Relative humidity above water-droplet surface

Exercise 2.9. What is the relative humidity at 10°C just above the surface of a water droplet with a radius of 0.010 /Ltm If the droplet were placed in an enclosure having this same relative humidity, would the droplet be in stable or unstable equilibrium (The surface energy of water at lO C is 0.076 J m, and the number density of molecules in water is 3.3 x 10 m" )... 

Fog droplets (10-50 m diameter) are formed in the water-saturated atmosphere (relative humidity = 100%) by condensation on aerosol particles (see Figure 5.2). The fog droplets absorb gases such as SO2, NH3, HCl, and NO. The water droplets are a favorable milieu for the oxidation of many reductants, above all, of SO2 to H2SO4. The liquid water content of a typical fog is often on the order of 10 liter water per m air. The concentrations of ions in fog droplets are often 10-50 times larger than those of rain (Figure 5.11). Clouds process substantial volumes of air and transfer gas and aerosols over large distances. On the other hand, fog droplets are important collectors of local pollutants in the proximity of the earth s surface. 

Thus (ph2so4/ h2so4) — 1 0017, and in this case the Kelvin effect is negligible the increase in water vapor pressure due to the droplet curvature is only 0.166% above that of a flat surface. The particle size growth factor at 90% relative humidity is 2.12. Thus the 1 pm diameter drop at 50% RH will grow to become a drop of (2.12/1.48) (1) = 1.43 pm at 90% RH. 

Solution, Kelvin s formula [Eq. (2.55)] allows us to determine the radius of a droplet that is in equilibrium (i.e., neither evaporating nor condensing) with a water vapor pressure e. However, if a droplet neither evaporates nor grows when the air surrounding it has vapor pressure e, it is because the vapor pressure just above the surface of the droplet is equal to e. ThuSj we can interpret Eq. (2.55) as giving the vapor pressure e (or relative humidity RH = 100 e/e ) xsi above the surface of a droplet of radius r. Hence, from Eq. (2.55)... 

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