Particle-size distribution polydisperse

Particle size distribution Polydisperse, requires refinement to give narrower fraction before use in column packing Monodisperse as produced in the reactor... 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

Even when carefully prepared, model colloids are almost never perfectly monodisperse. The spread in particle sizes, or polydispersity, is usually expressed as the relative widtli of tire size distribution,... 

In order to cadculate a particle size distribution directly from the output chromatogram for a polydisperse system, the integral, dispersion equation for the chromatogram signal, F(V), as a function of elution volume, V, needs to be evaluated (27) ... 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

Leblanc and Fogler developed a population balance model for the dissolution of polydisperse solids that included both reaction controlled and diffusion-controlled dissolution. This model allows for the handling of continuous particle size distributions. The following population balance was used to develop this model. 

Equation (28) is valid only for monodisperse drugs. For polydisperse drugs, the overall fraction of dose absorbed may be estimated on the basis of the particle size distribution [44],... 

The distribution of molecular weights of each generation was determined from measurements on about 50 molecules, with results shown in Figure 12.19 (the weight fraction is the percent dendrimer in each interval of molecular weight under consideration). Based on these distributions, the polydispersity index (.MJMa) of G5 to G10 can be calculated, with results shown in Table 12.1 [39], They are all less than 1.08, which means that the particle size distribution is very uniform for each generation. 

In the case of a polydisperse system the calculation of the particle size distribution is possible by using special transformation algorithms. For this purpose certain requirements need to be fulfilled, such as a spherical particle shape, sufficient dilution, and a large difference between the refractive indices of the inner and the outer phases. Since usually not all requirements can be fulfilled, the z-average is preferred as a directly accessible parameter rather than the distribution fimction depending on models. 

In practice, we have a number of solid fuels, for example biofuels (forest or agricultural derived biofuels), coal, municipal solid waste (MSW) and many others [23]. A fuel bed is composed of varying sizes of solid-fuel particles, also called polydispersed solid-.fuels [15]. The fuel chemistry is different depending on whether it is coal, biofuel or MSW. The fuel bed can be dry or consist of moisture. The fuel physics are for example, particle size distribution, particle shape, particle density and bed permeability. 

The results were obtained for the polydispersed mixtures possessing the following characteristic properties of particle size distribution function (Figs. 14.1-14.2) ... 

Solid particles are not likely to be uniform spheres, even if the sample is carefully fractionated rather, they will be irregularly shaped and polydisperse, although the particle size distribution may be narrow. The smallest particles will have the largest effect on the solubility, but they may be the hardest to measure. 

The emulsion free-radical polymerization carried out in different steps ensures a precise control of the particle size and particle size distribution. The particle diameter can be adjusted between 100 nm and 1000 nm, with a low polydispersity (generally less than 1.1) (Chapter 8). Rubber particles with sizes lower than 100 nm are ineffective for toughening purposes (Sec. 13.3.2b). 

Colloidal systems are generally of a polydispersed nature - i.e. the molecules or particles in a particular sample vary in size. By virtue of their stepwise build-up, colloidal particle and polymer molecular sizes tend to have skew distributions, as illustrated in Figure 1.2, for which the Poisson distribution often offers a good approximation. Very often, detailed determination of relative molecular mass or particle size distribution is impracticable and less perfect experimental methods, which yield average values, must be accepted. The significance of the word average depends on the relative contributions of the various molecules or particles to the property of the system which is being measured. 

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

The minimum fluidisation velocity represents the lower limit of the range of operative conditions at which a fluid-bed process can be operated, while the particle terminal fall velocity represents the upper limit beyond which the particles will start leaving or elutriating from the bed. To avoid or reduce carryover of particles from a fluidised bed, gas velocity has to be kept between um( and ut. For polydisperse systems, in calculating wmr, the mean diameter dvs is used for the particle size distribution present in the bed. In calculating nt, the smallest size of solids present in appreciable quantity in the bed is used. 

Thus, given gparticle size distribution. For narrow size distributions, the autocorrelation function is satisfactorily analyzed by the method of cumulants to give the moments of the particle size distribution.(7) However, the analysis of QELS data for samples with polydisperse or multimodal distributions remains an area of active research.(8)... 

For polydisperse systems, replacement of equation 13 into equation 2 for every particle diameter, yields an approximation to the turbidity in terms of ratios of moments of the particle size distribution without having to make assumptions regarding the shape of the distribution ... 

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