thereby the cleaning action of detergents, the occurrence of capillary
displacement, the wetting by and the dispersion of powders in a liquid; and
the adhesion of solid particles to a liquid interface. The contact angle can be
substantially affected by the addition of surfactant. The contact angle on a
solid surface is generally not an equilibrium property: an advancing angle
tends to be larger than a receding one.
It may be added here that the four basic laws of capillarity, i.e., the
equations of Gibbs [(10.2)], Laplace [(10.7)], Kelvin [(10.9)] and Young
[(10.10)], all describe manifestations of the same phenomenon: the system
tries to minimize its interfacial free energy. (Another manifestation is found
in the Hamaker equations; see Section 12.2.1.) These laws describe
equilibrium situations. Moreover, dynamic surface phenomena are of great
importance.
Interfacial Tension Gradient. An interfacial tension gradient can
occur in an interface containing surfactant. The tension then varies in the
direction of the interface. This creates a two-dimensional stress in that
direction. The gradient can be induced by flow of the bordering liquid, and if
the gradient is large enough, the interface is arrested (it does not move with
the flowing liquid). This is essential in making foam, since it greatly slows
down the drainage of liquid from it. A gradient can also be induced by
locally applying a surfactant or by locally increasing the interfacial area (by
bulging). Then the interface will move to even out the interfacial tension,
and this motion will drag bordering liquid with it, the Marangoni effect. The
latter is essential for the stability of thin films containing surfactant. Evening
of the interfacial tension proceeds as a longitudinal surface wave, which can
have a very high velocity.
Interfacial Rheology. The extent to which interfacial tension
gradients and the resulting effects occur depends on the surface dilatational
modulus. This concerns one type of surface rheology, where a surface
element is expanded or compressed without changing its shape, and the
change in interfacial tension is measured. The modulus is primarily
determined by the exchange of surfactant between interface and bulk and
thus is time dependent. In a thin film, it is determined by the limited amount
of surfactant present (twice its value is called the Gibbs elasticity). The
modulus is zero in the absence of surfactant and goes through a maximum
when the concentration is increased. For polymeric surfactants, the modulus
is also affected by changes in conformation.
Another kind of interfacial rheology is done in shear: a surface element
is sheared without altering its area, and the force needed is measured. It is
due to friction or attraction between surfactant molecules. Modulus and
viscosity tend to be negligible for amphiphiles but may become appreciable