Collision and Attachment Interactions of Single Air Bubbles with Flat Surfaces in Aqueous Solutions - Drops and Bubbles in Contact with Solid Surfaces - page 224

2. Non-DLVO Disjoining Pressures
The non-DLVO forces can be the (repulsive) hydration forces (between hydrophilic
surfaces) or the (attractive) hydrophobic forces (between hydrophobic surfaces).
Another important non-DLVO force is the steric force between adsorption layers of
macromolecular reagents used as depressants or flocculants.
Hydration forces have been extensively studied between clay, mica and silica
surfaces in water [28, 56]. In these systems, the surfaces and particles would remain
in strong adhesion or coagulate in salt solutions in a primary minimum only if the
forces were the DLVO forces. Indeed, water molecules are strongly hydrated by
the salt ions and/or strongly bounded to the hydrophilic surfaces. Theory [45] and
experiments [28] show the exponential decay of the hydration disjoining pressure
versus separation distance as follows:
h (H) H/λ), (14)

where λ is the decay length and K is a constant. The hydration force between two
mica surfaces is monotonically repulsive below H

= K exp ( −

= 5 nm. An oscillation with

a mean periodicity of about 0.25 nm ( ∼ water diameter) is observed below H =

1 . 5 nm [28].
Hydrophobic surfaces are inert to water as they are unable to interact or bind
with water either by electrostatic means or via hydrogen bonds. Hydrophobic forces
between microscopic hydrophobic surfaces have generally been found to increase
with the hydrophobicity of the surfaces, as conventionally defined by the water
contact angle. The first direct measurements of the hydrophobic force show that the
attraction has a very long range and decays exponentially as predicted by Eq. (14)
with K< 0 [27]. Since the first measurements, experimental data have shown that
the attraction between hydrophobic surfaces is strong and long-ranged and can be
empirically described by a double exponential function of two decay lengths as
h = K ∗ exp ( H/λ ∗ ). K exp ( − H/λ) + − (15)

Alternatively, the measured hydrophobic attraction can be described by a power law
similarly to the van der Waals interaction [9, 80] as

K 132
h 3 ,

h =

(16)

where the empirical constant can be correlated with the surface hydrophobicity
measured by the advancing and receding contact angle as K 132 =− exp [ a( cos θ R +

. The data for K,K ∗ ,a and b are summarised in the topic [53]. The
constant in the front of the single exponential term can also be determined using the
surface thermodynamics of acid-base interactions [49, 77].
There is no consensus on explaining the strong hydrophobic attraction between
hydrophobic surfaces despite a number of proposed mechanisms [52]. Since the
hydrophobic attraction is difficult to model at present, the empirical correlation fit-
ted with double exponentials is often used. The double exponential dependence has

cos θ A )/ 2 + b ]