Saturation ratios

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). 

Relative Humidity the ratio of the partial pressure of water to the saturation vapor pressure, also called saturation ratio often expressed as a percentage. 

NOTE The calcium carbonate limit that RO system designers typically require is +1.6 to 1.8 LSI in the concentrate or reject water, and the calcium sulfate design limit typically calls for a maximum reject water saturation ratio of 1.6 to 1.8 times solubility product. 

Fig. 7-10 Kohler curves calculated for the saturation ratio Phjo/PhjO of a water droplet as a function of droplet radius r. The quantity im/M is given as a parameter for each line, where m = mass of dissolved salt, M = molecular mass of the salt, i = number of ions created by each salt molecule in the droplet.

Update the Metastable set Compute the saturation ratio vector S and update the metastable set ... 

The capacity for aerosols to take on moisture by hygroscopicity gives rise to a kinetic phenomenon of change in particle size as a function of residence time at a particular ambient relative humidity. This phenomenon can best be described in terms of the relationship between saturation ratio and particle size according to the following expression [9] ... 

KEYWORDS precipitation rate, calciting, saturation ratio, boiling temperatures, Mindanao Geothermal Production field... 

Rate - precipitation rate, mole/kgw-s Kp - rate contant, mole/m2-s Q - saturation ratio (Q/K)... 

R - 8.315 J/mol-K T-Temperature in Kelvin Q/K - Saturation ratio taken from WATCHWORKS... 

The utilization periods for AP01D given by the direct deposition of the excess calcite method has a minimum of 1 month and maximum of 6 months as shown in Fig. 2. It should be noted that the calcite precipitation rate equation at a saturation ratio above 1.72 provided shorter utilization time than the direct deposition method, indicating that the rate law overestimated the amount of calcite deposited. At a saturation ratio below 1.72, however, the rate law indicated a longer utilization period, which was expected since the calcite deposition is kinetically controlled rather than instantaneous deposition of the excess calcite. 

Fig. 3. SP4D saturation ratio and utilization periods at different boiling temperatures.

The precipitation rate (Eq. 1) indicates comparable values for utilization period at calcite saturation ratio below 1.72 since the results are closer to the observed... 

The calcite precipitation rate (Eq. 1) should be further refined by calibrating the equation to the field condition particularly for saturation ratio above 1.72. 

The calcite saturation ratio is more responsive with regards to detecting the onset of calcite deposition through the sudden shift of the saturation ratio from consistently > 1 to < 1. 

The direct deposition of excess calcite method should be used in predicting the utilization period in cases where the flash point temperature of the well is known and the saturation ratio at this condition is above 1.72. 

In Fig. 6.2a AGj is plotted as a function of j for a few values of the saturation ratio a/ao = S. Obviously the activation energy AG decreases with increasing saturation ratio, as does the size of the critical nucleus, r or rj. 

As before, the saturation ratio S can also be expressed as a/ao, where a and a0 are the actual and equilibrium activities, respectively, of the solutes that characterize the solubility. Once nuclei of critical size Xj+1 (in Eq. 6.1) have been formed, crystallization is spontaneous. 

Heterogeneous nucleation, however, is in many cases the predominant formation process for crystals in natural waters. In a similar way as catalysts reduces the activation energy of chemical reaction, foreign solids may catalyze the nucleation process by reducing the energy barrier. Qualitatively, if the surface of the solid substrate matches well with the crystal, the interfacial energy between the two solids is smaller than the interfacial energy between the crystal and the solution, and nucleation may take place at a lower saturation ratio on a solid substrate surface than in solution. 

Schematic representation of the effect of a solid substrate to catalyze (for a given saturation ratio S) the nucleation.

Dissolution of carbonates can only occur if the solution is thermodynamically undersaturated, pH is an important variable affecting the saturation ratio (Appendix 8.1 gives a brief review of the CaC03 solubility characteristics in open and closed systems). 

Photosynthesis occurring in the upper layers of the oceans and of lakes removes C02 from the water and raises the saturation ratio of CaC03. In a simplified way ... 

Saturation ratios of CaCC>3 in Lake Constance and the corresponding sedimentation load. (From Sigg, Sturm, Davis and Stumm, 1982). 

From the above statements it follows that it should be possible to derive the growth kinetics and calculate the growth rate of uncontaminated electrolyte crystals when the following parameters are known molecular weight, density, solubility, cation dehydration frequency, ion pair stability coefficient, and the bulk concentration of the solution (or the saturation ratio). If the growth rate is transport controlled, one shall also need the particle size. In table I we have made these calculations for 14 electrolytes of common interest. For the saturation ratio and particle size we have chosen values typical for the range where kinetic experiments have been performed (29,30). The empirical rates are given for comparison. 

LIGAND BINDING COOPERATIVE LIGAND BINDING SATURATION KINETICS Saturation ratio,... 

Eckert, D.J. (1987) Soil test interpretations Basic cation saturation ratios and sufficiency levels. In Brown, J.R. (ed.) Soil Testing Sampling, Correlation,... 

Eckert, D.J. and McLean, E.O. (1981) Basic cation saturation ratios as a basis for fertilizing and liming agronomic crops I. Growth chamber studies. Agronomy Journal 73, 795-799. 

McLean, F.O. (1977) Contrasting concepts in soil test interpretation sufficiency levels of available nutrients versus basic cation saturation ratios. Soil testing correlating and interpreting the analytical results. A5A Special Publication No. 29, 39-54, American Society of Agronomy, Madison, Wisconsin. 

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