Particle—fluid flow system

An essential element in the progress of research and engineering of multiphase flow systems and specifically particle-fluid flow systems is improved instrumentation for measurements. They make possible validation of basic concepts in the formation, determination of design parameters, and design of systems. 

This volume brings together the most original and productive specialists who have conducted research on various aspects of instrumentation for particle-fluid flow systems. They might be associated with universities or industries, in the disciplines of chemical, mechanical, civil, aerospace engineering, and environmental and material science, as well as pharmaceutical processing. 

Generally, a particle in a particle—fluid flow system can have two types of motion translational and rotational, which are determined by Newton s second law of motion. The corresponding governing equations for particle i with radius R, mass m moment of inertia I and specific heat capacity Cp j can be written as ... 

There are numerous applications of particle-fluid flow in crystallization process systems including ... 

Zhu HP, Hou QF, Zhou ZY, Yu AB Averaging method of particulate systems and its application to particle-fluid flow in a fluidized bed. Chin Sci Bull 54 4309—4317, 2009. 

The gels precipitated as described above are not useful in ion-exchange systems because their fine size impedes fluid flow and allows particulate entrainment. Controlled larger-sized particles of zirconium phosphate are obtained by first producing the desired particle size zirconium hydrous oxide by sol—gel techniques or by controlled precipitation of zirconium basic sulfate. These active, very slightly soluble compounds are then slurried in phosphoric acid to produce zirconium bis (monohydrogen phosphate) and subsequently sodium zirconium hydrogen phosphate pentahydrate with the desired hydrauhc characteristics (213,214). 

The laser-Doppler anemometer measures local fluid velocity from the change in frequency of radiation, between a stationary source and a receiver, due to scattering by particles along the wave path. A laser is commonly used as the source of incident illumination. The measurements are essentially independent of local temperature and pressure. This technique can be used in many different flow systems with transparent fluids containing particles whose velocity is actually measured. For a brief review or the laser-Doppler technique see Goldstein, Appl. Mech. Rev., 27, 753-760 (1974). For additional details see Durst, MeUing, and Whitelaw, Principles and Practice of Laser-Doppler Anemometry, Academic, New York, 1976. 

If force P is greater than zero, the particle will be in motion relative to the continuous phase at a certain velocity, w. At the beginning of the particle s motion, a resistance force develops in the continuous phase, R, directed at the opposite side of the particle motion. At low particle velocity (relative to the continuous phase), fluid layers running against the particle are moved apart smoothly in front of it and then come together smoothly behind the particle (Figure 14). The fluid layer does not intermix (a system analogous to laminar fluid flow in smoothly bent pipes). The particles of fluid nearest the solid surface will take the same time to pass the body as those at some distance away. 

Gas-liquid-particle operations are of a comparatively complicated physical nature Three phases are present, the flow patterns are extremely complex, and the number of elementary process steps may be quite large. Exact mathematical models of the fluid flow and the mass and heat transport in these operations probably cannot be developed at the present time. Descriptions of these systems will be based upon simplified concepts. 

The RTD quantifies the number of fluid particles which spend different durations in a reactor and is dependent upon the distribution of axial velocities and the reactor length [3]. The impact of advection field structures such as vortices on the molecular transit time in a reactor are manifest in the RTD [6, 33], MRM measurement of the propagator of the motion provides the velocity probability distribution over the experimental observation time A. The residence time is a primary means of characterizing the mixing in reactor flow systems and is provided directly by the propagator if the velocity distribution is invariant with respect to the observation time. In this case an exact relationship between the propagator and the RTD, N(t), exists... 

A partial differential equation is then developed for the number density of particles in the phase space (analogous to the classical Liouville equation that expresses the conservation of probability in the phase space of a mechanical system) (32>. In other words, if the particle states (i.e. points in the particle phase space) are regarded at any moment as a continuum filling a suitable portion of the phase space, flowing with a velocity field specified by the function u , then one may ask for the density of this fluid streaming through the phase space, i.e. the number density function n(z,t) of particles in the phase space defined as the number of particles in the system at time t with phase coordinates in the range z (dz/2). 

Steps 1 and 7 are highly dependent on the fluid flow characteristics of the system. The mass velocity of the fluid stream, the particle size, and the diffusional characteristics of the various molecular species are the pertinent parameters on which the rates of these steps depend. These steps limit the observed rate only when the catalytic reaction is very rapid and the mass transfer is slow. Anything that tends to increase mass transfer coefficients will enhance the rates of these processes. Since the rates of these steps are only slightly influenced by temperature, the influence of these processes... 

Broadly speaking, for G/S systems, three modes of particle-fluid contacting may be recognized to take place simultaneously as shown in Fig. 43 bubbles containing sparsely disseminated particles, emulsion of densely suspended particles, and defluidized (transient as well as persistent) particles not fully suspended hydrodynamically by the flowing gas. For all intents and purposes, it is desirable to suppress bubbles and to prevent defluidization. 

The CFD model described above is adequate for particle clusters with a constant fractal dimension. In most systems with fluid flow, clusters exposed to shear will restructure without changing their mass (or volume). Typically restructuring will reduce the surface area of the cluster and the fractal dimension will grow toward d — 3, corresponding to a sphere. To describe restructuring, the NDF must be extended to (at least) two internal coordinates (Selomulya et al., 2003 Zucca et al., 2006). For example, the joint surface, volume NDF can be denoted by n(s, u x, t) and obeys a bivariate PBE. 

A reactor model based on solid particles in BMF may be used for situations in which there is deliberate mixing of the reacting system. An example is that of a fluid-solid system in a well-stirred tank (i.e., a CSTR)-usually referred to as a slurry reactor, since the fluid is normally a liquid (but may also include a gas phase) the system may be semibatch with respect to the solid phase, or may be continuous with respect to all phases (as considered here). Another example involves mixing of solid particles by virtue of the flow of fluid through them an important case is that of a fluidized bed, in which upward flow of fluid through the particles brings about a particular type of behavior. The treatment here is a crude approximation to this case the actual flow pattern and resulting performance in a fluidized bed are more complicated, and are dealt with further in Chapter 23. 

In fast-fluidized beds, which use extremely small catalyst particles, the flow of particles and fluid is cocurrent, and nearly PF, leading to high conversion and selectivity. However, severe erosion of equipment is common, and thus, the design of the solids recovery and recirculation system is important. 

Box models were used in a model to simulate particle transport in lacustrine systems that involve fluid flow, coagulation, and gravity. 

As mentioned earlier, Reynolds numbers determined for the bulk flow have to be discerned from Reynolds numbers characterizing a particle-liquid dissolution system. The latter were calculated for drug particles of different sizes using the Reynolds term according to the combination model. The kinematic viscosity of the dissolution medium at 37°C is about 7 x 10-03 cm2/sec. The fluid velocities (Ua) employing the paddle method at stirring rates of 50-150 rpm can be taken from the literature and may arbitrarily be used as the slip velocities at the particle surfaces. 

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