Two particle size distributions

Figure 11 Dissolution of two particle size distribution fractions of a water-insoluble drug (solubility in water at 37°C < 10 g/mL). Equation (41) was used to calculate the values shown by the dashed line, which represents the estimated dissolution of the drug based on the particle size distribution and solubility determined experimentally. 

To characterize a ceramic powder, a representative sample must be taken. Methods of sampling and their errors therefore are discussed. Powder characteristics, including shape, size, size distribution, pore size distribution, density, and specific surface area, are discussed. Emphasis is placed on particle size distribution, using log-normal distributions, because of its importance in ceramic powder processing. A quantitative method for the comparison of two particle size distributions is presented, in addition to equations describing the blending of several powders to reach a particular size distribution. 

For quality control purposes, ceramists are often required to determine if the particle size distribution of one batch of powder is the same or different from another. This determination is difficult when the two batches of powder have similar mean sizes. A statistical method [19] must be used to make this distinction. To determine if two particle size distributions are the same or different. Student s t-test is used by applying the null hypothesis to the two sample means. For normal distributions the f-statistic is defined as tl rati of the difference between the two sample arithmetic means (A and A2) to the standard deviation of the difference in the means [20] ... 

Viscosity is also a function of width of distribution. It appears that viscosity is reduced as polydispersity increases. Figure 28 depicts two particle size distributions that exhibit the same mean size however, the viscosity of the wider distrihu-... 

Which of the two particle size distributions given in Table 2.A1.1, if suspended in a liquid, would you expect to give higher mass recovery in a gravity settling tank and why ... 

Table 2.A1.1 Two particle size distributions determined by sedimentation (in per cent by mass)...

The relevant mean to be used in the comparison of the two particle size distributions of this example is, therefore, the quadratic mean of the mass distribution. The graphical method outlined in section 2.4, when applied to the data given in the above example, yields the plots in Figure 2.A1.2. As the question does not require numerical answers, it is merely necessary to decide from the plots which of the two would give the greater area between the curve and the y axis. 

Equations 3.22, 3.23 and 3.24 require plotting the composite functions of two solid size distributions and the total efficiency and finding the maximum (see the worked example elsewhere ), which requires no differentiation and can be performed easily in industrial production situations. Naturally, the test information necessary for this calculation is the same as for the grade efficiency curve itself two particle size distributions and the total efficiency Ej. 

Particle size measurements must always be related to their purpose, particularly the accuracy necessary in different regions of the particle size range. The determination of the grade efficiency of separation equipment is particulary difficult because it represents, essentially, the difference in two particle size distributions. At least one of the distributions must be accurately known at the ends of the distribution. In this paper we report on... 

In the second process, a small particle-size latex is prepared and treated so that a limited and controlled degree of particle agglomeration occurs. The agglomerated latex is then concentrated as before but, because of the particle-size distribution obtained, the soHds may be raised to ca 70 wt %. Two methods exist for agglomeration of latices, ie, chemical and freeze agglomeration (45,46). 

The two steps in the removal of a particle from the Hquid phase by the filter medium are the transport of the suspended particle to the surface of the medium and interaction with the surface to form a bond strong enough to withstand the hydraulic stresses imposed on it by the passage of water over the surface. The transport step is influenced by such physical factors as concentration of the suspension, medium particle size, medium particle-size distribution, temperature, flow rate, and flow time. These parameters have been considered in various empirical relationships that help predict filter performance based on physical factors only (8,9). Attention has also been placed on the interaction between the particles and the filter surface. The mechanisms postulated are based on adsorption (qv) or specific chemical interactions (10). 

Preparation of Dispersion. The reduction process is a two-phase reaction between soluble reducing agent and insoluble dye particles, and therefore the rate of reduction is influenced by the particle size distribution of the dye dispersion. The smaller the particle size the greater the surface area and hence the more rapid the reduction process. However, if the particles are too small, migration will occur in continuous dyeing. It is therefore extremely important to control the size and range of particle size and this is a closely guarded piece of dyestuff manufacturers know-how. 

Wagner (1961) examined theoretically the growdr kinetics of a Gaussian particle size distribution, considering two growth mechanisms. When the process is volume diffusion controlled... 

Where the polyurethane comprises <30% of the blend, the polyurethane remains in discrete droplets within the polyacetal matrix. In this range the particle size and particle size distribution of the elastomer particles are of importance. Where the elastomer component is in excess of 30%, interpenetrating polymer networks exist in the sense that there are two interpenetrating continuous phases (as opposed to two cross-linked interpenetrating polymer systems). 

In the production of particleboards, mixtures of particles are often used as raw material. The particles differ in size and shape. A particle size distribution can be done by screening, and two of the three dimensions of the particle must be smaller than the standard measure of the screen to be passed. An exact screening of the particles to their size is only possible for rather similar shapes. Particles, however, can widely differ in shape. For a simplifying description, the shape is assumed as a flat square of length I, width b and thickness d for medium and coarse particles and cubic for the fines. The mechanical screens are graded in... 

Equation 6-108 is also a good approximation for a fluidized bed reactor up to the minimum fluidizing condition. However, beyond this range, fluid dynamic factors are more complex than for the packed bed reactor. Among the parameters that influence the AP in a fluidized bed reactor are the different types of two-phase flow, smooth fluidization, slugging or channeling, the particle size distribution, and the... 

In principle, the velocities c and ti can be determined by taking a series of pictures at a very high frequency of the flow through a transparent plastic tube. Because of the particle size distribution, each particle moves at a different velocity, and this makes this method difficult to apply in practice. We have therefore used an indirect method, where we have measured the pressure losses of pneumatic conveying for two mixture ratios and then fit the parameters so that Eq, (14.126) coincides as accurately as possible with measured pressure losses. 

The complete mathematical definition of a particle size distribution is often cumbersome and it is more convenient to use one or two single numbers representing say the mean and spread of the distribution. The mean particle size thus enables a distribution to be represented by a single dimension while its standard deviation indicates its spread about the mean. There are two classes of means ... 

The general form of the population balance including aggregation and rupture terms was solved numerically to model the experimental particle size distributions. While excellent agreement was obtained using semi-empirical two-particle aggregation and disruption models (see Figure 6.15), PSD predictions of theoretical models based on laminar and turbulent flow considerations... 

Two-phase suspension systems produce beaded products with broader particle-size distribution (e.g., 1-50 /rm). The microspherical particles usually need to be classified repeatedly to reduce the particle-size distribution in order to improve the resolution and efficiency in the separation for use in chromatography. The actual classification process depends on the size range involved, the nature of the beaded product, and its intended applications. Relatively large (>50 /rm) and mechanically stable particles can be sieved easily in the dry state, whereas small particles are processed more conveniently in the wet state. For very fine particles (<20 /rm), classification is accomplished by wet sedimentation, countflow setting, countflow centrifugation, or air classification. 

The particle-size distribution of two test powders, spherical glass beads and crushed quartz was determined with different types of app (Ref 32), and indicate that the micro-mesh sieve data is in good agreement with those of other methods (Table 6) ... 

When Equation 9 is used in Equation 8 along with the relationships for the residence time distributions one obtains the following dimensionless particle size distributions for one- and two-tank systems. 

There are two notable features of the quantitative performance of this type of interface. It has been found that non-linear responses are often obtained at low analyte concentrations. This has been attributed to the formation of smaller particles than at higher concentrations and their more easy removal by the jet separator. Signal enhancement has been observed due to the presence of (a) coeluting compounds (including any isotopically labelled internal standard that may be used), and (b) mobile-phase additives such as ammonium acetate. It has been suggested that ion-molecule aggregates are formed and these cause larger particles to be produced in the desolvation chamber. Such particles are transferred to the mass spectrometer more efficiently. It was found, however, that the particle size distribution after addition of ammonium acetate, when enhancement was observed, was little different to that in the absence of ammonium acetate when no enhancement was observed. 

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