Particle radius, influence

Limitations It is desirable to have an estimate for the smallest particle size that can be effectively influenced by DEP. To do this, we consider the force on a particle due to DEP and also due to the osmotic pressure. This latter diffusional force will randomize the particles and tend to destroy the control by DEP Figure 22-32 shows a plot of these two forces, calciilated for practical and representative conditions, as a func tion of particle radius. As we can see, the smallest particles that can be effec tively handled by DEP appear to be in range of 0.01 to 0.1 piTidOO to 1000 A). 

If q fluid streomline passes within one particle radius of ihe collecting body, a particle traveling along Ihe streamline will touch ihe body and moy be collecled without the influence of inertia or brownian diffusion... 

Particle radius affects both the potential energy of interaction and the diffusion coefficient. Hence particle size influences the rate under all conditions. Under reaction-control conditions, Fig. 4 shows that a l-pm increase in particle radius reduces the deposition rate by a factor of 5, while under mass-transfer... 

Sample Preparation. The polystyrene spheres to be used should be monodis-perse with a particle radius i of about 50 nm, although any size in the range i = 30 to 100 nm is suitable. Such nanospheres are available commercially as aqueous latex suspensions with 1% to 10% PS by weight. A small amount of this latex suspension should be diluted 100- to 1000-fold. Using a microsyringe, take 0.1 mL from the PS stock, deliver this into a rinsed dilution bottle, and then add 10 mL of a hltered lO-mM solution of NaCl or other 1 1 electrolyte. The purpose of this electrolyte is to partially suppress coulombic interactions (electrostatic double-layer repulsion) that can influence the diffusion constant and lead to R values that are artificially high by —10%. The electrolyte solution should be prepared from distilled water and stored at room temperature. Before use, it must be hltered through a suitable membrane (0.1-jum pore size) to remove dust particles. Avoidance of dust is cracial, and capped dilution bottles should be used. 

For instance, the Bohr radius of in muonic Pb is only about 4 fm, whereas the radius of the nucleus is about 7 fm. Finally, the muon may be captured by the nucleus or it may decay as a free particle. The influence of the charge distribution in nuclei on muons is also greater than that on electrons, and X rays emitted by muonic atoms, in particular from inner orbitals, give information about the charge distribution and surface structure of nuclei. The influence of electron densities and chemical bonds has been studied by use of pionic atoms, such as p 7r. ... 

This shows that R is independent of both the field applied and the flow rate, and it is dependent only on the particle radius and the channel thickness. In fact, the retention ratio values corresponding to the pure steric elution mode have been seldom observed experimentally [12]. The observed values often correspond to the focusing elution mode as a result of the action of some additional forces influencing retention behavior of analytes. 

In the process involving inertialess approach of particles to the bubble surface, their size also plays an important role. It is in the equatorial plane that the closest approach of the streamline to the bubble surface is attained. In Fig. 10.3 the broken line (curve 1) represents the liquid streamline whose distance from the bubble surface in the equatorial plane is equal to the particle radius. Some authors erroneously believe that this liquid streamline is limiting for the particles of that radius. The error consists in that the SRHI is disregarded. Under the influence of the SRHI the particle is displaced from liquid streamline 1 so that its trajectory (curve 2) in the equatorial plane is shifted from the surface by a separation greater than its radius. Therefore, no contact with the surface occurs and, correspondingly, b(ap) is not a critical target distance, b. 

Electron transport in the nanoparticles may be influenced by bulk and surface scattering and trapping. If the mean free path of the electron is much smaller than the particle radius, additional surface scattering will not have much effect on the movement of electrons from particle to particle. However, if the mean free path of the electrons is larger than the particle radius, scattering at the surface becomes important. The geometry of the junction between particles is also likely to influence carrier... 

Before the critical moment of a-y transition, when particles are relatively small and electron attachment is not effective, the electron balance is determined by ionization and electron losses to the walls. The a-y transition is the moment when the electron attachment to the particles exceeds the electron losses to the walls. The electron temperature increases to support the plasma balance (Belenguer et al., 1992). The total mass and volume of the particles remain almost constant during coagulation therefore, the specific surface of the particles decreases with the growth of mean particle radius. Hence, the influence of the particle surface becomes more significant, when the specific surface area decreases. Relation (8-154) explains the phenomenon the exponential part of the electron attachment dependence on particle radius is much more important than the pre-exponential factor. Comparison of the first and second terms on the right-hand side of (8-154) gives a critical particle size required for the a-y transition ... 

With regard to particle size effects contradictory results have been published (11,12). Assuming that the filler particles change the properties of the resin In the Immediate neighbourhood (13), an Influence of particle size should be expected. A reduction of particle radius from 25 to 1 means a 1600 fold number of particles and a 300 fold surface area. Even if actually Important aspects like agglomeration of filler particles and filler/matrix adhesion are neglected it seems almost impossible to deduce effective mechanical properties from constituent properties without knowing more about bondary layers. 

This predicts that V2 should be inversely related to the square root of the particle radius. This relationship holds with the caveat that the particle size must be large in comparison with the size of the polymer chains. We further note that the presence of steric layers may dramatically influence any predicted dependence upon particle size. 

From (10.54), it follows that increase of the particle size and the shear rate makes the frequency of shear coagulation larger in comparison with that of Brownian one. The particle radius has an especially strong influence ( a ) on the ratio (10.54). It is worth to note that the parameter (10.54) is just the Peclet number, equal to the ratio of the characteristic time of Brownian coagulation to the characteristic time of gradient coagulation. 

Consider now motion of small particJes in turbulent flow of liquid. Assume that the volume concentration of particJes is small enough, so it is possible to neglect their influence on the flow of hquid. The large-scale pulsations transfer a particJe together with layers of hquid adjoining to it. Small-scale pulsations with A R, where R is particle radius, cannot involve the particJe in their motions -the particle behaves in this respect as a stationary body. Pulsations of intermediate scales do not completely involve the particle in their motion. Consider the case most interesting for apphcations, when respective densities of particle p and external liquid are only slightly different from one another, and radius of the particle is much less than inner scale of turbulence, that is R A . Thus, for water-oil emulsion pjp 1.1-1.5. Let Uq be the velocity of hquid at the particle s location, and Ui the velocity of particJe relative to hquid. At full entrainment of particle by the hquid, the same force would ad on the particle as on... 

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