RAMAN APPLICATIONS IN FOAMS - Raman Spectroscopy for Soft Matter Applications - page 182

with the liquid fi lms as their faces, which are not fl at. The fi lms (faces)
meet in lines (polyhedral edges) known as Plateau borders, and the
borders meet at vertices. If the liquid content increases beyond a
percent, the liquid is concentrated fi rst in the Plateau borders, which
become channels of fi nite width; polyhedral cells start to assume spheri-
cal shapes, and the foam turns into what we usually refer to as wet foam .
Further increase in the liquid content results in bubble separation, and
the foam loses its rigidity and turns into a bubbly liquid [24]. For aca-
demic purposes, 2-D foams have been utilized in a number of experi-
mental and simulation investigations. Foam is considered 2-D if the
thickness of the foam layer is smaller than the average size of the cell.
A classical model used in experimental investigations is the thin foam
layer sandwiched between two glass slides.
It is important to note that the pressure difference between adjacent
cells can be calculated using Equation 7.4, which is based on the
Laplace-Young equation. In 2-D foam, however, the equation has to
be modifi ed as follows:

2 γ .

Δ p = (7.5)

r

The disjoining pressure inside the liquid fi lm has to be taken into
consideration when calculating the pressure difference between adja-
cent cells using the Laplace-Young equation. However, in case of foams
with negligible fi lm thickness and fairly constant surface tension, dis-
joining pressures may be neglected when applying the theory [25] .
Experimentally measured joining pressures have been found to depend
on the fi lm thickness and to range between a very modest 500 and
5000 Pa [26,27] (Figure 7.5 ).
For the study of foam structure and properties, theory and experi-
ments can be focused on three different length scales depending on the
nature of the study. For chemistry and stability of the liquid fi lm inves-
tigation, molecular effects can be investigated on the nanometer length
scale. For studies investigating foam physics and the stability of the
structure, its equilibrium, coarsening, etc., foam can be investigated on
the millimeter length scale (several cells limit). Finally, to investigate
the mechanical behavior of foams and its engineering properties and
to develop continuum models of foams, the investigation can be focused
on the meter length scale.
As we mentioned before, understanding the physics of foam requires
investigating its properties on the micro level (the cell level in Figure
7.6). It is necessary to understand the correlation between structure