Effect of contact angle and contact angle hysteresis on the floatability of spheres at the air-water interface

The floatability of solid particles on the water surface governs many natural phenomena and industrial processes including film flotation and froth flotation separation of coal and valuable minerals. For many years, the contact angle (CA) has been postulated as the key factor in determining the particle floatability. Indeed, the maximum force (tenacity) supporting the flotation of fine spheres was conjectured to occur when the apical angle of the contact circle is equal to the contact angle. In this paper, the model predictions are reviewed and compared with experimental results. It is shown that CA can be affected by many physical and chemical factors such as surface roughness and chemical heterogeneity and can have a range of values known as the CA hysteresis. This multiple-valued CA invalidates the available theories on the floatability of spheres. Even the intuitive replacement of CA by the advancing (maximum) CA in the classical theories can be wrong. A few new examples are also reviewed and analyzed to demonstrate the significance of CA variation in controlling the particle floatability. They include the pinning of the contact line at the sharp edge, known as the Gibbs inequality condition, and the nearby interaction among floating particles, known as lateral inter-particle interaction. It is concluded that our quantitative understanding of the floatability of real particles being irregular and heterogeneous both morphologically and chemically is still far from being satisfactory.