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2.2.5 Surface tensions
Surface tension is caused by the inward attraction of molecules at a
boundary. This attraction produces curvature of free liquid surfaces, and
causes a pressure difference to exist at the curved boundary:
Δp = γ(1/R1 +
1/R2), where Δp = pressure difference,
R1 and R2 = principal radii of curvature.
γ, the
surface tension at a liquid–gas boundary, is usually measured in
mN m-1. At liquid–liquid boundaries there is interfacial
tension; at liquid–solid boundaries adhesion tension.
Temperature variation. γ decreases with increase of
temperature and vanishes at the critical temperature. For many liquids
− d[γ(M/ρ)2/3]/dt
= 2.12, where M = molecular weight; ρ = density (g
cm−3), t = temperature (°C) (Eötvös,
1886). (See Adam)
Surface tension of various liquids
|
Metallic elements.
γ =
γtm
+ |
dγ |
(t − tm), mN
m−1
|
|
dt |
|
Substance
|
|
|
|
Range, °C |
|
Aluminium . . . . |
660 |
871 |
−0.155 |
660–1400 |
|
Antimony . . . . |
630 |
371 |
−0.045 |
630–1600 |
|
Barium . . . .
. |
704 |
278 |
−0.075 |
1137–1580 |
|
Beryllium . . . . |
1500 |
1100 |
— |
— |
|
Bismuth . . . . . |
270 |
382 |
−0.080 |
270–1200 |
|
Boron
. . . . . |
2100 |
1060 |
— |
— |
|
Cadmium . . . . |
321 |
637 |
−0.150 |
320–800 |
|
Caesium . . . . . |
28 |
71.4 |
−0.050 |
28–1100 |
|
Calcium . . . . . |
850 |
360 |
−0.10 |
850–1500 |
|
Cerium . . . . . |
808 |
794 |
−0.074 |
808–1700 |
|
Chromium
. . . . |
1860 |
1642 |
−0.20 |
1860–2000 |
|
Cobalt . . . . . |
1500 |
1881 |
−0.34 |
1500–1800 |
|
Copper . . . . . |
1085 |
1330 |
−0.23 |
1085–1400 |
|
Dysprosium . . . |
1500 |
648 |
−0.13 |
1500–1750 |
|
Erbium . . . . . |
1530 |
637 |
−0.12 |
1530–1750 |
|
Europium . . . . |
826 |
264 |
−0.05 |
826–1700 |
|
Gadolinium . . . . |
1350 |
664 |
−0.058 |
1350–1750 |
|
Gallium . . . . . |
30 |
711 |
−0.070 |
30–1500 |
|
Germanium . . . . |
960 |
607 |
–0.12 |
960–1600 |
|
Gold
. . . . . |
1065 |
1145 |
−0.20 |
1065–1600 |
|
Hafnium . . . . . |
2220 |
1630 |
— |
— |
|
Holmium . . . . |
1500 |
650 |
−0.123 |
1500–1750 |
|
Indium . . . . . |
157 |
556 |
−0.090 |
157–1200 |
|
Iridium . . . . . |
2450 |
2264 |
−0.247 |
2450–2600 |
|
Iron . . . . . . |
1530 |
1862 |
−0.39 |
1530–1900 |
|
Lanthanum . . . . |
920 |
728 |
−0.10 |
920–1700 |
|
Lead
. . . . . |
327 |
457 |
−0.11 |
320–1100 |
|
Lithium . . . . . |
186 |
399 |
−0.15 |
186–1300 |
|
Lutetium . . . . |
1700 |
940 |
−0.073 |
1700–1750 |
|
Magnesium . . . |
650 |
577 |
−0.26 |
650–1100 |
|
Manganese . . . . |
1245 |
1152 |
−0.35 |
1245–1500 |
|
Mercury . . . . |
–38 |
489 |
−0.231 |
−38–200 |
|
Molybdenum . . .
|
2620 |
2250 |
— |
— |
|
Neodymium
. . . |
1024 |
687 |
−0.088 |
1024–1700 |
|
Nickel . . . . . |
1455 |
1796 |
−0.35 |
1455–1800 |
|
Niobium . . . . |
2468 |
1900 |
— |
— |
|
Osmium . . . . |
3050 |
2500 |
— |
— |
|
Palladium . . . . |
1552 |
1482 |
−0.279 |
1550–1750 |
|
Platinum . . . . |
1774 |
1746 |
−0.307 |
1774–1950 |
|
Potassium . . . . |
64 |
110 |
−0.070 |
64–1100 |
|
Praseodymium. . . |
932 |
716 |
−0.081 |
932–1600 |
|
Rhenium . . . . . |
3167 |
2700 |
— |
— |
|
Rhodium . . . . |
1966 |
1915 |
−0.664 |
1966–2150 |
|
Rubidium . . . . |
39 |
89.6 |
−0.056 |
39–1000 |
|
Ruthenium . . . |
2250 |
2250 |
— |
— |
|
Samarium . . . . |
1072 |
430 |
−0.072 |
1072–1700 |
|
Scandium . . . . |
1540 |
939 |
−0.124 |
1540–1750 |
|
Selenium . . . . |
220 |
103 |
−0.15 |
220–500 |
|
Silicon . . . . |
1410 |
775 |
−0.145 |
1410–1800 |
|
Silver . . . . . |
960 |
925 |
–0.21 |
960–1600 |
|
Sodium
. . . . |
98 |
197 |
−0.09 |
98–600 |
|
Strontium . . . . |
770 |
303 |
−0.085 |
770–1300 |
|
Tantalum . . . . |
2950 |
2150 |
— |
— |
|
Tellurium. . . . . |
460 |
239 |
−0.104 |
460–656 |
|
Terbium . . . . |
1356 |
669 |
−0.056 |
1356–1750 |
|
Thallium . . . . . |
305 |
459 |
−0.106 |
305–1200 |
|
Thorium . . . . . |
1690 |
1006 |
— |
— |
|
Tin . . . . . . |
232 |
562 |
−0.103 |
232–1400 |
|
Titanium . . . . |
1680 |
1650 |
— |
— |
|
Tungsten . . . . |
3370 |
2500 |
— |
— |
|
Uranium . . . . |
1130 |
1552 |
−0.27 |
1130–1600 |
|
Vanadium . . . . |
1735 |
1950 |
— |
— |
|
Ytterbium . . . . |
824 |
320 |
−0.102 |
824–1700 |
|
Yttrium . . . . . |
1500 |
872 |
−0.086 |
1500–1750 |
|
Zinc . . . . . |
420 |
789 |
−0.21 |
420–700 |
|
Zirconium . . . |
1850 |
1480 |
— |
— |
Inorganic. γ = a −
bt, mN m−1
|
Substance
|
|
|
Equation constants |
|
a |
b |
Range °C |
|
Lead
chloride . . |
520 |
135.3 |
199.8 |
0.124 |
510–580 |
|
Potassium chloride . |
780 |
100.3 |
160.4 |
0.070 |
770–970 |
|
Potassium nitrate
. |
340 |
111.0 |
136.5 |
0.0750 |
340–500 |
|
Sodium chloride . |
810 |
113.3 |
171.5 |
0.0719 |
805–970 |
|
Sodium
fluoride . |
1000 |
185.2 |
267.2 |
0.082 |
1000–1080 |
|
Sodium
nitrate. . . |
320 |
119.2 |
138.8 |
0.0613 |
320–600 |
|
Sodium sulphate . . |
900 |
194.5 |
239.6 |
0.0501 |
900–1080 |
|
Oxygen . . . . |
−184 |
13.40 |
–33.72 |
0.2561 |
−202 to − 184 |
|
Nitrogen . . . . |
−183 |
5.99 |
–35.48 |
0.2266 |
−195 to − 183 |
More data on molten salt in Janz (1969).
Organic γ = a −
bt, mN m−1
|
Substance
|
|
|
Equation constants |
|
a |
b |
Range °C |
|
Acetic acid
. . . |
20 |
27.59 |
29.58 |
0.099 4 |
20–90 |
|
Acetone . . . . |
20 |
23.46 |
26.26 |
0.112 |
20–50 |
|
Aniline . . . . . |
20 |
42.67 |
44.83 |
0.108 5 |
15–90 |
|
Benzene . . . . |
20 |
28.88 |
31.50 |
0.128 7 |
10–80 |
|
n-Butanol. . . . |
20 |
25.39 |
27.18 |
0.089 83 |
10–100 |
|
Carbon disulphide. . |
20 |
32.32 |
35.29 |
0.148 4 |
10–50 |
|
Carbon tetrachloride |
20 |
27.04 |
29.49 |
0.122 4 |
15–105 |
|
Chloroform . . . |
20 |
27.32 |
29.91 |
0.129 5 |
15–75 |
|
Di-ethyl ether
. . . |
20 |
17.10 |
18.92 |
0.090 8 |
15–30 |
|
Ethanol . . . . |
20 |
22.39 |
24.05 |
0.083 2 |
10–70 |
|
Ethyl
acetate . . . |
20 |
23.97 |
26.29 |
0.116 1 |
10–100 |
|
Glycerol . . . . |
20 |
63.4 |
65.17 |
0.088 45 |
20–150 |
|
n-Hexane . . . . |
20 |
18.40 |
20.44 |
0.102 2 |
10–60 |
|
n-Octane . . . . |
20 |
21.62 |
23.52 |
0.095 09 |
10–120 |
|
Methanol . . . . |
20 |
22.50 |
24.00 |
0.077 3 |
10–60 |
|
Methyl
acetate . . |
20 |
25.37 |
27.95 |
0.128 9 |
10–60 |
|
Phenol . . . . |
40 |
39.27 |
43.54 |
0.106 8 |
40–140 |
|
n-Propanol . . . |
20 |
23.71 |
25.26 |
0.077 7 |
10–90 |
|
Toluene . . . . |
20 |
28.52 |
30.90 |
0.188 9 |
10–100 |
More data see Jasper (1972).
Surface tension of water against
air
|
Temp/ °C |
0 |
10 |
15 |
20 |
25 |
30 |
40 |
50 |
60 |
70 |
80 |
100 |
|
γ/(mN
m-1) |
75.7 |
74.2 |
73.5 |
72.75 |
72.0 |
71.2 |
69.6 |
67.9 |
66.2 |
64.4 |
62.6 |
58.8 |
Surface tensions of aqueous salt solutions. Usually greater than
that of water. Approximately γ =
γH2O +
M .Δγ,
where M is concentration. Values below are for M = 1 mole
dm−3 at 20 °C.
|
Salt |
Δy/(mN m−1) |
|
KCl . . . . . |
1.4 |
|
NaCl . . . . . |
1.64 |
|
Na2CO3 . . .
. |
2.7 |
|
NaNO3
. . . . |
1.2 |
|
Na2SO4 . . . . |
2.7 |
Interfacial tensions of liquids at 20 °C
|
Liquids |
γ/(mN
m−1) |
Liquids |
γ/(mN
m−1) |
|
Water against: |
|
Mercury against: |
|
|
Benzene . . . . . |
35 |
Acetone . . . . . |
390 |
|
Carbon tetrachloride
. |
45 |
Benzene . . . . . |
357 |
|
Chloroform . . . . |
28 |
Chloroform . . . . |
357 |
|
Di-ethyl ether
. . . |
10 |
Di-ethyl
ether . . . |
379 |
|
Heptylic acid
. . . . |
7 |
n-Heptane . . . . |
379 |
|
n-Heptane . . . . |
51 |
Oleic acid
. . . . |
322 |
|
n-Octane . . . . . |
51 |
|
|
|
Olive oil
. . . . . |
20 |
|
|
|
Paraffin
oil . . . . |
48 |
|
|
References
Adam, The Physics and Chemistry of Surfaces.
Eötvös
(1886).
G. J. Janz (1969) NSRDS-NBS 28, report, Natl. Bur.
Standards, Washington.
J. J. Jasper (1972) J. Phys. Chem. Ref. Data,
I(4), 841–1010.
B.J.Keene
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