Vaporization evaporation coefficients

For the majority of metals, the evaporation coefficient is found to be unity, but, as mentioned before, the coefficient of many non-metallic elements with a complex vaporization mechanism such as... 

Finally, it is to be expected that the evaporation coefficient of a very stable compound, such as alumina, which has a large heat of sublimation resulting from the decomposition into the elements, will be low. Since the heat of evaporation must be drawn from the surface, in die case of a substance widr a low thermal conductivity such as an oxide, the resultant cooling of the surface may lead to a temperature gradient in and immediately below the surface. This will lower die evaporation rate compared to that which is calculated from the apparent, bulk, temperature of the evaporating sample as observed by optical pyromeuy, and thus lead to an apparently low free surface vaporization coefficient. This is probably die case in the evaporation of alumina in a vacuum. 

Offringa, J.C.A., de Kruif, C.G., Van Ekeren, P.J., Jacobs, M.H.G. (1983) Measurement of the evaporation coefficient and saturation vapor pressure of fraras -diphenylethene using a temperature-controlled vacuum quartz-crystal microbalance. J. Chem. Ther-modyn. 15, 681-690. 

In order to obtain the solution desired, a value of Ts is assumed, the vapor pressure of A is determined from tables, and mAs is calculated from Eq. (6.98). This value of mAs and the assumed value of Ts are inserted in Eq. (6.97). If this equation is satisfied, the correct Ts is chosen. If not, one must reiterate. When the correct value of Ts and mAs are found, BT or BM are determined for the given initial conditions Tx or mAco. For fuel combustion problems, mAcc is usually zero however, for evaporation, say of water, there is humidity in the atmosphere and this humidity must be represented as mAco. Once BT and BM are determined, the mass evaporation rate is determined from Eq. (6.87) for a fixed droplet size. It is, of course, much preferable to know the evaporation coefficient (5 from which the total evaporation time can be determined. Once B is known, the evaporation coefficient can be determined readily, as will be shown later. 

Richardson, Hightower and Pigg (1986) used a quadrupole mounted in a vacuum chamber to measure the vapor pressure of sulfuric acid as a function of temperature in the range 263 T < 303 K. They operated well into the free-molecule regime and assumed an evaporation coefficient of unity. Richardson et al. correlated their data by means of the equation... 

It can be seen that, once an assumption is made for the value of M, the only quantity still unknown in the above equation is a, the evaporation coefficient, which must have a finite value equal to or less than 1. If it is assumed that a is constant but unknown, then the vapor pressure at any given temperature is proportional to the vaporization rate, and the enthalpy of vaporization may be found from the Clausius-Clapeyron type treatment. If a value is assigned to a, then vapor pressure values and the entropy of vaporization can be calculated as well. If the entropy of vaporization found in this way is a reasonable value, then the assumed value of a receives support. The latter procedure has been adopted here, and a value of unity has been taken for a. The reasons for choosing this value are ... 

The effect of volatility in fractionating elements is due to the ratio of the saturation vapor pressures, but as shown by Equation (6), the relative masses of the gas species and possible differences in the evaporation coefficients also affect the degree of chemical fractionation produced by evaporation. When Equation (6) is used in connection with isotope fractionation, it is generally assumed that isotopes of the same element have the same evaporation coefficient and that the ratio of the saturation vapor pressures is equal to the isotopic ratio at the surface of the evaporating material (i.e., no equilibrium fractionation). This results in the following equation for the relative flux of the isotopes ... 

Vaues of a may be very much less than unity and be temperature dependent. Somoijai and Lester [40] comment that "all the kinetic information is contained in the evaporation coefficient and its variation with conditions of vaporization", and they recommend the avoidance of the use of ot, in describing the rates of evaporation of solids under non-equilibrium conditions. The rate of sublimation is dependent on the attaimnent of sufficient energy by suitably disposed siuface molecules (possibly accompanied by electron or proton transfer in ionic solids). The overall rate of reactant removal is sensitive to the presence of impurities at the surface. The reverse reaction may be significant if the volatile material is not immediately removed from the vicinity of the reactant particles. Arrhenius parameters measured for sublimation processes may include a term which represents a temperature dependent concentration of surface intermediates [42]. The observation that measured evaporation rates are lower than those estimated from equilibrium vapour pressures suggests that the kinetics may be determined by a surface dissociation that precedes evaporation. This view is supported by evidence that, in selected systems, specific additives can considerably promote evaporation rates. For example [40], the evaporation rate of red phosphorous between 550 and 675 K was found to be increased by three orders of magnitude by the presence of thallium. 

Next, a method was developed to determine the initial peripheral contact angle, 9, of sessile drops on solid surfaces from the diffusion controlled rate of drop evaporation, for the constant drop contact radius mode. Application of this method requires use of the product of the vapor diffusion coefficient of the evaporating liquid, with its vapor pressure at the drop surface temperature (l)APv), which can be found directly from independent experiments following the evaporation of fully spherical liquid drops in the same chamber. It is then possible to calculate 9,p, from... 

Erbil, H.Y. and Avci, Y. (2002). Simultaneous Determination of Vapor Diffusion Coefficient from Thin Tube Evaporation and Sessile Drop Evaporation on Solid Surfaces. Langmuir, 18,... 

A comparison of the vapor pressures of all three compounds, determined by the IQiudsen and Langmuir methods, showed that their evaporation coefficients differed from unity. Assuming that [2]... 

Our investigation shows that the vapor pressures of solid bismuth and antimony tellurides and of bismuth selenide are quite low. The working temperatures of thermoelements made of these substances do not exceed 700 C. Under such conditions, the evaporation of thermoelements should be of little significance, especially as the loss of matter from open surfaces occurs at a rate which is 6—65 times slower than the equilibrium rate of evaporation. The values of the evaporation coefficient (0.15-0.16) found in our study show that the evaporation process is fairly complex. This is supported by thermodynamic calculations, which demonstrate that the evaporation is of a dissociative nature. 

In practice, however, the actual vaporization rate may be less than that predicted by equation 8.17 and it is conventional to include a correction factor Q (< 1), generally referred to as an evaporation coefficient ... 

As indicated in a review by Davis [4], accommodation coefficients and evaporation coefficients are usually determined from experimental data, but a limited amount of information has been obtained from theoretical considerations such as molecular dynamics computations. Davidovits et al. [5] reviewed experimental techniques and results for mass accommodation coefficients and chemical reactions at gas-liquid interfaces. Simultaneous measurements of mass and thermal accommodation coefficients for water vapor condensation on droplets using an expansion cloud chamber reported by Winkler et al. [6, 7] indicate that Ou, > 0.8 and Kni > 0.4. Zientara et al. [8] used electrodynamic levitation to measure mass and thermal accommodation coefficients for evaporating water droplets, reporting otm = 0.12 0.02 and Oth = 0.65 0.09 at room temperature (Too 286 K). 

With the above information and the assumption of unity evaporation coefficients for U, Cj, C2, Cj, and UC2, the congruently vaporizing composition can be calculated. This was done by plotting the log evaporation rate ratio, C/U, against the composition of the solid, C/U, in Fig. 70. 

The vaporization of carbon is a major factor in the ablation of carbon. This ablation is the basic phenomena that controls the performance of rocket-nozzle throats, reentry nose cones and other components exposed to extremely high temperatures (see Ch. 9). The rate of ablation is related to the composition of the carbon vapor formed during ablation and to the heat of formation of the various carbon-vapor species and their evaporation coefficient. 

The gas phase temperature and the liquid phase temperature are also defined, which equal each other in the case of vapor-liquid equilibrium. The evaporation coefficient was introduced by Hertz to account for evaporating molecules colliding with molecules in the gas phase and getting reflected back into the liquid phase. Therefore, it is also a measure of the percent of the theoretical maximum evaporation rate reached. The condensation coefficient is analogously defined as the ratio of molecules actually condensing to molecules hitting the surface [225]. The phase change coefficients are similar... 

Not all molecules striking a surface necessarily condense, and Z in Eq. VII-2 gives an upper limit to the rate of condensation and hence to the rate of evaporation. Alternatively, actual measurement of the evaporation rate gives, through Eq. VII-2, an effective vapor pressure Pe that may be less than the actual vapor pressure P. The ratio Pe/P is called the vaporization coefficient a. As a perhaps extreme example, a is only 8.3 X 10" for (111) surfaces of arsenic [11]. 

---