The name is absent

Chapter 2

jy ₌ __^L
^e Pl

If We « 1, the stability criterion is suggested as ^{[181> [19]}

d²U(h) _ dU(h) _> __cç_
dh² hdh R²

Here U (h) is the energy in DLVO theory, C > O is a constant, σ is interfacial
tension. From Eq. [2.18], coalescence would only take place if the drops get close
enough as to reach the primary minimum (in Figure2.4).

When We » 1, large flat films will form. Deformation is favored by large drop
sizes and low interfacial tensions. In this case, coalescence is preceded by the
drainage of the liquid present in the film. Forthe symmetrical drainage of a film of
Newtonian liquid with viscosity η between two flat disks of radii rand separated by
a distance h (h∕r<< 1) with the pressure difference ΔP, the rate Ofthinning of the
film -dh∕dt is^[22]:

= [₂.₁₉]
dt 3 η r

If the electrostatic repulsion is strong enough as to balance van der Waals
attraction and the capillary pressure, the film is referred to as common black film
(h ~ 20-30 nm)^[2]. If the electrostatic repulsion is weak and short range repulsive
forces dominate instead, the film is very thin (h ~ 5-10 nm) and is referred to as
Newton black film.

21

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