Nucleation critical saturation ratios

Several modifications of this nucleation equation have been suggested by Zeldovitch [24] that allow Figure 7.5 [25] to be drawn, which shows the nucleation rate as a fimction of the saturation ratio and the number of atoms in the critical embiyo (see Section 6.3 for details). The nucleation rate is veiy low for small values of the saturation ratio. But, at a critical saturation ratio, the nucleation rate increases drastically and saturates at a maximum rate corresponding to the condensation rate, times the molecular density, PJk T. 

Two effects are observed in homogeneous nucleation experiments for all substances. First, the nucleation rate is always a steep function of saturation ratio S. The second feature common to all systems is that the critical saturation ratio Sc decreases as T increases, and J increases as T increases at constant S. Also, critical nuclei become smaller as 5 increases and as T increases. 

The traditional method of studying gas-liquid nucleation involves the use of a cloud chamber. In such a chamber the saturation ratio 5 is changed until, at a given temperature, droplet formation is observable. Because once clusters reach the critical size for nucleation, subsequent droplet growth is rapid, the rate of formation of macroscopically observable droplets is assumed to be that of formation of critical nuclei. In such a device it is difficult to measure the actual rate of nucleation because the nucleation rate changes so rapidly with S. J is very small for S values below a critical saturation ratio 5, and very large for S > 5,. Thus what is actually measured is the value of 5, defined rather arbitrarily by the point where the rate of appearance of droplets is 1 cm s . ... 

The self-similar solution of an unsteady rarefaction wave in a gas-vapour mixture with condensation is investigated. If the onset of condensation occurs at the saturation point, the rarefaction wave is divided into two zones, separated by a uniform region. If condensation is delayed until a fixed critical saturation ratio Xc > 1 is reached, a condensation discontinuity of the expansion type is part of the solution. Numerical simulation, using a simple relaxation model, indicates that time has to proceed over more then two decades of characteristic times of condensation before the self-similar solution can be recognized. Experimental results on heterogeneous nucleation and condensation caused by an unsteady rarefaction wave in a mixture of water vapour, nitrogen gas and chromium-K)xide nuclei are presented. The results are fairly well described by the numerical rdaxation model. No plateau formation could be observed. 

Similar to the case for homogeneous nucleation, Eq. 14.12 can be differentiated, set equal to zero, and used to determine an expression for the saturation ratio at critical drop diameter ... 

FIGURE 6.6 Generalized nucleation rate diagram that describes the homogeneous nucleation rate as a function of the saturation ratio. The number of ions in a critical nucleus, n. is given by equation (6.21) and A = 4j8 -y V / 27/ [feBTln(10)P. Experimental nucleation rates, , are from a BaS04 precipitation reaction. Redrawn, with permission... 

As already noted in the introductory sections, AIDA ice nucleation studies primarily focus on a precise determination of the critical ice saturation ratio for relevant aerosol types like H2SO4/H2O solution droplets, mineral dust and soot particles, as well as internally mixed aerosol particles. The ice saturation ratio Sice(T)... 

Ice particle measurements in the expansion experiment with 40% OC soot aerosol markedly differ from the 16% OC sample. Note that the optical particle spectrometer hardly detects any ice particles. Additionally, extinction signatures of ice are barely visible in the infrared spectra and diere is only a weak intensity increase of the back-scattered laser light in course of the expansion. The number concentration of ice crystals is less than 10 cm, thus < 1% of the seed aerosol particles act as deposition ice nuclei. In contrast to the 16% OC experiment, no precise critical ice saturation ratio can be specified for the 40% OC soot sample. RHi continues to increase to 190% because very little water vapour is lost on the small surface area of the scarce ice crystals. In summary, die comparison of the two expansion experiments provides first evidence that a higher fraction of organic carbon notably suppresses the ice nucleation potential of flame soot particles. 

Here, r is the particle radius, y is the surface energy of particles, and A v is specific volume energy change. From this formula, it can be understood that the solubility of nuclei depends on particle size and they cannot exist stably in a solution when their size is less than the critical size, whereas they are stable when their size exceeds it. The particles of critical size are generally called critical nuclei. Nucleation rate (7) can be determined by saturation ratio as shown in the following formula ... 

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