Agglomeration, shape factors

Agglomeration in a slurry causes a change in the packing factor at which flow is blocked, from 0.6 to 0.45 and causes a change in the hydrodynamic shape factor from 3.5 to 2.5. In both cases, the volume fraction of dispersed particles is 0.40. 

Besides the numerical calculation of shape factors, there are also qualitative descriptions of shape. For example, certain pharmacopoeias define shapes such as an agglomerate, needle, etc. Since no one method is best in all applications, the best method for determining particle shape depends on the application and nature of the particle being examined. 

Equation (7) is valid for agglomerates formed by approximately isodisperse, convex, and monosized particles. With the third moment M30 of the number density distribution n x) and a shape factor /q, a formula can be derived which is valid for distributions of similar, approximately isometric, and convex particles ... 

Zelenyuk, A., Cai, Y., and Imre, D. (2006) From agglomerates of spheres to irregularly shaped particles Determination of dynamic shape factors from measurements of mobility and vacuum aerodynamic diameters, Aerosol Sci. Technol. 40, 197-217. 

The coal particles can be tracked as parcels in an Eulerian-Lagrangian framework. Discrete phase model (DPM) are used to define the injected particles that enter the reactor. In the case of INCI, simulation values for axial velocity of -1.732 m/s and a radial velocity of -l.Om/s of the particles must be provided. If agglomeration is neglected, a maximum particle diameter of 0.1 mm, a mean diameter of 0.09 mm, and a minimum diameter of 0.001 mm are assumed according to a Rosin-Rammler-Sperling-Bennett distribution with a spread parameter of = 0.688 in 10 individual groups for fluid-bed coal (see also Section 3.12.3.3). Particles can be treated as nonspherical with a shape factor of 0.85. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

Separation depends on the selection of a process in which the behaviour of the material is influenced to a very marked degree by some physical property. Thus, if a material is to be separated into various size fractions, a sieving method may be used because this process depends primarily on the size of the particles, though other physical properties such as the shape of the particles and their tendency to agglomerate may also be involved. Other methods of separation depend on the differences in the behaviour of the particles in a moving fluid, and in this case the size and the density of the particles are the most important factors and shape is of secondary importance. Other processes make use of differences in electrical or magnetic properties of the materials or in their surface properties. 

The first factor is that the agglomerates are not necessarily spherical in shape. A more general representation would be to assume that they are spheroids in shape with fore and aft symmetry. This case was treated in detail by Manas-Zloczower et al. (97). These particles enter the high shear zone in random orientation, and therefore some may rupture and others will pass without rupturing. The fraction of particles that rupture in a given set of condition can be calculated. 

The influence of a number of the system variables relating to powder and liquid properties, etc., has already been discussed in Section 1 above. With proper control of these variables and of the pan operating conditions, it is possible within limits to influence agglomerate properties such as shape, size and porosity. A discussion of such factors has been given by Pietsch [24] and by Ball [25]. 

Unfortunately, the percolation approach is also not really able to predict accurately the critical volume fraction in real composites, because so many different factors, like filler shape, size, distribution and particle agglomeration, come into play. Lux (1993) has reviewed the various percolation models that have been proposed in theoretical treatments of the problem. 

Besides these models there are many others models, but no single model explains the effective thermal conductivity in all cases. Besides the thermal conductivities of the base fluid and nanoparticles and the volume fraction of the particles, there are many other factors influencing the effective thermal conductivity of the nanofluids. Some of these factors are the size and shape of nanoparticles, the agglomeration of particle, the mode of preparation of nanofluids, the degree of purity of the particles, surface resistance between the particles and the fluid. Some of these factors may not be predicted adequately and may be changing with time. This situation emphasizes the importance of having experimental results for each special nanofluid produced. 

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