Particle-free voids

Beyond the minimum fluidization velocity bubbles or particle-free voids may appear in the fluidized bed. Figure 7.3 shows bubbles in a gas fluidized bed. The... 

Liquid holdup is critical in the downflow operation of fixed beds, in contrast to the upflow operation where the liquid occupies practically the whole external free void volume of the bed. Total liquid holdup ht consists of two parts static h, and dynamic holdup liA. Static holdup is related to the volume of liquid that is adherent to the particles surface, whereas dynamic holdup is related to the flowing pari of the liquid. 

Hydraulic number for close-packed spheres. We consider a volume V which contains n spheres. Here, n is assumed to be a large number so that it is practically continuous. The volume filled by particles is V) = n 4/3 nR3. The total surface area of all particles is A = n 4ttR2. The free ( void ) volume is Vv = 0.26 V = 0.26 n 4/3 ttR3/0.74. Thus the hydraulic number is... 

Conceptually, besides the assembly of the templating particles, the second logical step is to fill the free voids with the material of which the final porous specimen should consist. Three fundamental cases should be distinguished ... 

Equation (29) would appear to tell us what is required for efficient clarification. The most important term, because of its exponent, is the particle diameter. This is why it is so important to allow particles to grow during precipitation. The density of the solid particle should also be maximized. There is a fundamental limit at the true solids density, but it is possible to approach this if the process forms particles free of voids and with compact structure. Also important, although not shown in- an equation developed for spherical particles, is the question of shape. Irregular particles will develop more frictional resistance and be more likely to be carried out of the clarifier by the rising flow of brine. 

Transition section (transition zone, compression section) n. In a metering-type screw for a single-screw extruder the section of decreasing channel volume per turn between the feed and metering sections, in which the plastic is changing state from a loosely packed bed of particles-cwm-voids, to a void-free melt. The transition may be... 

Core-shell emulsion polymerisation. VanderholF et al. (1991) prepared particles consisting of a core of a copolymer of methacryUc acid and methyl methacrylate and a shell of crosslinked material. After neutralisation with NH4OH, the core material collapses and the particles contain voids of between 130 and 760 run. A similar approach was applied by Okubo and Ichikawa (1994) where the particles were produced by an emulsion-free terpolymerisation of styrene, butyl acrylate and methacrylic acid. The effect of pH, temperature and time of acid treatment on the multi-hoUow structure formed were investigated. 

It might seem at first glance that arriving at the dipole moment p of an ellipsoidal particle via the asymptotic form of the potential < p is a needlessly complicated procedure and that p is simply t>P, where v is the particle volume. However, this correspondence breaks down for a void, in which P, = 0, but which nonetheless has a nonzero dipole moment. Because the medium is, in general, polarizable, uP, is not equal to p even for a material particle except when it is in free space. In many applications of light scattering and absorption by small particles—in planetary atmospheres and interstellar space, for example—this condition is indeed satisfied. Laboratory experiments, however, are frequently carried out with particles suspended in some kind of medium such as water. It is for this reason that we have taken some care to ensure that the expressions for the polarizability of an ellipsoidal particle are completely general. 

It is far more likely that heterogeneous nucleation plays the governing role in nucleation of voids. The effect of a particle or substrate is to lower the free energy barrier AF. Thus, Equations 6.1 and 6.3 remain unchanged, and Equation 6.2 takes on the new form... 

In the area of pharmaceuticals, particle formation is currently one of the most popular applications of supercritical fluids. The reasons can be found in the wide variety of particles obtained by the supercritical techniques. Void free particles or very soft particles, composed of polar or non-polar compounds, and with size ranging from 50 nanometr to 50 microns can be produced easily. 

Up to this point we have been discussing diffusion in terms of molecular or free diffusion where the diffusion rate is determined by molecular collisions and the particle voids which are larger than the mean free path. In packed gas chromatographic columns the diffusion process follows other laws. Under these conditions we can encounter four types of diffusion. 

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