§8.2 Surface phenomenon of liquid
Out-class reading:
Levine p. 387-390
13.2 Curved interfaces
§8.2 Surface phenomenon of liquid
8.2.2 Curved surface and additional pressure
Convex surface
Concave surface
pex
pex
pin  pex  p
pin  pex  p
p additional pressure
For convex surface: p>0 For concave surface: p < 0
§8.2 Surface phenomenon of liquid
8.2.2 Curved surface and additional pressure
For curved surface:
1 1
p    
 r1 r2 
Laplace-Young equation
r is the radius of curvature.
2
p 
r
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, pex = pin,
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
Δ  r     Vm dp  Vm Δp
For liquid with plain surface:
    RT ln p*
For liquid in droplet:
r    RT ln pr
The droplets gradually
disappear and the water
level in the beaker
increases.
For droplet or bubble
pr
M 2
Δ  RT ln *  Vm Δp 
 r
p
pr
2M 
ln * 
RT  r
p
Kelvin equation
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
(1) supersaturated vapor / supercooling
If a vapor is cooled or compressed to a pressure equal to the
vapor pressure of the bulk liquid, condensation should occur.
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.
pr = 2.95p*
p = p*
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
Relative humidity:
30 oC, 100%, 4.242 kPa
70%, 2.969 kP (45~65 %)
For condensation: 30 oC (23 oC)
For forming 1 nm droplet, vapor
pressure should be as low as 1.438
kPa, (1.006 kPa) corresponding to
ca. 12 oC (7 oC )
Plain liquid surface vs. droplet
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
Artificial rainfall
1) Depress temperature using dry ice
ln p  
vap H m
RT
k
2) Increase the initial radius of the embryo: dust, AgCl
particles
Adsorption;
larger liquid diameter
干天的雨难下！
§8.2 Surface phenomenon of liquid
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.
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
fluctuation
§8.2 Surface phenomenon of liquid
pex
8.2.3 Vapor pressure under curved surface
2) superheated liquid:
pl
pin
p
pin  pex  pl  Δp
r  0,Δp  
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
Boiling of a
superheated water
drop in sunflower oil。
The temperature of
the system is 190 oC
at ambient pressure
Once the bubble of relative large diameter
formed, the evaporation would proceed in an
explosion manner—explosive boiling.
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
Superheating:
When temperature is over boiling point, liquid does not boil.
 2 
1 1
R
 
ln 1 

T T0
 H vap  rp0 
The smaller the bubble, the higher the boiling
temperature.
For water with air bubble with diameter of 10-6 meter
as seed, it boils at 123 oC.
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
Unsaturated, Saturated or Supersaturated?
Video provided by Prof. Guo
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
3) condensation in capillary:
When liquid forms concave surface in capillary, r < 0
pr
2M 
ln * 
RT  r
p
pr < p*, it is easy for vapor to
condense in capillary.
vapor
Constant-temperature
evaporation
liquid
Porous
materials
§8.2 Surface phenomenon of liquid
8.2.3 Vapor pressure under curved surface
沐雾甲虫（Onymacris unguicularis），
§8.2 Surface phenomenon of liquid
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.
Decrease in diameter of
S r 2M
solid will increase surface
ln

area and thus specific
S RTr
surface energy of the system
and lower melting point,
increase solubility of the
solid.
ageing of crystal
The melting point of
ultrafine powder may be
only 2/3 of its normal one.
Thermal plating
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
Superhydrophobic, superhydrobicity
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(1) Adhesion
g-l + g-s  s-l
G = s-l – (g-l + g-s) = -Wa
S
Work of Adhesion
g
l
Wa = g-l + g-s – s-l
Wa > 0
The solid can be wetted by the liquid.
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(2) Immersion
g-s  s-l
G = s-l - g-s = -Wi
Work of immersion
Wi = g-s - s-l > 0
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(3) Spreading
g-s  s-l + l-g
G = s-l + l-g - s-g = -S
spreading coefficient
S = s-g - s-l - l-g > 0
The liquid spreads over the solid spontaneously.
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
The contact angle () is the angle
(4) Contact angle ()
measured through the liquid, where
a liquid/vapor interface meets a solid
surface
Hydrophobicity of conversion layer on Mg alloy
goniometer
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(4) Contact angle ()
g-l
g-s

s-l
 s g   l s
cos  
 g l
The direction of surface tension
Under equilibrium:
g-l cos  + s-l = g-s
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.
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(5) Lyophobic and lyophilic solids
g-l
g-s
g-s – g-l – s-l > 0

g-s > g-l + s-l
s-l
g-s > g-l
The greater the specific energy, the easier the spreading of
liquid over solid.
§8.2 Surface phenomenon of liquid
8.2.5 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  18 mN m-1
Nonstick cooker
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(5) Lyophobic and lyophilic solids
How can we judge the cleanness of
the glass surface?
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(6) Spreading over liquid
SO/W = - G = W - O - W/O
SO/W > 0,
oil can spread over water
SO/W < 0,
oil floats in shape of lens.
Liquids
Iso-C5H12O
C6H6
C6H12
CS2
CH2I2
SO/W
44.0
8.8
3.4
-8.2
-26.5
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(6) Spreading over liquid
Clapham Common (2000 m2)
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
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(6) Spreading over liquid
Floating oil drop on
chicken soup (lense)
Floating oil on sea
surface
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(6) Spreading over liquid
wreck of a tanker
Spreading of oil over seawater
A environmental disaster
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
(6) Spreading over liquid
2010年5月5日，美国墨西哥湾原油泄漏事件
§8.2 Surface phenomenon of liquid
8.2.5 Interaction between two phases--Wetting and spreading
§8.2 Surface phenomenon of liquid
8.2.4 Capillarity Capillary rise / depression
§8.2 Surface phenomenon of liquid
8.2.4 Capillarity
 p  pl
2
r
h
 h( 1   2 ) g
2
( 1   2 ) gr
r cos   R
2 cos 
h
( 1   2 ) gR
Discussion
§8.2 Surface phenomenon of liquid
8.2.4 Capillarity
§8.2 Surface phenomenon of liquid
8.2.4 Capillarity
§8.2 Surface phenomenon of liquid
8.2.4 Capillarity
2 cos 
h
( 1   2 ) gR
Measurement of porosity
distribution:
p
This relation can be used to
determine the surface tension
of liquids – capillary rise
method
Mercury
method
§8.2 Surface phenomenon of liquid
Why cloud is white?
And why does it turn dark
before storm?