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```Measuring Surface Tensions
(Chapter 4, pp. 69-76 in Shaw)
Measurement techniques can be
classified in three catagories:
• Static Methods (most accurate)
• Detachment Methods
• Dynamic Methods (short term effects)
ALL EXPERIMENTS MUST BE
CONDUCTED UNDER EXTREMELY
CLEAN CONDITIONS – YOU DO NOT
WANT TO MEASURE THE EFFECT
OF DIRT!!
1. Maximum Bubble Pressure Method
Liquid surface
h
d = density
P
Maximum
Bubble
Pressure
 = r/2 (P – hdg)
An Example: Glacial Acetic Acid
r = 1.10 mm
d = 1049 kg/m3
P = 420 Pa
h = 3.56 cm
 = r/2 (P – hdg) =
0.00055(420-0.0356x 1049 x 9.81) = 29 mN/m
= 29 mN/m
Why is this so low for an acid?
2. Capillary Rise Method
Young-Laplace:
DP = 2/r
And
h
DP = Dr g h
Thus: Dr g h = 2/r or
a2 = 2/Drg = rh
Where a is defined as the capillary constant.
For a liquid which only wets the wall
partially:
Dr g h = 2 cos Q/r or
 = Dr r g h/2cosQ
where Q is the contact angle
between the liquid and the glass.
Q
If the liquid does not wet the glass (e.g. Hg),
a depression of the liquid level occurs:
For all practical purposes a zero contact
angle is required (the liquid should wet
the glass). And fairly large volumes are
required. With glass capillaries there are
limitations as to the alkalinity of the
solutions.
For accurate work a meniscus correction
 = ½ r(h + r/3) Dr g
Contact Angle Hysteresis:
To check for zero contact angle, a
capillary is allowed to equilibrate in turn
from below and above. If the contact
angle is zero (i.e. the capillary is clean)
then the equilibrium height should be
independent of direction.
3. Wilhelmy Plate Method
Plate:
length = x
width = y
Wdet – Wplate = 2 (x + y) 
4. Du Nouy Ring Method
Force
Wtot = Wring + 4pR 
Or:
 = bF/4pR
where b is a complicated correction factor.
5. Drop Volume and Drop Weight Methods
= f mg/2pr =
f Vrg/2pr
f is a correction factor:
1) The drop does not completely
leave the tip.
2) The surface tension forces are not
completely vertical.
3) There is a pressure difference
across the curved surface.
6. Drop and Bubble Shape Methods
The pendant drop method is similar to
the falling drop weight method. It is
useful for the observation of slow
changes in surface tension and only a
very small sample is required. The drop
is deformed by gravitational forces.
Pendant Drop
Sessile Drop
6. Rotating Drop Shape Methods
A ro
B
w
wis the angular speed of revolution
Dr is the density difference
between phases A and B
w2Drro2

4
This equation is named after Vonnegut.
7. Oscillating Jet Methods
Dynamic methods measure interfacial
tensions milliseconds after surfaces are
formed:
JET
l


apparent 
6rl2 1  5p2r 2 / 3l2 
4r2 1  37b2 / 24r 2
n is fluid velocity; r is fluid density;
r is the sum of the min and max half diameters;
and b is the difference of the min and max half
diameters
Some actual data from an oscillating jet:
, mN/m
0.05 g/100 mL
70
Sodium di-(2-ethylhexyl)
sulfosuccinate solution
50
30
10
20
30
40
time, msec
50
A Final Word:
Surface tensions for pure liquids
should and does come out the same
irrespective of the methods used to
determine it.
Next lectures: Surfactants and Micelles
```