Fine particles definition

Using this definition of the Thiele modulus, the reaction rate measurements for finely divided catalyst particles noted below, and the additional property values cited below, determine the effectiveness factor for 0.5 in. spherical catalyst pellets fabricated from these particles. Comment on the reasons for the discrepancy between the calculated value of rj and the ratio of the observed rate for 0.5 in. pellets to that for fine particles. 

This result can also be applied directly to coarse particle swarms. For fine particle systems, the suspending fluid properties are assumed to be modified by the fines in suspension, which necessitates modifying the fluid properties in the definitions of the Reynolds and Archimedes numbers accordingly. Furthermore, because the particle drag is a direct function of the local relative velocity between the fluid and the solid (the interstitial relative velocity, Fr), it is this velocity that must be used in the drag equations (e.g., the modified Dallavalle equation). Since Vr = Vs/(1 — Reynolds number and drag coefficient for the suspension (e.g., the particle swarm ) are (after Barnea and Mizrahi, 1973) ... 

It is not clear where cohesive forces will become important. The use of very dense particles (for the models of the one atmospheric bed) will cause a shift of the boundary of cohesive influence as given, for example, by Geldart s classification. However, adequate experimental data is still lacking with such dense fine particles to definitely set the limits of cohesive influence. 

The definition of a fine particle can be made more quantitative by introducing the article Stokes number St, which measures the particle-to-fluid response-time ratio to changes in the velocity (Fuchs, 1964) ... 

In this definition, ps and pt are the solid and fluid densities, respectively. The characteristic diameter of the particles is ds (which is used in calculating the projected cross-sectional area of particle in the direction of the flow in the drag law). The kinematic viscosity of the fluid is vf and y is a characteristic strain rate for the flow. In a turbulent flow, y can be approximated by l/r when ds is smaller than the Kolmogorov length scale r. (Unless the turbulence is extremely intense, this will usually be the case for fine particles.) Based on the Stokes... 

Many studies present and discuss in vitro and in vivo drug deposition resnlts obtained with inhalation systems. It is often difficult to compare in vitro results from different studies, because different testing equipment and different definitions for the fine particle dose may have been used. 

Dry-powder inhalers (DPIs) deliver the drug to the respiratory tract in aerosol form. An aerosol is by definition a suspension of free liquid or solid fine particles in a gas phase, which is air in the case of DPIs (and a compressed gas in the case of needle-free injection). The most prominent characteristic that determines the delivery of drug particles to the lungs is the particle size, although particle shape and density are also of considerable importance for the behavior of an aerosol in the respiratory tract (Brain and Blanchard 1993 Gonda 1992 Heyder et al. 1986 Agnew 1984 Heyder et al. 1980). 

Ultrafine particles have been defined as those, which are smaller than 0.1 pm. Another classification is into submicrometre particles, which are smaller than 1 pm, and supermicrometre particles, which are larger than 1 pm. The terminology that has been used in the wording of the ambient air quality standards, and also for characterisation of indoor and outdoor particle mass concentrations, includes PM2.5 and PM fractions and the total suspended particulate (TSP). PM2.5 (fine particles) and PM, are the mass concentrations of particles with aerodynamic diameters smaller than 2.5 and 10 pm, respectively (more precisely the definitions specify the inlet cutoffs for which 50% efficiency is obtained for these sizes). TSP is the mass concentration of all particles suspended in the air. There have been references made in the literature to PMj or PMq 1 fractions, which imply mass concentrations of particles smaller than 1 and 0.1 pm, respectively. These terms should be used with caution, as particles below 1 pm, and even more those below 0.1 pm, are more commonly measured in terms of their number rather than their mass concentrations, and therefore these terms could be misleading. 

Separation operations are frequently classified according to the size of particles. No precise size definitions exist for terms such as ultra-, micro-, nano-, colloidal, and fine particle filtration. Different authors use different nomenclature in classifying separations in terms of size. A simplified classification is shown in Table 22.1. 

Definition of Suspension. The rheology of suspensions deals with how suspensions respond to an applied stress or strain. The term suspension refers, in general, to dispersions of solids in fluids, although the term aerosol is conventionally used to refer to dilute suspensions of fine particles in a gas and the term emulsion is used to identify (concentrated) suspensions of particles in a gas or liquid in the field of fluidization. However, emulsion is conventionally defined as the dispersion of a liquid in another (immiscible) liquid. In a broader sense, emulsions are also considered as suspensions. In this chapter, we deal mainly with suspen-... 

An important feature of atmospheric aerosol size distributions is their multimodal character. Mass distributions, measured in urban centers, are characterized by three modes with a minimum between 1.0 and 3 The size range of particles larger than the minimum (supermicron particles) is termed coarse, while the smaller particles are called fine. The three modes present in the mass distribution of Figure 7.14 correspond to the nuclei mode (particles below 0.1 /zm), accumulation mode (0.1 < Dp < /.tm), and coarse mode Dp > )Lim) (Whitby and Sverdrup, 1980). Thus the fine particles include both accumulation and nuclei modes. The boundaries between these sections are not precise (recall in Chapter 2 that we divided fine and coarse modes at 2.5 /zm diameter). Note that our definition of modes has been based on the mass (or volume distribution). The location of modes may be different if they are based on the number or surface distribution. 

Further distinction has to be made between conventional filtration of fine particle less than 10 pm in diameter, and microfiltration. It would be unusual for the filtration of such particles on a conventional fiher cloth to be described as ndcrofiltratian. Thus microfihration is constituted by the filtration of small particles and by the medimn which is used for the filtration. Conventional fihration is undertaken on filter cloths with a very open structure, see Chapter 4, whereas membrane fihration is usua% concerned with fihration enq>loying membrane media where the equivalent pore size is of the order of 10 pm, or less. These definitions are, however, becoming less distinct as it is now possible to obtain conventional fihration equ ment employing membrane-type fiher media, as discussed in Chapter 4, and crossflow microfilters enqploying conventional filter cloth. 

The term particle (or grain) size refers to the structural make-up of such substances as granulates, powders, dusts, granular mixes, and suspensions. Knowledge of the particle size, in conjunction with the comminution process, determines such details as grinding efficiency and ultimate product fineness. To establish particle sizes and their distribution within powdered systems, the user can have recourse to a number of different measuring processes designed to indicate, with appropriate particle definition, details of the probable equivalent diameter of a particle. 

Most rubber is reinforced by carbon black silicone rubber is not. Instead, it is reinforced by fine-particle-size fumed silica. This definitely improves tensile strength, though it still cannot equal most other types of elastomers (Table 3.38). Other fillers do not increase strength tjut may be used to improve processability, increase hardness and reduce tack and compression set. Carbon black is used to increase electrical conductivity. 

It will be noted that there is a definite relationship between the process in which fine particles stick to coarse particles, i.e., the ratio KfjKff, and the adhesion of particles to a surface, i.e., the adhesion number yp. The greater the ratio > the greater the adhesion number. This indicates a direct relationship between adhesion processes when a suspension comes into contact with a vessel wall and the sticking of fine particles to larger particles in a suspension. 

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