Particle growth rate, total

An expression for the number of particles formed during Stage I was developed, assuming micellar entry as the formation mechanism (13), where k is a constant varying from 0.37 to 0.53 depending on the relative rates of radical adsorption in micelles and polymer particles, r is the rate of radical generation, m is the rate of particle growth, is the surface area covered by one surfactant molecule, and S is the total concentration of soap molecules. 

Equation 2 describes the growth of each individual particle when its growth rate is determined by the diffusion of the solute from the bulk of the solution to the particle surface. The total consumption of solute from the solution may be obtained by expressing the growth rate as dn/dt = dV/dt = -4irr dr/dt, and adding the values of dn/dt for all the particles. This is simplest for a mono-disperse suspension, but may also be done for a polydisperse system. See Reference ( 3), page 301, and (34,35). ... 

To demonstrate the main features of the flow in horizontal CVD reactors, the deposition of silicon from silane is used as an example (87). The conditions are as follows an 8-cm-wide reactor with either adiabatic side walls or side walls cooled to the top wall temperature of 300 K, a 1323 K hot susceptor (bottom wall), a total pressure of 101 kPa, and an initial partial pressure of silane in H2 of 101 Pa. The growth rate of silicon is strongly influenced by mass transfer under these conditions. Figure 8 shows fluid-particle trajectories and spatially varied growth rates for three characteristic cases. 

Information on particle growth during either a seeded polymerization or during the growth stage of an un-seeded polymerization at different degrees of conversion also could enhance the understanding of the kinetics. In earlier work (4,5) the rate of polymerization, for polystyrene latexes primarily, has been related to the latex particle diameter and the total number of particles in the reactor. It would be useful to obtain kinetic data and develop the kinetic relationships for styrene (S)-butadiene (B) latexes. 

The total rate of particle growth is expressed by Eq. (39), ouly the micellar volume t>m should be exchanged by the volume of the precipitated oligomers. We do not differentiate between the volumes of dead and living particles, since the particles rapidly change from active to inactive and vice versa. 

Equation (4Ib) is valid when there are no polymer particles flowing into the reactor with all the particles nucleated within the reactor. It is assumed that density changes can be neglected and that particles follow the streamlines. These are reasonable assumptions in view of the small size of particles and the small density difference between particle and water. When two or more CSTRs are employed in series, however, one must remember that the total residence time of a polymer particle is made up of different times in each reactor in the train. The relative amounts of time spent in each reactor will not matter when the volumetric growth rate of a particle is the same in each. This would require that the temperature, monomer concentration, and average number of radicals per particle he the same for each reactor, an unlikely possibility. This idealization is useful, however, when illustrating the effect of increasing the number of CSTRs in series on the breadth of the particle size distribution. 

Figure 27. Detailed in vitro mechanism of RNA replication by Q/ -replicase [59]. RNA grows exponentially as long as template concentration is below enzyme concentration. Growth rate becomes constant and hence RNA concentration rises linearly when template concentration exceeds that of enzyme, while, finally, at large template excess, rate decreases down to zero due to enzyme inhibition and template double-strand formation. In these in vitro experiments, Q -replicase is present as environmental factor. In vivo the enzyme is formed during the first 20 rain after infection of host cell followed by RNA replication during second half of infectious cycle. After about 40 min, about a thousand infectious phage particles per cell are released in burst. These thousand infectious particles usually are minor part of total burst size.

The population balance approach to measurement of nucleation and growth rates was presented by Randolph and Larson (1971, 1988). This methodology creates a transform called population density [n(L)], where L is the characteristic size of each particle, by differentiating the cumulative size distribution N versus L. shown in Fig. 4-22, where N is the cumulative number of crystals smaller than L. Per unit volume, the total number of particles, total surface area, and total volume/mass are calculated as the first, second, and third moments of this distribution. 

Figure 16. Total and regional distribution of hygroscopic particles in the lung. Oral breathing tidal volume, 500 ml breathing rate, 13.7 breaths per minutes. 1, non-hygroscopic 2, hygroscopic. Solid line, total deposition dotted line, deposition in pulmonary region dashed line, deposition in tracheobronchial region. Reproduced from Pritchard JN (1987). Particle growth in the airways and the influence of airflow. In A New Concept in Inhalation Therapy (SP Newman, F Moren and GK Crompton, eds), Medicom...

During diffusionally controlled particle growth the rate at which the radius of the spherical particle, r, increases, is related to the total flux of substance to its surface, js (moles s 1), as... 

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