Vapor pressure above curved surface

The equation AP = 2y/r is very important because it says if r oo, then AP O. The vapor pressure above a curved surface is not the same as the pressure above a flat surface due to AP. 

Figure 5 summarizes the low pressure end of water vapor adsorption isotherms obtained on quartz A. Bound water loss, above the surface condition resulting from 400° C. outgassing in vacuum, is indicated by displacement of the adsorption origin to reflect total water content (bound water plus adsorbed water) as a function of water vapor relative pressure. Vapor desorption curves show that... 

The concentration for dichlofluanid decreases with time from about 20 pg/m to less then 1 pg/m. This was the expected lapse, although starting concentration was above the saturation concentration if calculated by vapor pressure (1. 3 X 10- Pa to 1.4 X 10-5 Pa at 20 °C). In contrast to this normal decrease are the curves for permethrine and tebuconazole. At the beginning of the measurements the concentrations were Just detectable. During the first weeks there was a slight increase up to 10 ng/m. Then there was a further increase to about 30 ng/m. After 150 days a slight decrease in the air concentration started. This course of the concentration increase might be explained by sink effects. Because of their low vapor pressure tebuconazole and permethrine are more likely to be adsorbed onto the inside surface of the chamber. Before the air concentration can rise to the steady state concentration the chamber walls must be saturated with the biocides. 

We can now transform the Kelvin equation (4.223), valid for pure water, by consideration of Raoulfs equation for a droplet with dissolved matter. The total change in vapor pressure consists of the vapor change above the curved surface and the vapor change of the solution ... 

It may be seen from Figure 11.11 that the intersection of the two branches of the adiabatic desorption curves, corresponding to the plateau point, may occur at a point which lies above the saturation vapor pressure of the adsorbate, and under these conditions condensation will occur. Indeed, because of surface tension, condensation in the smaller macropores may occur at a vapor pressure appreciably below the saturation limit (Section 2.5), Friday and LeVan have investigated this phenomenon in detail and have shown that condensation probably occurs in many gas driers under normal operating condition. (See Figure 11.13). In aqueous systems condensation is undesirable since most desiccants have limited hydrothermal stability and premature deterioration of the adsorbent is a likely consequence of such operation. The consequences with organic sorbates are generally less serious. 

Figure 4. Cavitation pressure as a fimction of temperature for two scenarios for water reentrant spinodal scenario (a) and liquid-liquid critical point scenario (b). These scenarios predict a different temperature behavior for the liquid-vapor spinodal (dotted curve), eitha- with a minimum (a. based on extrapolation of positive pressure data [40]), or monotonic (b. based on molecular dynamics simulations with theTIPSP potential [41]). The solid curve shows the prediction of CNT based on the bulk surface tension of water it becomes unphysical when it goes beyond the liquid-vapor spinodal. The dashed curve is the DPT prediction [40] that correctly remains above the spinodal, and reflects its temperature dependence.

It can see from the above-mentioned discussion that capillary cohesion is closely related to the curved liquid surface. The pressme boimdary causes capillary cohesion — the critical vapor pressure relates to the cmvatme radius of liquid surface. Kelvin equation has been derived from thermodynamics, where the curvature radius (rjs) of the meniscus of hemispherical (concave) liquid and the equilibrium vapor pressure (p) has the following relationships ... 

The above examples show that, for certain systems, deviations from Raoult s law can cause a maximum or a minimum in the vapor pressure to appear at a certain temperature and composition. At constant pressure, the boiling point or bubble point temperature curve could have a maximum or a minimum. Liquid mixtures whose vapor pressure curve or surface exhibits a maximum or a minimum are said to form azeotropes. The composition at which the azeotrope occurs is the azeotropic composition. Binaries are likely to form azeotropes if they deviate from Raoult s law... 

This result has implications for droplets, which have their surface convex toward the vapor. Consider a pure liquid drop of radius r. Then fyp is equal to the vapor pressure of the pure liquid (on a flat surface), if the fiigacity coefficient under the conditions of P and T is assumed to he unity. However, equation (3.3.53) implies that the vapor pressure of the pure liquid in the space above the convex curved surface of the drop, Pf , is higher than PJJ at equilibrium (Figure 3.3.2B) ... 

The BET (Brunauer-Emmett-Teller)-type isotherm in Figure 3.3.8B reflects multilayer adsorption of the adsorbate. After a monolayer adsorbate coverage is achieved in the adsorbent pores, additional molecular layers are formed on top of the adsorbed monolayer by condensation of vapors. In adsorbents having small-diameter pores, multilayer condensation of the adsorbate vapor can fill the pore completely with the liquid adsorbate. This phenomenon is called capillary condensation (Figure 3.3.8C). Consider the curved interface between the vapor phase and the condensed phase of species i in the micropore in this figure. The vapor pressure of the condensed liquid above the concave curved liquid surface in the capillary F utved less than that over a plane condensed liquid surface F pi ... 

In principle, then, the temperature at a point in a bath of He I should be given by the surface temperature plus a correction determined only by the hydrostatic pressure at the point and by the slope of the vapor pressure curve. In practice, however, this is not the case. Temperatures determined in the above manner are nearly always too low, by amounts ranging from 2 to 10 mdeg[2]. This situation is readily apparent in the discontinuity observed at the x-point in the resistance-temperature relation obtained by calibration of a carbon resistor above and below the X -point, even when the hydrostatic correction is made. Similar difficulties are encountered in the calibration of magnetic thermometers [3]. The use of a vapor pressure bulb to determine the liquid temperature is a common technique... 

Now let us consider curved interfaces. As mentioned in Section 9.1, to calculate the shift of the triple point in a system containing phases confined by curved interfaces, compared to the triple point for the bulk phases, on the basis of Equation 9.4 one needs to establish a relation between the pressure of vapors in equilibrium with bulk condensed phases and the corresponding phases confined by curved interfaces. To determine the vapor pressure in equilibrium with the condensed phase under the curved interface, it is necessary to take into account two physical reasons for the deviation of this pressure from the pressure above a plane interface (p°). These are the increasing (decreasing) pressure inside a condensed phase under a convex (concave) meniscus and the surface forces-induced non-uniformity of structure of the condensed media near the interface. We will analyze the influence of above factors separately and show that they additively contribute to the shift of the triple point of boundary layers. 

A very important aspect of phase behavior in a system consisting of a volatile organic solvent, such as ethanol, and a supercritical fluid, such as CO2, is that the mixture critical pressure coincides with the liquid vapor phase transition. This means that above a single phase exists for all solvent compositions, whereas the (ethanol-rich and C02-rich) two-phase region lies below this curve. This fact has important implications for the mass transfer and precipitation mechanisms. Complete miscibility of fluids above P means that there is no defined or stable vapor liquid or liquid liquid interface, and the surface tension is reduced to zero and then thermodynamically becomes... 

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