8.2 Surface phenomenon of liquid. Out-class reading: Levine p Curved interfaces

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1 Out-class reading: Levine p Curved interfaces

4 8.2.1 Some interesting phenomena

5 8.2.1 Some interesting phenomena Provided by Prof. Yu-Peng GUO of Jilin University

6 8.2.1 Some interesting phenomena Unsaturated, Saturated or Supersaturated?

7 8.2.2 Curved surface and additional pressure 1. Curved liquid surface drop Convex surface Concave surface In graduated cylinder

8 8.2.2 Curved surface and additional pressure Convex surface Concave surface p ex p ex p p p in ex p p p in ex p additional pressure For convex surface: p>0 For concave surface: p < 0

9 8.2.2 Curved surface and additional pressure p p Δp in pdv ex da ( p dp) dv da da p dv p in p ex V p 4 r 3 A 4r rdr 2 4 r 2 r dr To increase the volume (dv) of liquid at p ex = p + dp p 2 r Laplace equation

10 For curved surface: 1 1 p r1 r2 Laplace-Young equation Curved surface and additional pressure 2 p r For convex surface, r > 0, p > 0, point to the interior of liquid; r is the radius of curvature. For concave surface, r<0, p < 0, point to the gaseous phase; For plane surface, r, p 0, p ex = p in,

11 8.2.2 Curved surface and additional pressure For bubble p 4 r

12 8.2.3 Vapor pressure under curved surface Δ r Vmdp VmΔp For liquid with plane surface: RT ln p For liquid in droplet: * r RT ln p r pr Δ RT ln V Δ * m p p M 2 r The droplets gradually disappear and the water level in the beaker increases. ln p p r * 2M RT r Kelvin equation For droplet or bubble

13 8.2.3 Vapor pressure under curved surface ln p p r * 2M RT r 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 > 10-7 m, or 0.1 m.

vapor pressure of the bulk liquid, condensation should

14 8.2.3 Vapor pressure under curved surface If a vapor is cooled or compressed to a pressure equal to the vapor pressure of the bulk liquid, condensation should occur. cloud chamber---- Charles Thomson Rees Wilson, 1894

15 8.2.3 Vapor pressure under curved surface (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 r = 2.95p * p = p *

8.2.3 Vapor pressure under curved surface Artificial rainfall vap Hm ln p k RT Relative humidity: 30 o C, 100%, 4.242 kpa 70%, 2.

16 8.2.3 Vapor pressure under curved surface Artificial rainfall vap Hm ln p k RT Relative humidity: 30 o C, 100%, kpa 70%, kp (45~65 %) For condensation: 30 o C (23 o C), For forming 1 nm droplet, vapor pressure should be as low as kpa, (1.006 kpa) corresponding to ca. 12 o C (7 o C ) 2) Increase the initial radius of the embryo: dust, AgCl particles

17 8.2.3 Vapor pressure under curved surface Droplet can not form from the pure saturated vapor spontaneously. Therefore, in clean systems, large degrees of supersaturation or super-cooling are possible. Is embryo of a new phase possible? fluctuation Microscopic fluctuation plays important role in formation of new phase.

18 8.2.3 Vapor pressure under curved surface 2) superheated liquid: p ex p l p in p p p p Δp in ex l r 0,Δp

19 8.2.3 Vapor pressure under curved surface Superheating: When temperature is over boiling point, liquid does not boil. 1 T 1 T 0 R H v ln 1 2 rp 0 For water with air bubble with diameter of 10-6 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. The smaller the bubble, the higher the boiling temperature.

20 8.2.3 Vapor pressure under curved surface 2) superheated liquid: p p p Δp in ex l Once the bubble of relative large diameter formed, the evaporation would proceed in an explosion manner explosive boiling.

21 8.2.3 Vapor pressure under curved surface 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. ln p p r * 2M RT r Constant-temperature evaporation vapor liquid Porous materials

22 8.2.3 Vapor pressure under curved surface 沐雾甲虫 (Onymacris unguicularis),

8.2.3 Vapor pressure under curved surface 3) supersaturated solution and ageing of crystal By simple modification of the above analysis, the same equations apply to the supercooling / supersaturated

23 8.2.3 Vapor pressure under curved surface 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. ln S r S 2M RTr 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. ageing of crystal Thermal plating

24 8.2.4 Interaction between two phases--wetting and spreading Superhydrophobic, superhydrobicity

25 8.2.4 Interaction between two phases--wetting and spreading (1) Adhesion g-l + g-s s-l S G = s-l ( g-l + g-s ) = -W a g Work of Adhesion W a = g-l + g-s s-l l W a > 0 The solid can be wetted by the liquid.

26 8.2.4 Interaction between two phases--wetting and spreading (2) Immersion (3) Spreading g-s s-l g-s s-l + l-g G = s-l + l-g - s-g = -S spreading coefficient G = s-l - g-s = -W i W i = g-s - s-l > 0 Work of immersion S = s-g - s-l - l-g > 0 The liquid spreads over the solid spontaneously.

27 8.2.4 Interaction between two phases--wetting and spreading (4) Contact angle () The direction of surface tension g-l g-s s-l Under equilibrium: g-l cos + s-l = g-s cos sg gl ls Young equation When : g-s - s-l = g-l, cos =1, = 0 o, Complete wettable. When : g-s - s-l < g-l, 0<cos <1, <90 o, wettable. When : g-s < s-l, cos < 0, > 90 o, nonwettable.

through the liquid, where a liquid/vapor interface meets a

28 8.2.4 Interaction between two phases--wetting and spreading (4) Contact angle () The contact angle () is the angle measured through the liquid, where a liquid/vapor interface meets a solid surface Hydrophobicity of conversion layer on Mg alloy goniometer

g-l + s-l g-s > g-l Why the water drop is white?

29 8.2.4 Interaction between two phases--wetting and spreading (5) Lyophobic and lyophilic solids g-l g-s s-l g-s g-l s-l > 0 g-s > g-l + s-l g-s > g-l Why the water drop is white? The greater the specific energy, the easier the spreading of liquid over solid.

30 8.2.4 Interaction between two phases--wetting and spreading (5) Lyophobic and lyophilic solids g-s > 100 mn m -1, high-energy surface: Metals, oxides, chlorides, inorganic salts. g-s 500 ~ 5000 mn m -1 g-s < 100 mn m -1, low-energy surface: organic solids, polymers. PTFE: g-s Nonstick cooker 18 mn m -1

31 8.2.4 Interaction between two phases--wetting and spreading (5) Lyophobic and lyophilic solids How can we judge the cleanness of the glass surface?

32 8.2.4 Interaction between two phases--wetting and spreading (6) Spreading over liquid Liquids Iso-C 5 H 12 O C 6 H 6 C 6 H 12 CS 2 CH 2 I 2 S O/W S O/W = - G = W - O - W/O S O/W > 0, oil can spread over water S O/W < 0, oil floats in shape of lens.

33 8.2.4 Interaction between two phases--wetting and spreading (6) Spreading over liquid Clapham Common (2000 m 2 ) 1774 Benjamin Franklin (2.4 nm) The film formed over water is of one molecule thick. (proved by Pockels and Rayleigh): Unimolecular film, monolayer, Insolvable film

34 8.2.4 Interaction between two phases--wetting and spreading (6) Spreading over liquid wreck of a tanker Spreading of oil over seawater

35 8.2.5 Capillarity Capillary rise / depression

36 8.2.5 Capillarity p p l 2 h( 12) g r 2 h ( 1 2 ) gr r cos R h 2 cos ( 1 2 ) gr Discussion

37 8.2.5 Capillarity 2 cos h ( 1 2 ) gr Measurement of porosity distribution: p Mercury method This relation can be used to determine the surface tension of liquids capillary rise method

8.2 Surface phenomena of liquid. Out-class reading: Levine p Curved interfaces

8.2 Surface phenomena of liquid. Out-class reading: Levine p Curved interfaces Out-class reading: Levine p. 387-390 13.2 Curved interfaces 8.2.1 Some interesting phenomena Evolution of bubbles on porous surface. 8.2.1 Some interesting phenomena Addition of a seed in Supersaturated