For small particle sizes

The size of particles is of great importance, and particle size determinations should be carried out in preformulation as well in formulation functions. For small particle sizes, simple microscopy [41] may be used, but again imaging techniques, particularly with motorized stages, are more representative and much easier to carry out [42],... 

For small particle sizes the kinetic theory is applicable, whereas for large particle sizes the diffusion theory applies. A useful approximation is therefore to use the kinetic theory in the small particle range and the diffusion theory in the large size region. 

Ctl is the mass transfer term and arises because of the finite time taken for solute molecules to move between the two phases. Consequently, a true equilibrium situation is never established as the solute moves through the system, and spreading of the concentration profiles results. The effect is minimal for small particle size and thin coatings of stationary phase but increases with flow rate and length of column or surface. 

Case 1 h < 0.5. The average number of radicals per particle can drop below 0.5 if radical desorption from particles and termination in the aqueous phase are not negligible. The decrease in n is larger for small particle sizes and low initiation rates. 

Collective motion. A large number of small particles may move as a unit, carrying along part of the atmosphere. It has been shown (5) that for small Reynolds numbers the velocity of such systems with total number of particles between 25 and 125 is from 30 to 100% higher than the velocity of an isolated particle. This effect would certainly increase the correction factor dzjdz for small particle size and would probably... 

The penalty for small particle size is resistance to solvent flow. The pressure required to drive solvent through a column is... 

Adhesion — (a) When two compact materials, be they solid or liquid, are in intimate contact, attractive forces may act between their surface atoms or molecules. These forces are typically - van der Waals forces and electrostatic forces. The work of adhesion W (b)b(a) between the two phases (denoted A and B) is WAB = yA+yB -yAB> where yA and yg are the - interfacial tensions of A and B when each is interfaced only with the vapor phase, and yAB is the interfacial tension of the interface between A and B. In a more rigorous treatment (at thermodynamic equilibrium) each phase is regarded as saturated with the other phase [i]. In the case of liquid phases the equation for the work of adhesion is referred to as the -> Dupre equation. Adhesion forces between particles, or between particles and surfaces, dominate gravity for small particle sizes (pm and sub-pm range). In electrochemistry, increasing attention is being given to various phenomena related to the adhesion of vesicles [ii], particles [iii], droplets [iv], cells [v], etc. to electrode surfaces. 

The rate-limiting step in the Boudouard reaction is the chemical reaction at lower temperature (T< 1000°C) for small particle sizes (dp < 300/tin). Under these conditions, the reaction takes place on the internal surface of the coal particle. 

An attempt to account for the sensitivity of w on process variables, especially for small particle size distributions, appeared in 1957 and was later revised by Allander, Matts, and Ohnfeldt, who derived the expression... 

Microwave propagation in carbon black/epoxy resin composites shows that for small particle size inclusions, magnetic wave propagation increases with filler concentration but for large particles the propagation of magnetic waves does not depend on the concentration of the inclusions. ... 

In most cases, the shape of mineral particles could be considered more or less spherical, especially for small particle size, while the waste particles are of variant shape (spherical, wiry, platy etc). This shape variance in some cases hinders their effective separation, but in others it has a beneficial effect. 

At speeds higher than the reaction occurs with different particle sizes, and a graph of the overall rate of reaction vs. particle size is plotted. Such a graph is shown in Figure CSll.lc. For small particle sizes, the pore diffusional limitations are essentially absent (e = 1), and the overall rate of reaction is controlled by the chemical reaction. As the particle size is increased, the diffusional limitations become increasingly important, and above a certain particle size dp, the overall rate of reaction is determined by the diffusion of the reactants into the catalyst pores. The evaluation of the kinetic parameters for the reaction should be performed at impeller speeds higher than and particle sizes lower than dp. The reaction taking place on the catalyst surface itself is composed of various steps, such as (1) adsorption of the reactants on the active sites, (2) chemical reaction at the active sites, and (3) desorption of the products from the active sites. The rate of reaction can be written in terms of these varions steps (see Section 11.3). 

As part of this investigation, kerogen pyrolysis models different from the one proposed here were considered. One such model of theoretical appeal is similar in structure to the one given in Figure 9 but with a pure diffusion process for the heavy oil production. However, this alternative model is incompatible with some experimental findings It predicts lower coke concentrations on the surface of the particle than in the interior, whereas microprobe results indicate a uniform coke distribution. Further, this diffusion model predicts zero coke yield for infinitely small particles, whereas the limited amount of data available for small particle sizes suggest a leveling-off of the coke yield below a particle size of 0.4 mm. 

Using lower flow rate, efficiency is in general better, but the Van Deemter curve is non-uniform. It depends essentially on the particle size, the nature of the stationary phase, the structure of the solute and the temperature. For small particle sizes (3-5 Xm) the minimum is relatively flat and the slope of the Van Deemter curve is not steep. In reality, this means, that with 3-5 pm columns it is possible to work at higher flow rates - pressure permitting. The chromatographic analysis is faster and you do not lose a lot in separation performance. A decreased flow rate would not lead to a noticeable improvement of the separation. (A note in parenthesis for those interested improving... 

For small particle sizes (<25 nm diameter for gold), Cabs is the dominant term and Csca can be neglected [63], But with increasing particle size, Csca becomes larger, owing to the dependence on radius. Therefore, the behavior of the plasmon can be tuned with particle size. 

Itabirite mud system exhibited higher cumulative fluid loss volumes than barite mud system. It was observed that 0..5 Ibm/bbI concentration of DS or KXCD polymer for a large particle size of itabirite (between 74 and 125 microns), and 0.75 Ibm/bbI for small particle size of Itabirite (between 34-44 microns) were adequate to improve the filtration properties. 

In this study, Drispac Superlo or Kelzan XCD polymer with concentration of 0.25, 0.5, and 0.75 Ibm/bbI were used as coating agents for the purpose of lowering the abrasiveness. It is apparent from the results (Table 3) that 0.75 Ibm/bbI concentration of DS or KXCD for large particle sizes (74-125 microns) and 0.5 Ibm/bbI for small particle sizes (37-44 microns) were adequate for lowering the abrasivity of the itabirite mud system to the barite level. 

To accoimt for the effect of the particle velocity, the expression for VLIM was multiphed with a parameter of hnear function of particle velocity. For particles of diameter smaller than 20 pm, the particle—surface adhesion energy was calculated using the Bradley—Hamaker theory. ° In this theory, the particle—surface adhesion energy is determined through the concept of London—van der Waals forces (this assumption is only vahd for small particle sizes). For the case of a particle colliding with a cylindrical fibre, the adhesion energy is given by ... 

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