internal stress. The latter is simply given by the Laplace pressure (2g/a). The
external stress may be due to colloidal attraction, to hydrodynamic forces,
or to gravity as in a sediment layer. Since initially the area over which the
external force acts may be much smaller that the cross-sectional area of a
droplet (pa^2 ), the external stress sE must be multiplied by a stress
concentration factorL. Figure 13.15b illustrates that fora 4 hthe area of
close contact is of orderpah, which leads to L&a=h. Generally, the
magnitude ofhupon droplet encounter is determined by colloidal repulsion.
A dimensionless Weber number can be defined as the quotient of the local
external force over the internal one, which would equal
We¼
s
pL¼
sEL
pL¼
sEa^2
2 ghð 13 : 31 ÞFor We<1, the drops remain almost undeformed, for We>1, a flat film
between them will be formed.
FIGURE13.15 (a) Formation or not of a flattened film between droplets (thickness
hof the film is greatly exaggerated). (b) Derivation of the nominal radius of the film
between close spheres.