W. Richard Bowen and Nidal Hilal 4

3.5 EFFECT OF sURFACE PREPARATION ON PARTICLE–BUBBLE INTERACTIONs 91
then the advancing contact angle � a may be obtained from the retract
part of the force trace. Here the adhesion force F AD can be related to the
advancing contact angle:
2
a
2 �
FAD � 2πR�
sin
2
(3.15)
Other methods have been developed to measure contact angles using
the AFM in tapping mode. Pompe et al. [40] scanned liquid drops on surfaces.
By then using a cross section of the topography, they measured the
contact angle and three-phase line tension parameters for the liquid drops.
3.5 EFFECt oF SurFACE PrEPArAtIon on
PArtICLE–BuBBLE IntErACtIonS
3.5.1 Effect of Particle Surface Chemistry on Particle–Bubble
Interactions
As would be expected, the surface chemistry of the colloid probes has
an important effect on their attachment to bubbles in aqueous solutions.
In the literature there have been a number of studies in which the effect
of the surface chemistry of various probes has been investigated for their
importance in particle attachment to bubbles.
In the first set of AFM-based experiments to measure particle–bubble
interactions in the literature, as described by Butt [10], untreated hydrophilic
glass particles were allowed to interact with air bubbles in aqueous
media. When the glass approached the surface, a linear repulsive force
was measured on contact, with no jump-in prior to contact. This was
echoed in the work by Fielden et al. using hydrophilic silica particles [37],
who also noted a linear repulsion with no jump-in. This is hardly surprising
as both silica and glass have a tendency to carry a negative charge in
water due to Si–OH groups on the surface [41], and the air–water interface
of air bubbles also tends to be negatively charged for the majority of
pH values, as evidenced by �-potential measurements [42, 43], leading to
repulsive electrical double layer forces. In addition it would be expected
that van der Waals forces between silica and air in water would also be
repulsive, due to a negative Hamaker constant for the interaction of silica
and air across water [26, 44]. This means that the DLVO forces in general
will all tend towards repulsion in this case.
Interestingly, a different result was reported by Ducker et al. [11] when
interacting a silica sphere with an air bubble in water. Jump-in events
were observed prior to contact, at a distance of 50 nm, before being followed
by a linear repulsion after contact was made. It was speculated by
the authors that at small separations, the air–water interface may change