Population of particles

Distribution Averages. The most commonly used quantities for describing the average diameter of a particle population are the mean, mode, median, and geometric mean. The mean diameter, d, is statistically calculated and in one form or another represents the size of a particle population. It is usefiil for comparing various populations of particles. 

If the secondary stream contains emulsifier it can function in three ways. When the emulsion feed is started quickly the added emulsifier can serve to lengthen the particle formation period and hence to broaden the particle size distribution. When the emulsion feed is started later and added in such a manner that the emulsifier is promptly adsorbed on existing particles, one can obtain quite narrow size distributions. If the emulsion feed is started later but added rapidly enough to generate free emulsifier in the reaction mixture a second population of particles can be formed, again yielding a broad size distribution. 

Thermodynamic processes play an important, or even dominant, role in all branches of science, from cosmology to biology and from the vastness of space to the microcosmos of living cells. Energy and entropy determine and direct all the processes which occur in the observable world. Thermodynamics only describes the properties of large populations of particles it cannot make any statements about the behaviour of single atoms or molecules. The most important properties of a system are determined by ... 

Since none of the surfactants used are liquids, oil-in-water microemulsions or emulsions cannot be the basis for the existence of the larger-diameter population (or even the smaller-diameter population) of particles detected. 

Interval II) of a 0-1-2 system. By a 0-1-2 system, we imply one in which particles can contain only 0, 1 or 2 free radicals, the populations of particles containing more than two free... 

Cover illustration Left panel Stochastic description of the kinetics of a population of particles, Fig 9.15. Middle panel Dissolution in topologically restricted media, Fig. 6.8B (reprinted with permission from Springer). Right panel A pseudophase space for a chaotic model of cortisol kinetics, Fig.11.11. 

Strawbridge, K.B., Ray, E, Hallett, F.R., Tosh, S.M., Dalgleish, D.G. 1995. Measurement of particle size distributions in milk homogenized by a microfluidizer estimation of populations of particles with radii less than 100 nm.. /. Coll. Interface Sci. 171, 392-398. 

These two equations are similar but have very different interpretations. Equation (2.7) describes an n-particle system in 3-dimensional space. Equation (2.8) can be considered to describe the diffusion of a collection of particles (called walkers here to avoid confusion) in 3n-dimensional space with a source or sink. The function T gives the distribution of the walkers in this space. Each walker is a point in 3n-dimensional space. Equation (2.8) can be solved by permitting each of the walkers to make a 3n-dimensional random walk, and for the population of particles to grow or shrink according to the potential term. 

The microscopic size data for a population of particles shown in Table... 

With a reactor in which single-point nucleation, giving a population with particles all the same size, is followed by growth, the population of particles has the following form [33], plotted in Figure 7.15 as cumulative distribution ... 

Appl5ing the new birth and death functions given in equations (7.53) and (7.55), respectively, the governing differential equation for the population of particles, rj(r, t), becomes... 

The size of a particle may be expressed by a single dimension using one of the diameters defined in Table 2.1. The differences between these dimensions increase as the particle diverges in shape from a sphere. For a population of particles whose shape is not size dependent, distributions obtained using different methods of analysis may be homologous. Multiplying the sizes of one distribution by a constant (shape) factor will therefore generate the other distribution. 

Lipschultz, F. (1995). Nitrogen-specific uptake rates of marine phytoplankton isolated from natural populations of particles by flow cytometry. Mar. Ecol. Prog. Ser. 123, 245—258. 

The development here follows that of Lichti et af. (1980). By analogy with the MWD calculation for bulk and solution polymerizations presented earlier, the MWD formalism for monodisperse emulsion systems requires the evaluation of certain types of free-radical growth time distributions. Because of the variable nature of the reaction loci (depending on the state i), a separate growth time distribution is required for the population of particles in each state i. It is therefore convenient to define the distribution of singly distinguished latex particles in state i. denoted as the... 

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