Sherwood number for the mass transfer can become lower than Sh = 2, found for a single particle stagnant relative to the fluid [5]. We refer to the relevant papers. For the practice of catalytic reactors this is not of interest at too low velocities the danger of particle runaway (see Section 4.3) becomes too large and this should be avoided, for very small particles suspension or fluid bed reactors have to be applied instead of packed beds. For small particles in large packed beds the pressure drop become prohibitive. Only for fluid bed reactors, like in catalytic cracking, may Sh approach a value of 2. 

Although particles in two-phase flow are not uniformly distributed, the dense and the dilute phases can be considered, each in its own, as uniform suspensions, and the global system can thus be regarded as consisting of dense clusters dispersed in a broth of separately distributed discrete particles, as shown in Fig. 1. The preceding correlations will therefore be used respectively in the dilute and the dense phases, for calculating micro-scale fluid-particle interaction, and also for evaluating meso-scale interphase interaction between clusters and the broth, as shown in Table I, for CD, CD[ and CD. ... 

Obviously, the different energy terms characterize different aspects of particle-fluid two-phase flow, among which those related to particle suspension and transport are of importance in analyzing fluid-particle interaction, and, in particular, for identifying system stability ... 

Stable particle suspensions exhibit an extraordinarily broad range of rheological behavior. which depends on particle concentration, size, and shape, as well as on the presence and type of stabilizing surface layers or surface charges, and possible viscoelastic properties of the suspending fluid. Some of the properties of suspensions of spheres are now reasonably well understood, such as (a) the concentration-dependence of the zero-shear viscosity of hard-sphere suspensions and (b) the effects of deformability of the steric-stabilization layers on the particles. In addition, qualitative understanding and quantitative empirical equations... 

The viscosity of some fluids (particle solutions or suspensions) measured at a fixed shear rate that places the fluid in the non-Newtonian regime increases with time as schematically shown by curve C of Figure 13.39. This behavior can be explained by assuming that in the Newtonian region the particles pack in an orderly manner, so flow can proceed with minimum interference between particles. However, high shear rates facilitate a more random arrangement for the particles, which leads to interparticle interference and thus to an increase in viscosity. Models that illustrate the thixotropic and rheopectic behavior of structural liquids can be found elsewhere (58,59). 

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