Shape factor dispersion

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. 

Here, fp is once again the volnme fraction of dispersed spheres, and /Ch is the apparent hydrodynamic shape factor, bnt a new parameter, /., is introduced which accounts... 

The discussion of dispersion in linear kinematic waves (Chapter 7, pp. 136, [7] = C see also [3b] and [314]) brings out another shape factor, this... 

Shape factors of a different sort are involved in the Taylor dispersion problem. With parabolic flow at mean speed U through a cylindrical tube of radius R, Taylor found that the longitudinal dispersion of a solute from the interaction of the flow distribution and transverse diffusion was R2U2/48D. The number 48 depends on both the geometry of the cross-section and the flow profile. If, however, we insist that the flow should be laminar, then the geometry of the cross-section determines the flow and hence the numerical constant in the Taylor dispersion coefficient. 

These practical issues of particle shape and dispersion are not intended to cast aspersions on the laser diffraction technique rather, these factors have been discussed to bring awareness around the analytical results that are obtained when these factors are present. Laser diffraction has proven itself to be a reliable, robust technique for particle size analysis. When the assumption of nonaggregated spherical particles is violated, there are clear manifestations in the calculated particle size distribution. When analyzing drug substances that are used in low-dose solid oral formulations, the impact of these manifestations can be particularly impactful as there is often a limited number of API lots to be used for method development. Therefore, the analyst must be aware of these issues prior to the commencement of method development to avoid these pitfalls. In addition to the information contained in ISO 13320, Snorek et al. have written a summary around the general practices of laser diffraction measurements in the pharmaceutical industry.19... 

There are two variables to consider, K and a (the shape factor). If the material being studied and the reference material are molecularly dispersed in a single sample tube (i.e., an internal reference), then there is only one value of k, and both sample and reference molecules experience the same magnetic field. Hence, the effect of magnetic susceptibility can be ignored. 

CCT, critical cracking thickness Boltzmann constant (1.381x10 local permeability [m ] fracture resistance [N m ] average permeability in/of compact [m ] particle shape factor compact thickness [m] initial particle number concentration [m refractive index of particle material refractive index of dispersion material number density of ion i dimensionless number dimensionless number Stokes number Peclet number capillary pressure [N-m ] dynamic pressure [N m ] local liquid pressure in the compact [N-m local solid pressure in the compact [N-m ] superficial fluid velocity [m-s q gas constant [J K ] centre to centre distance [m]... 

When the elements of the disperse phase can be classified as equidimensional, namely they have nearly the same size or spread in multiple directions, and have constant material density, typically a single internal coordinate is used to identify the size of the elements. This could be particle mass (or volume), particle surface area or particle length. In fact, in the case of equidimensional particles these quantities are all related to each other. For example, in the trivial cases of spherical or cubic particles, particle volume and particle surface area can be easily written as Vp = k d and Ap = k d, or, in other words, as functions of a characteristic length, d (i.e. the diameter for the sphere and the edge for the cube), a volume shape factor, k, and a surface-area shape factor, k. For equidimensional objects the choice of the characteristic length is straightforward and the ratio between kp, and k is always equal to six. The approach can, however, be extended also to non-equidimensional objects. In this context, the extension turns out to be very useful only if... 

The morphology of the incompatible blends depends on two factors dispersion degree of the two phases, and shape and dimensions of the dispersed particles. In turn, these factors are determined by the rheological characteristics of the two components and by the mixing conditions. 

The nature of the carbon used as an electronic conductor may vary carbon black from different sources with particle size distributions (PSDs) of 30-40 nm and specific surface areas of 100-2,000 mVg (BET surface), activated carbons, carbon fibers or indeed carbon nanotubes (CNTs). The type of carbon, its morphology and its mode of dispersion or coating play a part in the resulting electrical properties of the electrode. For instance, carbon fibers or CNTs improve the electronic conductivity of thick electrodes, because their high shape factor enables them to form a good electronic percolation lattice.In the presence of CNTs, a capacity of 900 mAh/gs in the first cycle and 75% retention of capacity after 60 cycles (with a charge/discharge current density of 100 mA/g and 68% sulfur in the... 

The passage sea state IS characterized, in deepwater, by a narrow band Jonswap spectrum with significant wave height Hg = 3.8 m, peak period Tp = 9 s, and shape factor 7 = 3.3. The mean sea state duration is = 1.8 h. As Tc [Pg.945]

Where P is the effective permeabiUly of a gas penetrant in a MMM with a volume fraction of (pd of the dispersed phase d in a continuous matrix phase c, P and Pj represent the permeability in the continuous and dispersed phase, respectively, and n is the shape factor of the dispersed particles. The limit of n=0 corresponds to the parallel transport of gas through side by side layers of continuous and dispersed phase. In this case Eq. (8.29) is simplified by... 

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