Question
Assume that the experiment illustrated in Figure 10.31 is done with a solution of Na-
stearate and with one of Na-myristate. Each solution has a surface tension of
50 mN?m^1. The barrier is moved over 5 cm, thereby increasing the A–W surface
area by a factor of two. For which solution is the spreading of surfactant fastest?
What is the time needed to restore the initial value ofgfor each solution?
Answer
To calculate the spreading time, Eq. (10.19) is needed. The variablesz(5 cm),Z
(1 mPa?s) andr(10^3 kg?m^3 ) are the same for both solutions, and this would also
hold forDg¼g 0 g¼0.0720.05¼0.22 N?m^1. A spreading time of 0.23 s then
follows. Adsorption is needed to restoreg, and the data in Figure 10.6 give atg¼
0.05, that for C18c¼0.16 mol?m^3 , andG¼8.8mmol?m^2 ; for C14, these values
would be 7.1 and 4.0, respectively. Inserting these data into Eq. (10.6) yields for the
adsorption time a value of 100 s for the stearate solution and of 0.01 s for the
myristate.
We may conclude that for Na-stearate the spreading is much faster than the
adsorption (because of its low bulk concentration). This implies that during
adsorption the initialGvalue is half of 8.8mmol?m^2 (since the surface area was
doubled) and also half that amount would have to be adsorbed. Equation (10.6) has
G^2 in the denominator, and replacingGby half the final value leads to an adsorption
time of 25 rather than 100 s, which is still very much longer than the spreading time.
Consequently, we have spreading first, followed by adsorption, as shown in panels 3
and 4 of Figure 10.31.
For Na-myristate, the adsorption is much faster (because of its relatively high
bulk concentration) than the spreading, by a factor 23. This means that the value of
jDgjdecreases rapidly, greatly slowing down the spreading rate. In fact, very little
spreading will occur, and the adsorption time is indeed about 0.01 s. In the sequence
given in Figure 10.31, panel 3 can thus be omitted.
If the same calculations are done for Na-palmitate, spreading and adsorption
cannot be so nicely separated, and calculation of the times involved is far more
intricate.
10.8 INTERFACIAL RHEOLOGY
Basic aspects of rheology are discussed in Sections 5.1.1 and 2. This
concerns ‘‘bulk rheology.’’ Rheological theory can also and usefully be
applied to the deformation of fluid interfaces. A main problem is that an
interface cannot exist by itself; it is the boundary between two phases and
these phases must be deformed with the interface. Surface or interfacial