Monosized particles

FIGURE 1.4 Optical micrograph of macroporous chromatographic column materials, (a) Monosized particles of 20 tm. (b) Commercial column filling of 12-28 tm. [Reprinted from T. Ellingsen et al. (1990). Monosized stationary phases for chromatography.7. Chromawgr. 535,147-161 with kind permission from Elsevier Science-NL, Amsterdam, The Netherlands.]... 

A trend in chromatography has been to use monosized particles as supports for ion-exchange and size-exclusion chromatography and to minimize the column size, such as using a 15 X 4.6-mm column packed with 3-/rm polymer particles for size exclusion chromatography. The more efficient and lower back pressure of monosized particles is applied in the separation. 

Figure 1.5 shows the cumulative pore volume curve for 5-/rm monosized porous PS-DVB particles with 50, 60, and 70% porosity. The curves were drawn by overlapping the measurements from nitrogen adsorption-desorption and mercury intrusion. A scanning electron micrograph of 5-/rm monosized particles with 50% porosity is shown in Fig. 1.6 (87). 

The particles build up Iqr layers because it has been found that all monosized particles can be removed from suspension by rotating at a specific speed. Thus, one runs the instrument at a series of rotational speeds, measuring the weight of the build-up layers in between each run. The overall analysis is run at specified rpm s which correspond to selected particle diameters, resulting in data sufficient to characterize the particle distribution. 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

The addition of fines to a powder system allows a larger top size of particle to be agglomerated due to the attendant increase in cohesive forces caused by a decrease in surface mean particle diameter and increase in agglomerate density. Thus, although eqn. (1) indicates a top size of about 150 pm for monosized particles with aqueous binders, the top size of feed for industrial disc pelletizers is usually higher at 30 to 50 mesh (300 to 600 /zm) with the provision that at least 25% should be finer than 200 mesh (75 /zm) [7]. Other liquids with surface tensions lower than that of water, or liquid/ solid systems in which the particle surface is imperfectly wetted, require finer particle sizes to make successful balling possible. 

The diffusion coefficient for a suspension of monosized particles can be measured directly by photon correlation spectroscopy [12] (quasielastic light scattering). For distributions of different particle sizes, the average diffusion coefficient is determined by photon correlation spectroscopy. 

When an ordered array of monosized particles is sintered, the vacancies and grain boundaries create pores, cracks, and other flaws which are difficult to remove dming sintering. Pores are flaws about the size of the original ceramic particles in the final sintered ceramic. Grain boundaries are flaws that lead to cracks of a size equivalent to the size of the ordered domain. Both these flaws lead to the failure of the final ceramic piece according to Griffiths s analysis ... 

Brus et al. prepared isolated silicon particles by high temperature pyrolysis of disilane with a subsequent passivation of the surface by oxidation [33]. The particles of various size are then processed by high-pressure, liquid-phase, size exclusion chromatography to separate sizes and obtain various fractions of monosize particles. Such particles represent an almost ideal model of silicon quantum dots. 

If the calibration constant as determined by equation (9.15) is significantly smaller Irom that using monosize particles it is likely that the whole range of powder has not been examined. In that case, equation (9.15) may be used to determine the fraction undersize by comparing the experimental value of with the expected value. 

For Rayleigh scattering / = 0 at 90°. As R increases, theory shows that X is a periodic function of diameter for monosize particles, and this has been used to measure particle size [78] specifically the size of aerosols in the size range 0.1 to 0.4 pm [79]. It has also been used to determine the sizes of sulfur solutions [80] In this work, transmission and polarization methods yielded results in accord with high order Tyndall spectra (HOTS) for sizes in the range 0.365 to 0.62 pm. In the limited region where (0.45[Pg.537]

Figure 6.3 Relative viscosity as a function of the fraction of large spheres in a bimodal distribution of particle sizes with a 5 1 ratio of diameters, at various total volume percentages of particles. The arrow P Q illustrates the 50-fold reduction in viscosity that occurs when monosized particles in a 60 vol% suspension are replaced by a 50-50 mixture of large and small spheres. The arrow P S shows that if monosized spheres are replaced by a bimodal size distribution, the concentration of spheres can be increased from 60% to 75% without increasing the viscosity. (Reprinted from Barnes et al., An Introduction to Rheology (1989), with kind permission from Elsevier Science - NL, Sara Burger-hartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The second condition can be obtained only with mixtures having an infinitely wide distribution. For monosized particles, C can not be greater than the maximum packing concentration (Cm). Furthermore, the third condition can be used to measure the solids conductivity by using solutions of known conductivities. 

Assuming that the pore diameter is characterized by the mean half hydraulic radius of the pore system, further assuming complete wetting and spherical monosized particles, the following equation is obtained ... 

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 ... 

Debbas" determined the distribution of the volume porosity of packings by saturating the pores with a filler material that hardens without shrinkage. The solid sample was then machined step by step in a lathe. The porosity of the concentric volume elements was calculated from the volume and weight of each portion thus removed and the densities of particles as well as filler material. Debbas found that it is easier to produce random packings by vibration with wide particle size distributions than with narrower ones it was most difficult with monosized particles. 

The most frequently used method for particle size distribution is based on an optical particle counter. Determination of monosize particles, flakes, and fibers is not accurate. In these cases either electron or optical microscopy are the most suitable techniques. 

Yan and Barbosa-Canovas (2000) also studied the effect of mixture conditions on particles, using ground coffee and cornmeal within different size ranges at proportions 1 3, 1 1, and 3 1 on their compressibility (C2) values. Compressibility results for each mixture showed a linear relationship with that of the monosize particles. The relationship can be described as... 

Fig. 10.1 shows a model with uniformly sized, spherical particles to explain the permanent attachment of a new particle into the surface of a growing wet agglomerate, yet narrowly sized particles of similar shape are not well-suited for growth agglomeration. In fact, only submicron (nano) monosized particles do naturally adhere to each other and form loose aggregates (Chapter 11). To be applicable for growth agglomeration, technical powders should feature a particle size distribution it is especially desirable that a sufficient amount of fines is present. 

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