Supersaturation critical, particles

As we have already seen, the critical supersaturation Sc. corresponding to the peak of the Kohler curve depends on a number of parameters unique to the aerosol particle. Thus, at a given supersaturation some particles will form cloud droplets and some will not. As a result, the total number of CCN will vary with the supersaturation used in the CCN measurement. This is illustrated in Fig. 14.39, which shows the concentration of CCN measured in Antarctica as a function of the percentage supersaturation for CCN that grow into droplets larger than 0.3 and 0.5 gm, respectively (Saxena, 1996). This particular set of measurements... 

Figure 14.7 Plot of saturation ratio or supersaturation as a function of critical particle diameter for soluble nuclei of 10-1B and 10-16 g.

In eq. (IV.3) the first term is positive and increases proportionally to r2 with increasing r. The second term may be negative (in the case of supersaturation - Ap>0), with absolute value increasing proportionally to r3. Thus, in the case of supersaturation, the W(r) curve must pass through a maximum. This maximum is characteristic to some critical particle size, rcr, corresponding to the critical nucleus of a new phase. The critical nucleus of size rzx exists in equilibrium (unstable equilibrium) with the mother medium, i.e. the p = ir condition (p,. is the chemical potential of the substance in the nucleus) stays valid. For such a nucleus, one can write in agreement with eq. (1.13) that... 

When describing the separation of a supersaturated solution in a small Particle, one must distinguish between the solubility Hmit (maximal concentration of impurity before separation) and the equilibrium concentration of the depleted parent phase after separation, the difference being called a critical supersaturation. Critical supersaturation is the thermodynamic characteristic depending on temperature and size. So, one can call it a size-dependent critical supersaturation. The solubihty in a small particles increases even without accounting for interactions with the boundaries of the particle (if the density change is neglected). 

A reduction in the magma density will generally increase nucleation and decrease the particle size. This technique has the disadvantage that crystal formation on the equipment surfaces increases because lower shiny densities create higher levels of supersaturation within the equipment, particularly at the critical boiling surface in a vaporization-type ciystaUizer. 

When a droplet reaches the peak of its appropriate curve, due to being in a region of RH greater than the RH for that critical size, it will continue to grow in an uncontrolled fashion. As it gets larger, the curvature effect decreases its vapor pressure and it enters a region of increased supersaturation relative to that at the peak of the Kohler curve. A particle that turns into a droplet and passes the critical size is said to be an activated CCN. 

Calculate the critical radius /y and critical supersaturation Sc. for activation into a cloud droplet of a 10-l5-g NaCl particle. Assume the surface tension is 72 dyn cm-1 and the liquid density is that of water. 

In many cases in drug development, the solubility of some leads is extremely low. Fast dissolution rate of many drug delivery systems, for example, particle size reduction, may not be translated into good Gl absorption. The oral absorption of these molecules is usually limited by solubility (VWIImann et al., 2004). In the case of solubility limited absorption, creating supersaturation in the Gl Luids for this type of insoluble drugs is very critical as supersaturation may provide great improvement of oral absorption (Tanno et al., 2004 Shanker, 2005). The techniques to create the so-called supersaturation in the Gl Luids may include microemulsions, emulsions, liposomes, complexations, polymeric micelles, and conventional micelles, which can be found in some chapters in the book. 

The operation of crystallizers and precipitators is critically dependent upon the supersaturation environment prevailing within the crystal magma because this influences both the nucleation of new particles and the growth of those that... 

The droplet current / calculated by nucleation models represents a limit of initial new phase production. The initiation of condensed phase takes place rapidly once a critical supersaturation is achieved in a vapor. The phase change occurs in seconds or less, normally limited only by vapor diffusion to the surface. In many circumstances, we are concerned with the evolution of the particle size distribution well after the formation of new particles or the addition of new condensate to nuclei. When the growth or evaporation of particles is limited by vapor diffusion or molecular transport, the growth law is expressed in terms of vapor flux equation, given by Maxwell s theory, or... 

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