§ 8.2 Surface phenomenon of liquid Chapter 8 Surface phenomenon and dispersion system

1. Curved surface and additional pressure drop bubble 1) Curved liquid surface In graduated cylinder Convex surface Concave surface

 p additional pressure Convex surfaceConcave surface For convex surface:  p>0 For concave surface:  p < 0 p ex

To increase the volume (dV) of liquid at p ex =  p + dp Laplace equation p in

For curved surface: Laplace-Young equation r is the radius of curvature. For convex surface, r > 0,  p > 0, point to the interior of liquid; For concave surface, r<0,  p < 0, point to the gaseous phase; For plane surface, r ,  p  0, p ex = p in,

For bubble

8.2.2 Vapor pressure under curved surface The droplets gradually disappear and the water level in the beaker increases. According to Laplacian equation, a droplet is subject to an excess / additional pressure. Any pressure change may affect the vapor pressure of a liquid. Under certain temperature, the chemical potential of 1 mole plane liquid and that of droplet with radius r is different.

For liquid with plane surface:For liquid in droplet: Kelvin equation As r of the droplet decreases, the vapor pressure of the droplet increases exponentially. Because radius of curvature for the bubble is negative, this suggests that, as r of the bubble decreases, the vapor pressure of the liquid in the bubble decreases exponentially.

r / m p r / p * The change in vapor pressure is not large enough to be of any concern in the case of macroscopic systems, such as d > m, or 0.1  m.

For me, the vapor is oversaturated! But for me, it is unsaturated!  evaporate condenses 

2) some phenomena related to vapor pressure If a vapor is cooled or compressed to a pressure equal to the vapor pressure of the bulk liquid, condensation should occur. (1) supersaturated vapor / supercooling The difficulty is that the first few molecules condensing can only form a minute drop and the vapor pressure of such a drop will be much higher than the regular vapor pressure. p = p * p r = 2.95p *

The crucial step in the condensation process is the formation of droplets big enough that their further growth by condensation of vapor onto them is rapid. Such droplets are called nuclei and their formation is called nucleation. The theory of homogeneous nucleation calculates the excess surface free energy of a drop as a function of its size. The free energy necessary to form a given drop is then determined by size and by the ratio of the actual pressure.

Artificial rainfall 1) Depress temperature using dry ice 2) Increase the initial radius of the embryo: dust, AgCl particles

Is embryo of a new phase possible? Microscopic fluctuation plays important role in formation of new phase. fluctuation Droplet can not form from the pure saturated vapor spontaneously. Therefore, in clean systems, large degrees of supersaturation or super-cooling are possible.

2) superheated liquid: p ex p in plpl pp

Superheating: When temperature is over boiling point, liquid does not boil. The smaller the bubble, the higher the boiling temperature. For water with air bubble with diameter of meter as seed, it boils at 123 o C. Once the bubble of relative large diameter formed, the evaporation would proceed in an explosion manner.

3) condensation in capillary: When liquid forms concave surface in capillary, r < 0 p r < p *, it is easy for vapor to condense in capillary. Constant-temperature evaporation vapor liquid Porous materials

Waterfall in Sahara desert ? Condensation of water vapor in micropores between grains of sand.

纳米比沙漠的沐雾甲虫（ Onymacris unguicularis ），

3) supersaturated solution and ageing of crystal Unsaturated, Saturated or Supersaturated?

3) supersaturated solution and ageing of crystal By simple modification of the above analysis, the same equations apply to the supercooling / supersaturated liquid or solution. ageing of crystal Decrease in diameter of solid will increase surface area and thus specific surface energy of the system and lower melting point, increase solubility of the solid. The melting point of ultrafine powder may be only 2/3 of its normal one. Thermal plating