W. Richard Bowen and Nidal Hilal 4

3.7 EFFECT OF HyDRODyNAMICs ON PARTICLE–BUBBLE INTERACTIONs 99
AFM Measured interaction force, F (nN)
6
4
2
0
0
Approach speeds (µm/s)
0.6
3.0
5.9
12.2
17.8
27.9
39.1
65.4
97.8
100 200 300 400 500 600
Separation distance, D (nm)
FIGurE 3.7 Effect of the speed of approach between a particle and bubble on the measured
forces. Reprinted from [12]. Copyright 2004, with permission from Elsevier.
also been characterised using the colloid probe technique for a sphere
approaching a solid confining wall in a fluid environment [67–71]. Due to
the change in deflection of the cantilever as a result of the action of forces
upon it, the actual velocity experienced by the particle differs from that
applied by the piezo. A plot of the actual velocity against measured force
and calculated hydrodynamic force as determined by Nguyen et al. [12] is
presented in Figure 3.8. As can be seen the velocity actually decreases as
the particle–bubble separation distance is decreased due to the increase in
repulsive force, causing the cantilever to become deflected upwards, away
from the bubble surface. A similar effect was observed by Aston and Berg
[72] when approaching a droplet of n-hexadecane with a glass sphere in an
SDS solution. It was found that the oil–water interface became dimpled on
approach, with the distance at which this occurred increasing with increasing
approach speed.
Another study by Nguyen et al. [38] examined the effect of the speed
of approach of spherical polyethylene particles on the receding contact
angles measured, obtained from force curves as described earlier. It was
found that at relatively high approach speeds of �10 �m s �1 , there was
a strong influence of the approach speed on measured contact angle.
At speeds below this there was little influence on contact angle. It was
surmised by the authors that at the lower speeds, the measurements
represented a ‘static’ contact angle.