Vapor, supersaturated Vaporization

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

The dynamic picture of a vapor at a pressure near is then somewhat as follows. If P is less than P , then AG for a cluster increases steadily with size, and although in principle all sizes would exist, all but the smallest would be very rare, and their numbers would be subject to random fluctuations. Similarly, there will be fluctuations in the number of embryonic nuclei of size less than rc, in the case of P greater than P . Once a nucleus reaches the critical dimension, however, a favorable fluctuation will cause it to grow indefinitely. The experimental maximum supersaturation pressure is such that a large traffic of nuclei moving past the critical size develops with the result that a fog of liquid droplets is produced. 

Frequently, vapor-phase supersaturation is studied not by varying the vapor pressure P directly but rather by cooling the vapor and thus changing If To is the temperature at which the saturation pressure is equal to the actual pressure P, then at any temperature T, Pjf = x is given by... 

Calculate the value of the Zeldovich factor for water at 20°C if the vapor is 5% supersaturated. 

Fig. 8. Morphological effects of supersaturations and temperature on vapor deposited materials (12).

Evaporative crystalli rs generate supersaturation by removing solvent, thereby increasing solute concentration. These crystallizers may be operated under vacuum, and, ia such circumstances, it is necessary to have a vacuum pump or ejector as a part of the unit. If the boiling poiat elevation of the system is low (that is, the difference between the boiling poiat of a solution ia the crystallizer and the condensation temperature of pure solvent at the system pressure), mechanical recompression of the vapor obtained from solvent evaporation can be used to produce a heat source to drive the operation. 

Mixing of two saturated streams at different temperatures. This is commonly seen in the plume from a stack. Since vapor pressure is an exponential function of temperature, the resultant mixture of two saturated streams will be supersaturated at the mixed temperature. Uneven flow patterns and cooling in heat exchangers make this route to supersaturation difficult to prevent. 

Although surface-cooled types of MSMPR crystalhzers are available, most users prefer crystallizers employing vaporization of solvents or of refrigerants. The primary reason for this preference is that heat transferred through the critical supersaturating step is through a boil-ing-hquid-gas surface, avoiding the troublesome solid deposits that can form on a metal heat-transfer surface. 

The transfer of supersaturated liquor from the vaporizer (point B, Fig. 18-69) often causes salt buildup in the piping and reduction of the operating cycle in equipment of this type. The rate of buildup can be reduced by circulating a thin suspension of solids through the vaporizing chamber however, the presence of such small seed ciystals tends to rob the supersaturation developed in the vaporizer, thereby lowering the efficiency of the recirculation system. 

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. 

The real atmosphere is more than a dry mixture of permanent gases. It has other constituents—vapor of both water and organic liquids, and particulate matter held in suspension. Above their temperature of condensation, vapor molecules act just like permanent gas molecules in the air. The predominant vapor in the air is water vapor. Below its condensation temperature, if the air is saturated, water changes from vapor to liquid. We are all familiar with this phenomenon because it appears as fog or mist in the air and as condensed liquid water on windows and other cold surfaces exposed to air. The quantity of water vapor in the air varies greatly from almost complete dryness to supersaturation, i.e., between 0% and 4% by weight. If Table 2-1 is compiled on a wet air basis at a time when the water vapor concentration is 31,200 parts by volume per million parts by volume of wet air (Table 2-2), the concentration of condensable organic vapors is seen to be so low compared to that of water vapor that for all practical purposes the difference between wet air and dry air is its water vapor content. 

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

Condensation is the result of collisions between a gaseous molecule and an existing aerosol droplet when supersaturation exists. Condensation occurs at much lower values of supersaturation than nucleation. Thus, when particles already exist in sufficient quantities, condensation will be the dominant process occurring to relieve the supersaturated condition of the vapor-phase material. 

Supersaturation An unstable condition in which the concentration of a solution or a vapor is greater than that corresponding to saturation. 

Essentially, the higher the pressure or temperature, the greater the potential for vaporous silica carryover and steam dissolution. When pressure or temperature falls, the steam becomes supersaturated and various forms of crystalline silica deposition begin to occur. As temperatures continue to fall, the deposits become increasingly amorphous in nature and also more insoluble. 

If we could prevent the mixture from separating into two phases at temperatures below Tc, we would expect the point of inflection to develop into curves similar to those shown in Figure 8.17 as the dotted line for /2, with a maximum and minimum in the fugacity curve. This behavior would require that the fugacity of a component decreases with increasing mole fraction. In reality, this does not happen, except for the possibility of a small amount of supersaturation that may persist briefly. Instead, the mixture separates into two phases. These phases are in equilibrium so that the chemical potential and vapor fugacity of each component is the same in both phases, That is, if we represent the phase equilibrium as... 

The manner in which a film is formed on a surface by CVD is still a matter of controversy and several theories have been advanced to describe the phenomena. ] A thermodynamic theory proposes that a solid nucleus is formed from supersaturated vapor as a result of the difference between the surface free energy and the bulk free energy of the nucleus. Another and newer theory is based on atomistic nucle-ation and combines chemical bonding of solid surfaces and statistical mechanics. These theories are certainly valuable in themselves but considered outside the scope of this book. 

Only two possibilities exist for explaining the existence of cloud formation in the atmosphere. If there were no particles to act as cloud condensation nuclei (CCN), water would condense into clouds at relative humidities (RH) of around 300%. That is, air can remain supersaturated below 300% with water vapor for long periods of fime. If this were to occur, condensation would occur on surface objects and the hydrologic cycle would be very different from what is observed. Thus, a second possibility must be the case particles are present in the air and act as CCN at much lower RH. These particles must be small enough to have small settling velocity, stay in the air for long periods of time and be lofted to the top of the troposphere by ordinary updrafts of cm/s velocity. Two further possibilities exist - the particles can either be water soluble or insoluble. In order to understand why it is likely that CCN are soluble, we examine the consequences of the effect of curvature on the saturation water pressure of water. 

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. 

The overall rainfall rate and amoimt depend on these microphysical processes and even more greatly on the initial amount of water vapor present, and on the vertical motions that transport water upward, cool the air, and cause supersaturation to occur in the first place. Thus the delivery of water to the Earth s surface as one step in the hydrologic cycle is controlled by both microphysical and meteorologic processes. The global average precipitation amounts to about 75 cm/yr or 750 L/(m yr). 

A difiiculty with this mechanism is the small nucleation rate predicted (1). Surfaces of a crystal with low vapor pressure have very few clusters and two-dimensional nucleation is almost impossible. Indeed, dislocation-free crystals can often remain in a metastable equilibrium with a supersaturated vapor for long periods of time. Nucleation can be induced by resorting to a vapor with a very large supersaturation, but this often has undesirable side effects. Instabilities in the interface shape result in a degradation of the quality and uniformity of crystalline material. 

Another thin film technology based nanoparticle preparation route is gas condensation, in which metal vapor is cooled to high levels of supersaturation in an inert gas ambient [126-128]. In these experiments particles necessarily nucleate in the gas phase. In a promising extension of this technique a pulsed laser beam replaces the conventionally used thermal metal vapor source [120,121,129-134]. 

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