W. Richard Bowen and Nidal Hilal 4

102 3. QUANTIFICATION OF PARTICLE–BUBBLE INTERACTIONs
F e Electrical double layer forces N
F h Hydrophobic force N
k Spring constant N m �1
k b Boltzmann’s constant (1.38 � 10 �23 ) J K �1
k bubble Bubble spring constant N m �1
k c Cantilever spring constant N m �1
k m Uncorrected measured spring constant N m �1
k ref Reference cantilever spring constant N m �1
k tot Total spring constant of system N m �1
P a
P c
P d
Probability of adhesion
Probability of collision
Probability of detachment
r Radius of TPC circle m
R Radius of sphere m
V Velocity of particle m s �1
W Interaction energy J m �2
W a Work of adhesion J
z Distance travelled by z-piezo m
� Immersion angle °
� Interfacial tension N m �1
� c
Slope of contact region of force curve
� hard Slope of contact region against hard surface nA m �1
�l Distance of probe from end of cantilever m
� Contact angle °
� a Advancing contact angle °
� r Receding contact angle °
� Geodesic curvature of TPC
� f Density of fluid Pa s
� Line tension N m �1
�i Imaginary component of hydrodynamic function
references
[1] J. Leja, Surface Chemistry of Froth Flotation, Plenum Press, New York, 1982.
[2] B.A. Wills, Wills’ Mineral Processing Technology, seventh ed., Elsevier, Oxford, 2006.
[3] V.I. Klassen, V.A. Mokrousov, An Introduction to the Theory of Flotation, second ed.,
Butterworth & Co, London, 1963.