Characterization of materials by Hallimond tube flotation, Part 3. Maximum size of floating and interacting particles

The tests carried out with solids of different hydrophobicities and densities, floated individually and as a collection of particles in the monobubble Hallimond tube, allowed to characterize flotation in this small-scale laboratory flotation device and determine the maximum size of entrained particles, maximum size of floating particles, particle hydrophobicity, increase of the apparent density of the particle in contact with air bubble due to aggregation with other particles, and flotometric equations interrelating these parameters. Hydrophilic particles do not float in the Hallimond tube but there is some mechanical entrainment governed by the equations: a(max)(rho(p) - rho(w))/rho(w) = 0.023 +/- 0.002 valid for particles with density greater than 2 g/cm(3) and a(max)((rho(p) - rho(w))/rho(w))(0.75) = 0.0225 +/- 0.0025 (cm) applicable for less dense particles, where a(max) is the maximum size of entrained particles (in cm), rho(p) is the particle density, and rho(w) denotes density of the aqueous phase (in g/cm(3)). Hydrophobic particles tend to form aggregates and float as a cluster but no interaction was detected for contact angles (theta(s)) below 20 degrees. Thus, for theta(s) < 20 degrees the flotation of a collection of particles can be characterized by the same equations as for flotation of individual particles including the simplified formula of Scheludko D-max(2)(rho(p) - rho(w)) = 6 sigma g(-1) sin(2)(theta(s)/2) in which g is the acceleration due to gravity, sigma stands for the surface tension of water, and D-max is the maximum size of floating particles. Hydrophobic interactions between particles become significant for theta(s) > 20 degrees. When 20 degrees > theta(s) > 55 degrees and the number of particles in the cluster is greater than 1, the flotation of an ensemble of particles is given either by: d(max)(2)n(rho(p) - rho(w)) = 6 sigma g(-1) sin(2)(theta(s)/2) or by: d(max)(rho(p) - rho(w)) = k sin(2)(theta(s)/2) (g/cm(2)), where n is defined as (D-max/d(max))(2) and the term n(rho(p) - rho(w)) represents a new apparent density of the particle in contact with air due to aggregation with other particles which do not touch the bubble, d(max) is the maximum size of floating and interacting particles, and k is a constant equal to 2.08 g/cm(3). It was established that the clustering does not occur sharply at theta(s) = 20 degrees but it depends on the density of particles and that for less dense particles occurs at higher hydrophobicity. For theta(s) > 55 degrees the flotation of a cluster of particles is not influenced by hydrophobicity and the equation: d(max)(rho(p) - rho(w)) = 0.40 +/- 0.05 (g/cm(2)) is valid. (C) 1999 Elsevier Science B.V. All rights reserved.