Particle dependence

When used to separate solid-solid mixtures, the material is ground to a particle size small enough to liberate particles of the chemical species to be recovered. The mixture of solid particles is then dispersed in the flotation medium, which is usually water. Gas bubbles become attached to the solid particles, thereby allowing them to float to the surface of the liquid. The solid partices are collected from the surface by an overflow weir or mechanical scraper. The separation of the solid particles depends on the different species having different surface properties such that one species is preferentially attached to the bubbles. A number of chemicals are added to the flotation medium to meet the various requirements of the flotation process ... 

It is helpful to distinguish three different types of problem to which Newton s laws of motion may be applied. In the simplest case, no force acts on each particle between collisions. From one collision to the next, the position of the particle thus changes by v,5f, where v, is the (constant) velocity and 6t is the time between collisions. In the second situation, the particle experiences a constant force between collisions. An example of this type of motion would be that of a charged particle moving in tr uniform electric field. In the third case, the force on the particle depends on its position relative to the other particles. Here the motion is often very difficult, if not impossible, to describe analytically, due to the coupled nature of the particles motions. 

Nonsplierical Rigid Particles The drag on a nonspherical particle depends upon its shape and orientation with respect to the direction of motion. The orientation in free fall as a function of Reynolds number is given in Table 6-8. 

Even the void fraction together with particle size distribution does not provide all of the necessary information on the kind of flow. The mutual forces between distinct particles depend not only on the distance between the particles but also on the surface properties of the particles. The strength of the attractive forces between particles depends on conditions. For instance, the moisture content of the solid is essential for determining the attractiv c forces between particles, especially for hydroscopic materials such as wood. Airflow between particles usually tends to separate particles, whereas the surface forces, adhesion forces, tend to bring them together. 

Moderate tolerance of dirt particles, depending on hardness of bearing... 

Third, a complicated question on the role of the dispersion of particles dimensions of particles dimensions is of independent value it is known that the viscosity of equi-concentrated dispersions of even spherical particles depends on the fact if spheres of one dimension or mixtures of different fractions were used in the experiments and here in all the cases the transition from monodisperse particles to wide distributions leads to a considerable decrease in viscosity [21] (which, certainly, is of theoretical and enormous practical interest as well). 

The Emerman quantitative model [40] makes it possible, with sufficient accuracy, to predict the redistribution of filler particles depending on the parameters of processing and to explain the existing (still not extensive) experimental data. Good agreement should be noted between the experimental data and those calculated according to the Emerman model [40],... 

The y-ray absorption method of determining in-line concentration (hold-up) of particles depends on the different degree to which the solid and the liquid attenuate y-rays details of the method are given in the literature 1314). 

The rate of polymerization with styrene-type monomers is directly proportional to the number of particles formed. In batch reactors most of the particles are nucleated early in the reaction and the number formed depends on the emulsifier available to stabilize these small particles. In a CSTR operating at steady-state the rate of nucleation of new particles depends on the concentration of free emulsifier, i.e. the emulsifier not adsorbed on other surfaces. Since the average particle size in a CSTR is larger than the average size at the end of the batch nucleation period, fewer particles are formed in a CSTR than if the same recipe were used in a batch reactor. Since rate is proportional to the number of particles for styrene-type monomers, the rate per unit volume in a CSTR will be less than the interval-two rate in a batch reactor. In fact, the maximum CSTR rate will be about 60 to 70 percent the batch rate for such monomers. Monomers for which the rate is not as strongly dependent on the number of particles will display less of a difference between batch and continuous reactors. Also, continuous reactors with a particle seed in the feed may be capable of higher rates. 

Airborne particulate matter may comprise liquid (aerosols, mists or fogs) or solids (dust, fumes). Refer to Figure 5.2. Some causes of dust and aerosol formation are listed in Table 4.3. In either case dispersion, by spraying or fragmentation, will result in a considerable increase in the surface area of the chemical. This increases the reactivity, e.g. to render some chemicals pyrophoric, explosive or prone to spontaneous combustion it also increases the ease of entry into the body. The behaviour of an airborne particle depends upon its size (e.g. equivalent diameter), shape and density. The effect of particle diameter on terminal settling velocity is shown in Table 4.4. As a result ... 

Hence, we conclude that the translational partition function of a particle depends on its mass, the temperature, the dimensionality as 3vell as the dimensions of the space in vhich it moves. As a result, translational partition functions may be large numbers. The translational partition function is conveniently calculated per volume, which is the quantity used, for example, when the equilibrium conditions are determined, as we shall see later. The partition function can conveniently be written as... 

Hence, the concentration in the particle depends only on the Thiele modulus, s and a normalized radius r/R as illustrated in Fig. 5.34. 

As at other interfaces, the effective snrface charge of colloidal particles depends on the total concentration and composition of the solution, particnlarly on polyvalent or snrface-active ions that may be present. When the zeta potential is reduced below a certain critical (absolute) value, which is approximately 25 to 30 mV, the colloidal solution becomes nnstable. 

Thus, the probability density of the pair of particles depends on how we label the two particles. Since the two particles are indistinguishable, we conclude that neither 1 (1, 2) nor (2, 1) are desirable wave functions. We seek a wave function that does not make a distinction between the two particles and, therefore, does not designate which particle is at rj and which is at... 

Leggett (1992) also proposed a respiratory tract model. Deposition of americium particles, depending on their size, are assumed to deposit in three compartments representing extrathoracic, fast-clearing thoracic, and slow-clearing thoracic regions of the respiratory tract (Figure 3-8). 

The velocity of motion of the particles depends on their dimensions and shape, on the interaction (e.g. association) between the solvent molecules and finally on the interaction between particles of the dissolved substance and solvent molecules. Consider the simplest case, where the molecule of the dissolved substance is much larger than the solvent molecule, is spherical and the interaction between the solute molecules and the solvent is negligible. Then the motion of the particles of the solute can be considered as the motion of spherical particles with radius rf through a viscous medium with viscosity coefficient rj. The velocity v is then described by the Stokes law ... 

The restricted access principle is based on the concept of diffusion-based exclusion of matrix components and allows peptides, which are able to access the internal surface of the particle, to interact with a functionalized surface (Figure 9.2). The diffusion barrier can be accomplished in two ways (i) the porous adsorbent particles have a topochemically different surface functionalization between the outer particle surface and the internal surface. The diffusion barrier is then determined by an entropy controlled size exclusion mechanism of the particle depending on the pore size of adsorbent (Pinkerton, 1991) and (ii) the diffusion barrier is accomplished by a dense hydrophilic polymer layer with a given network size over the essentially functionalized surface. In other words, the diffusion barrier is moved as a layer to the interfacial... 

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