Particle number density

In the MSMPR crystallizer at steady state, the increase of particle number density brought about by particle growth and agglomeration is compensated by withdrawal of the product from the crystallizer. 

Film-crystal model concentration profiles of A, B and C and particle number density distributions are shown in Figure 8.14(a). 

At high-particle number densities or low coefficients of normal restitution e, the collisions will lead to a dramatical decrease in kinetic energy. This is the so-called inelastic collapse (McNamara and Young, 1992), in which regime the collision frequencies diverge as relative velocities vanish. Clearly in that case, the hard-sphere method becomes useless. 

Thus, the source terms for each environment S(c) and Sk ((/)) will be closed. Of particular interest are the local nucleation rates /(c ). As discussed in Wang and Fox (2004), due to poor micromixing the local nucleation rates can be much larger than those predicted by the average concentrations /((c)). This results in a rapid increase in the local particle number density mo due to the creation of a very large number of nuclei. As discussed below, this will have significant consequences on the local rate of aggregation. 

The Einstein equations Eqs. (6)-(9) contain two extra variables compared to the more familiar 4 dimensional case, namely P5 and 4>. However, P (n) is a known function of the particle number density and specified by the actual interaction in the matter. Thus (r ) is the only new degree of freedom determined by the extra equation. 

First, there are constraints among the material quantities, which are rather straightforward for ideal quantum fluids. In case of interacting matter one can recall the self-consistent description of the interacting fermions in the 4 dimensional analogy [13], Second, the particle number density in the center, n(r = 0), is a free initial condition, as it was in the 4 dimensional case. Instead of density, we may use energy density, e(r = 0) = 0 as well. 

Although might be anything at rs from the matching conditions, it will be zero for all general (not very exotic) systems. Namely, P = 0 is expected at some low particle number density ns on the surface, which is generally much below Po = h/Rc. So motions in the hth dimension cease already somewhere in the interior of the star. 

One of the earliest detailed diagnostic efforts on sooting of diffusion flames was that of Wagner et al. [86-88], who made laser scattering and extinction measurements, profile determinations of velocity by LDV, and temperature measurements by thermocouples on a Wolfhard-Parker burner using ethene as the fuel. Their results show quite clearly that soot particles are generated near the reaction zone and are convected farther toward the center of the fuel stream as they travel up the flame. The particle number densities and generation rates decline with distance from the flame zone. The soot formation rate appeared to... 

Fig. 38 (Upper panel) Scanning force microscopy images of gold nanoparticles (diameter 17 nm) adsorbed along a surface-anchored poly(acryl amide) brush with a molecular weight gradient (Edge of each image = 1 p.m). (Lower panel) Dry thickness of poly(acryl amide) on the substrate before particle attachment (right, ) and particle number density profile (left, ). (Reproduced with permission from [140])...

At a certain temperature, therefore, the pressure exerted by a gas depends only on the particle number density and not on the nature of the gas. The nature of a gaseous particle is characterized, among other facters, by its... 

The product of the particle number density n and the particle mass m is the gas density p ... 

Thus the mean free path length X for the particle number density n is, in accordance with equation (1.1), inversely proportional to pressure p. Thus the following relationship holds, at constant temperature T, for every gas... 

The gas molecules fly about and among each other, at every possible velocity, and bombard both the vessel walls and collide (elastically) with each other. This motion of the gas molecules is described numerically with the assistance of the kinetic theory of gases. A molecule s average number of collisions over a given period of time, the so-called collision index z, and the mean path distance which each gas molecuie covers between two collisions with other molecules, the so-called mean free path length X, are described as shown below as a function of the mean molecule velocity c the molecule diameter 2r and the particle number density molecules n - as a very good approximation ... 

Classical physics teaches and provides experimental confirmation that the thermal conductivity of a static gas is independent of the pressure at higher pressures (particle number density), p > 1 mbar. At lower pressures, p < 1 mbar, however, the thermal conductivity is pressure-dependent (approximately proportional 1 / iU). It decreases in the medium vacuum range starting from approx. 1 mbar proportionally to the pressure and reaches a value of zero in the high vacuum range. This pressure dependence is utilized in the thermal conductivity vacuum gauge and enables precise measurement (dependent on the type of gas) of pressures in the medium vacuum range. 

The particle characteristics such as particle size, crg, yield, and particle number density were independent on the reaction time and temperature examined in the formation of Fe203 particles from an emulsion state. However, the particle characteristics are generally influenced by the reaction time and temperature in the particle formation from the hydrolysis in alcohol solution, because the reaction time and temperature promote the hydrolysis reaction. 

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