Chemistry Reference
In-Depth Information
effect is usually of importance in fairly dilute surfactant solutions and over a rela-
tively narrow concentration range. In the absence of external agitation, the amount
of surfactant adsorbed at a new interface can be estimated by the equation
1
=
2
D
p
N
1000
ct
1
=
2
n
¼
2
ð
8
:
5
Þ
where n is the number of molecules per square centimeter, D is the bulk diffusion
constant (cm
2
/s), c is the bulk concentration of the surfactant (mol/L), t is the time
in seconds, and N is Avogadro's number. Using Eq. (8.5), it is possible to estimate
the time required for the adsorption of a given amount of surfactant at a new inter-
face compared to the rate of generation of that interface. If the surfactant solution is
too dilute, the surface tension of the solution will not differ sufficiently from that of
the pure solvent for the restoring force to counteract the effects of thermal and
mechanical agitation. As a result, the foam produced will be very transient. In
line with the Marangoni theory, there should be an optimum surfactant concentra-
tion for producing the maximum amount of foam in a given system, under defined
circumstances. Such effects have been verified experimentally (see Table 8.1).
In the case of the Gibbs effect, the increase in surface tension occurring as the
film is stretched results from a local depletion of the surfactant concentration in the
bulk phase just below the newly formed interface. Obviously, in systems such as
foams where the available bulk phase in the narrow lamellae may be small com-
pared to the amount of interface being formed, the effect will be enhanced. As
with the Marangoni effect, if the surfactant concentration in the bulk phase is too
low, a surface tension gradient of sufficient size to produce the necessary ''healing''
action will not be produced. Conversely, if the concentration is too large, well
above the cmc, the amount of ''immediately'' available surfactant will be such
that no gradient is formed.
TABLE 8.1. Typical Surfactant Concentrations Required to Attain
Maximum foam Height, MFH
cmc
Concentration for
Surfactant
(mM)
MFH (mM)
C
12
H
25
SO
3
Na
þ
11
13
C
12
H
25
OSO
3
Na
þ
9
5
C
14
H
29
SO
3
K
þ
3
3
C
14
H
29
OSO
3
Na
þ
2.3
3
C
16
H
33
SO
3
K
þ
0.9
0.8
C
16
H
33
OSO
3
Na
þ
0.7
0.8
p-C
8
H
17
C
6
H
4
SO
3
Na
þ
16
13
p-C
10
H
21
C
6
H
4
SO
3
Na
þ
3
4.5
p-C
12
H
25
C
6
H
4
SO
3
Na
þ
1.2
4
o-C
12
H
25
C
6
H
4
SO
3
Na
þ
3
4
(C
8
H
17
)
2
CHSO
4
Na
þ
2.3
4
