Question
An emulsion technologist wishes to compare two commercial water-soluble small-
molecule surfactant preparations, A and B, to be used for making O–W emulsions.
The interfacial tension is measured between the aqueous phase and the oil to be used,
in the presence of either surfactant. For A it is observed thatg¼6mN?m^1 ; for B
the value is not immediately constant and decreases from about 6 to 2 mN?m^1 in
two minutes. It is concluded that with preparation B the emulsion droplets will
obtain a smaller interfacial tension than with A. Is this conclusion warranted?
Answer
No. The fact thatgdecreases with time for surfactant B implies that the latter must
contain some component(s) in small concentrations that decreasegto a lower value
than the main component(s) can. Application of Eq. (10.6) withtads¼120 s andD¼
3? 10 ^10 m^2 ?s^1 leads to a thickness of the layerdthat provides the minor surfactant
of about 60mm; in other words, the effective surface-to-volume ratio would be 1/
60? 10 ^6 ¼ 17? 103 m^1. In the emulsion, however, the ratio of O–W surface area to
the volume of the surfactant solution may be far greater. It would be given by 6?j/
d 32 (1j); for an assumed oil volume fractionj¼0.25 and average droplet sized 32
¼ 1 mm, this leads to a value of 2? 106 m^1 , i.e., more than 100 times that during the
macroscopic measurement ofg. This implies that the concentration of the minor
components at the droplet interface would be very small, probably having a
negligible effect ong.
10.5 CURVED INTERFACES
10.5.1 Laplace Pressure
We all know that the pressure inside a bubble is higher than atmospheric.
When we blow a soap bubble at the end of a tube and then allow contact
with the atmosphere, the air will immediately escape from the bubble: it
shrinks and rapidly disappears. This is a manifestation of a more general
rule: if the interface between two fluid phases is curved, there always is a
pressure difference between the two sides of the interface, the pressure at the
concave side being higher than that at the convex side. The difference is
called the Laplace pressurepL.
Figure 10.19 serves to give an explanation for a sphere. At any equator
on the sphere, the surface (or interfacial) tension pulls the two ‘‘halves’’
toward each other with a force that equalsgtimes the circumference. The
surface tension thus causes the sphere to shrink (slightly), whereby the
substance in the sphere is compressed and the pressure is increased. At
equilibrium, the excess inside pressure times the area of the cross section of